Cooperative Cellular Wireless Networks

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Author: Ekram Hossain | Dong In Kim | Vijay K. Bhargava

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Cooperative Cellular Wireless Networks A self-contained guide to the state-of-the-art in cooperative communications and networking techniques for next-generation cellular wireless systems, this comprehensive book provides a succinct understanding of the theory, fundamentals, and techniques involved in achieving efficient cooperative wireless communications in cellular wireless networks. It consolidates the essential information, addressing both theoretical and practical aspects of cooperative communications and networking in the context of cellular design. This one-stop resource covers the basics of cooperative communications techniques for cellular systems, advanced transceiver design, relay-based cellular networks, and game-theoretic and micro-economic models for protocol design in cooperative cellular wireless networks. Details of ongoing standardization activities are also included. With contributions from experts in the field divided into five distinct sections, this easyto-follow book delivers the background needed to develop and implement cooperative mechanisms for cellular wireless networks. Ekram Hossain is a Professor in the Department of Electrical and Computer Engineering at the University of Manitoba, Canada, where his current research interests lie in the design, analysis, and optimization of wireless/mobile communications networks. He serves as an Editor for IEEE Transactions on Mobile Computing, IEEE Communications Surveys & Tutorials, and IEEE Wireless Communications, and is an Area Editor for IEEE Transactions on Wireless Communications. Dong In Kim is a Professor and SKKU Fellow in the School of Information and Communication Engineering at Sungkyunkwan University (SKKU), Korea, and Director of the Cooperative Wireless Communications Research Center. He is currently an Editor for IEEE Transactions on Communications, an Area Editor for IEEE Transactions on Wireless Communications and co-Editor-in-Chief for Journal of Communications and Networks. Vijay K. Bhargava is a Professor in the Department of Electrical and Computer Engineering at the University of British Columbia, Canada. He has served on the Board of Governors of the IEEE Information Theory Society and the IEEE Communications Society and was President of the IEEE Information Theory Society. He is now the President-Elect of the IEEE Communications Society and will serve as its President during 2012 and 2013.

“Edited by three of the most prominent experts in the field of cooperative communications, this is the defining book on this topic. It is a must have for any practicing researcher/engineer in this field.” Vahid Tarokh, Harvard University “Cooperative communications has been one of the most active areas of research in the communications field over the past decade. This research effort has now produced a significant body of work in the area, and this book is a valuable resource for students or practitioners wanting to enter the field, or simply to understand the scope and implications of the research.” H. Vincent Poor, Princeton University

Cooperative Cellular Wireless Networks Edited by EKRAM HOSSAIN University of Manitoba, Canada

DONG IN KIM Sungkyunkwan University, Korea

VIJAY K. BHARGAVA University of British Columbia, Canada

CAMBRIDGE UNIVERSITY PRESS

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Tokyo, Mexico City Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521767125 C

Cambridge University Press 2011

This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2011 Printed in the United Kingdom at the University Press, Cambridge A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data Cooperative cellular wireless networks / edited by Ekram Hossain, Dong In Kim, Vijay K. Bhargava. p. cm. Includes index. ISBN 978-0-521-76712-5 (hardback) 1. Wireless communication systems. 2. Cell phone systems. I. Hossain, Ekram, 1971– II. Kim, Tong-in, 1958– III. Bhargava, Vijay K., 1948– IV. Title. TK5103.2.C6625 2011 621.384 – dc22 2010048066 ISBN 978-0-521-76712-5 Hardback

Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

For our families

Contents

List of contributors Preface

Part I Introduction 1

Network architectures and research issues in cooperative cellular wireless networks

page xvi xx 1

3

Aria Nosratinia and Ahmadreza Hedayat

1.1 1.2

1.3

1.4 1.5 2

Introduction Base station cooperation 1.2.1 Downlink cooperation 1.2.2 Uplink cooperation Dedicated wireless relays 1.3.1 IEEE 802.16j 1.3.2 High-spectral-efficiency relay channels Mobile relays Conclusion

Cooperative communications in OFDM and MIMO cellular relay networks: issues and approaches

3 4 4 6 7 7 8 10 11

13

Mohammad Moghaddari and Ekram Hossain

2.1 2.2

Introduction Cooperative relay networks 2.2.1 Cooperative communication 2.2.2 Relay channel 2.2.3 Overview of relay protocols 2.2.4 Strategies of relay-assisted transmission 2.3 General system model of cellular relay networks 2.4 General system model for virtual antenna arrays (VAAs) 2.5 RRA in OFDMA-based relay systems: general form 2.6 Dynamic RA RRA in OFDMA relay networks 2.6.1 Centralized RA RRA schemes in single-cell OFDMA relay networks

13 15 15 16 17 18 19 20 21 23 24

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Contents

2.6.2

Centralized RA RRA schemes in multicell OFDMA relay networks 2.6.3 Distributed RA RRA schemes in OFDMA relay networks 2.6.4 RA RRA schemes with fairness in OFDMA relay networks 2.7 Dynamic centralized margin adaptive RRA schemes in OFDMA relay networks 2.8 MIMO communications systems 2.8.1 RRA in MIMO relay networks 2.8.2 Optimal design and power allocation in single-user single-relay systems 2.8.3 Optimal design and power allocation in single-relay multiuser systems 2.9 RRA in MIMO multihop networks 2.10 Conclusion

26 27 28 30 31 31 32 35 36 38

Part II Cooperative base station techniques

45

3

47

Cooperative base station techniques for cellular wireless networks Wibowo Hardjawana, Branka Vucetic, and Yonghui Li

3.1

3.2

3.3

3.4 3.5 3.6 3.7 3.8

3.9

4

Introduction 3.1.1 Related work 3.1.2 Description of the proposed scheme 3.1.3 Notation System model 3.2.1 Transmitter structure 3.2.2 THP precoding structure Cooperative BS transmission optimization 3.3.1 Iterative weight optimization (first step) 3.3.2 Power allocation (second step) Modification of the design of R Geometric mean decomposition Adaptive precoding order (APO) The complexity comparison of the proposed and other known schemes Numerical results and discussions 3.8.1 Convergence study 3.8.2 Performance of the individual links 3.8.3 Overall system performance Conclusion Appendix

Turbo base stations

47 47 48 49 49 49 51 53 55 57 58 59 60 61 63 64 65 66 70 72 77

Emre Aktas, Defne Aktas, Stephen Hanly, and Jamie Evans

4.1

Introduction

77

Contents

4.2

4.3

4.4

4.5

4.6 5

Review of message passing and belief propagation 4.2.1 Factor graph review 4.2.2 Factor graph examples Distributed decoding in the uplink: one-dimensional cellular model 4.3.1 Hidden Markov model and the factor graph 4.3.2 Gaussian symbols Distributed decoding in the uplink: two-dimensional cellular array model 4.4.1 The rectangular model 4.4.2 Earlier methods not based on graphs 4.4.3 State-based graph approach 4.4.4 Decomposed graph approach 4.4.5 Convergence issues: a Gaussian modeling approach 4.4.6 Numerical results 4.4.7 Ad-hoc methods utilizing turbo principle 4.4.8 Hexagonal model Distributed transmission in the downlink 4.5.1 Main results for the downlink of a single-cell network 4.5.2 Main results for downlink of a multicellular network 4.5.3 BS cooperation schemes with message passing Current trends and practical considerations

Antenna architectures for network MIMO

ix

81 82 85 88 89 91 96 96 98 98 102 102 107 109 110 110 110 114 115 122 128

Li-Chun Wang and Chu-Jung Yeh

5.1 5.2 5.3

5.4

5.5

5.6 5.7

Introduction System model Network MIMO 5.3.1 ZF network MIMO transmission 5.3.2 ZF-DPC network MIMO transmission Effects of intergroup interference 5.4.1 SINR analysis 5.4.2 Example of IGI: network MIMO with omni-directional cell planning 5.4.3 Unbalanced signal quality caused by IGI Frequency-partition-based three-cell network MIMO 5.5.1 Fractional frequency reuse (FFR) 5.5.2 FFR-based network MIMO with regular frequency partition 5.5.3 FFR-based network MIMO with rearranged frequency partition 5.5.4 Effect of frequency planning among coordinated cells 5.5.5 Effect of cell planning with different sectorization Simulation setup numerical results Conclusion

128 130 132 133 133 134 134 134 135 136 136 138 140 142 143 145 147

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Part III Relay-based cooperative cellular wireless networks

151

6

153

Distributed space-time block codes Matthew C. Valenti and Daryl Reynolds

6.1 6.2 6.3 6.4

6.5

6.6

6.7 7

Introduction System model Space-time block codes (STBCs) DF distributed STBC 6.4.1 Performance analysis 6.4.2 Numerical results AF distributed STBC 6.5.1 Performance analysis 6.5.2 Practical distributed STBC for AF systems The synchronization problem 6.6.1 Delay diversity 6.6.2 Delay-tolerant space-time codes 6.6.3 Space-time spreading (STS) Conclusion

Collaborative relaying in downlink cellular systems

153 155 157 162 162 165 168 169 170 170 171 171 172 173 176

Chandrasekharan Raman, Gerard J. Foschini, Reinaldo A. Valenzuela, Roy D. Yates, and Narayan B. Mandayam

7.1

7.2 7.3 7.4

7.5

7.6

7.7

Introduction 7.1.1 Research challenges 7.1.2 Related work 7.1.3 Overview of contribution System model Collaborative relaying in cellular networks CPA with peak power transmissions (P-CPA) 7.4.1 Principle of operation 7.4.2 User discarding methodology 7.4.3 Network operation and simulation aspects 7.4.4 Simulation results Power-control-based collaborative relaying (PC-CPA) 7.5.1 Principle of operation 7.5.2 Optimization framework 7.5.3 User discarding methodology 7.5.4 Network operation and simulation aspects 7.5.5 Simulation results Orthogonal relaying 7.6.1 Network operation and simulation aspects 7.6.2 User discarding method 7.6.3 Simulation results Conclusion

176 176 178 179 180 184 186 186 188 190 190 192 192 194 197 198 199 199 200 201 202 202

Contents

8

Radio resource optimization in cooperative cellular wireless networks

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205

Shankhanaad Mallick, Praveen Kaligineedi, Mohammad M. Rashid, and Vijay K. Bhargava

8.1 8.2

8.3

8.4 8.5 9

Introduction Networks with single source–destination pair 8.2.1 Three-node relay network 8.2.2 Dual-hop relay networks Multiuser cooperation 8.3.1 System model 8.3.2 Centralized power allocation 8.3.3 Distributed power allocation Relay selection Conclusion

Adaptive resource allocation in cooperative cellular networks

205 206 207 213 220 221 222 223 228 230 233

Wei Yu, Taesoo Kwon, and Changyong Shin

9.1 9.2

Introduction System model 9.2.1 Orthogonal frequency-division multiplexing (OFDM) 9.2.2 Adaptive power, spectrum, and rate allocation 9.2.3 Cooperative networks Network optimization 9.3.1 Single-user water-filling 9.3.2 Network utility maximization 9.3.3 Proportional fairness 9.3.4 Rate region maximization Network with base station cooperation 9.4.1 Problem formulation 9.4.2 Joint scheduling and power allocation 9.4.3 Performance evaluation Cooperative relay network 9.5.1 Problem formulation 9.5.2 Joint routing and power allocation 9.5.3 Performance evaluation Conclusion

233 235 235 237 237 238 238 240 241 242 244 244 245 248 250 251 254 254 256

Cross-layer scheduling design for cooperative wireless two-way relay networks

259

9.3

9.4

9.5

9.6 10

Derrick Wing Kwan Ng and Robert Schober

10.1 Introduction 10.2 Cross-layer scheduling design – some basic concepts 10.2.1 Utility function-based cross-layer optimization 10.2.2 Quality-of-service (QoS) measure 10.2.3 Multiuser diversity gain

259 263 264 266 266

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10.3 Network model for relay-assisted OFDMA system 10.3.1 System model 10.3.2 Channel model 10.3.3 Channel state information (CSI) 10.4 Cross-layer design for two-way relay-assisted OFDMA systems 10.4.1 Instantaneous channel capacity and system goodput 10.4.2 Cross-layer design problem 10.5 Cross-layer optimization solution 10.5.1 Transformation of the optimization problem 10.5.2 Dual problem formulation 10.5.3 Distributed solution – subproblem for each relay station 10.5.4 Solution of the master problem at the BS 10.6 Asymptotic performance analysis and computational complexity reduction scheme 10.6.1 Asymptotic analysis of system goodput 10.6.2 Scheme for reducing computational burden at each relay 10.7 Results and discussions 10.7.1 Convergence of the distributed resource allocation algorithm 10.7.2 Average system goodput vs. transmit power and user mobility 10.7.3 Asymptotic system goodput performance of PF scheduling 10.8 Conclusion Appendix

270 270 271 273 274 274 275 276 276 279 279 280

Green communications in cellular networks with fixed relay nodes

300

281 281 283 283 284 284 289 290 292

Peter Rost and Gerhard Fettweis

11.1 Introduction 11.1.1 Two motivating examples 11.1.2 Scope and key problems 11.1.3 Outline and contributions 11.2 System model 11.2.1 Propagation scenarios 11.2.2 Air interface and scheduling 11.3 System and protocol design 11.3.1 Non-relaying protocols 11.3.2 Relay-only protocol 11.3.3 An integrated approach 11.3.4 Simplifications 11.4 Numerical analysis 11.4.1 Simulation methodology 11.4.2 Throughput performance in the wide-area scenario 11.4.3 Throughput performance in the Manhattan-area scenario 11.4.4 Femto-cells vs. relaying 11.4.5 Computation-transmission-power tradeoff

300 300 302 303 303 303 305 306 307 307 308 309 309 309 310 312 313 315

Contents

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11.4.6 Reduced backhaul requirements 11.4.7 Cost–benefit tradeoff 11.5 Conclusion

316 317 320

Network coding in relay-based networks

324

Hong Xu and Baochun Li

12.1 Introduction 12.2 Network coded cooperation 12.2.1 Simple network coded cooperation 12.2.2 Joint network and channel coding/decoding 12.3 Physical-layer network coding 12.4 Scheduling and resource allocation: cross-layer issues 12.5 Conclusion

324 326 327 331 334 337 341

Part IV Game theoretic models for cooperative cellular wireless networks

345

13

347

Coalitional games for cooperative cellular wireless networks Walid Saad, Zhu Han, and Are Hjørungnes

14

13.1 Introduction 13.2 A brief introduction to coalitional game theory 13.3 A coalition formation game model for distributed cooperation 13.3.1 Motivation and basic problem 13.3.2 Distributed virtual MIMO coalition formation game 13.4 Coalitional graph game among relay stations 13.4.1 Motivation and basic problem 13.4.2 A network formation game among relay stations 13.5 Conclusion

347 348 350 351 355 368 368 369 378

Modeling malicious behavior in cooperative cellular wireless networks

382

Ninoslav Marina, Walid Saad, Zhu Han, and Are Hjørungnes

14.1 Introduction 14.2 Cooperating jammers 14.2.1 System model 14.2.2 The game 14.2.3 Simulation results 14.3 Cooperating relays 14.3.1 System model 14.3.2 Secrecy capacity 14.3.3 Simulation results 14.4 Eavesdroppers cooperative model

382 384 385 386 393 398 399 400 404 407

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Contents

14.4.1 Coalition formation games for distributed eavesdroppers cooperation 14.4.2 Simulation results 14.4.3 Conclusion

411 416 418

Part V Standardization activities

423

15

425

Cooperative communications in 3GPP LTE-Advanced standard Hichan Moon, Bruno Clerckx, and Farooq Khan

15.1 Introduction 425 15.2 LTE and LTE-Advanced 426 15.2.1 Carrier aggregation 428 15.2.2 Latency improvements 429 15.2.3 DL multiantenna transmission 430 15.2.4 UL multiantenna transmission 431 15.3 Cooperative multipoint transmission 431 15.3.1 Interference mitigation techniques in previous releases of LTE 432 15.3.2 Overview of CoMP techniques 433 15.3.3 Release 10 of LTE-Advanced 450 15.4 Wireless relay 451 15.4.1 Key technologies 452 15.4.2 Standard trends on Release 10 and future works 454 15.5 Heterogeneous network 454 15.5.1 Key technologies 454 15.5.2 Standard trends on Release 10 and future work 457 15.6 Conclusion 457 16

Partial information relaying and relaying in 3GPP LTE

462

Dong In Kim, Wan Choi, Hanbyul Seo, and Byoung-Hoon Kim

16.1 Introduction 16.2 Partial information relaying with multiple antennas 16.2.1 Per-antenna superposition coding (PASC) 16.2.2 Multilayer superposition coding (MLSC) 16.2.3 Rate matching for superposition coding 16.2.4 Overall rate capacity 16.2.5 Features of partial information relaying 16.3 Analysis of PASC with zero-forcing decorrelation 16.4 Multinode partial information relaying 16.4.1 Two-stage superposition coding 16.4.2 Successive decoding in cooperating phase 16.4.3 Relay selection for maximum capacity 16.5 Concluding remarks on partial information relaying 16.6 Relaying in 3GPP LTE-Advanced

462 463 465 466 468 469 470 470 474 475 477 477 479 480

Contents

16.6.1 Functionality of RNs 16.6.2 Separation of the backhaul and access links 17

Coordinated multipoint transmission in LTE-Advanced

xv

481 488 495

Sung-Rae Cho, Wan Choi, Young-Jo Ko, and Jae-Young Ahn

17.1 Introduction 17.2 CoMP architecture 17.2.1 Joint processing and transmission (JPT) 17.2.2 Coordinated scheduling and beamforming (CS/CB) 17.2.3 Cell clustering 17.2.4 Inter-eNodeB and intra-eNodeB coordination 17.3 CoMP design parameters 17.3.1 Reference signal (RS) 17.3.2 Precoding 17.3.3 Feedback 17.4 CoMP performance evaluation methodologies 17.4.1 Link level simulation 17.4.2 System level simulation 17.5 Conclusion

495 496 497 497 497 499 499 499 501 502 504 504 506 509

Index

514

Contributors

Jae-Young Ahn Electronic Telecommunication and Research Institute (ETRI), Korea Defne Aktas Bilkent University, Turkey Emre Aktas Hacettepe University, Turkey Vijay K. Bhargava The University of British Columbia, Canada Sung-Rae Cho Korea Advanced Institute of Science and Technology (KAIST), Korea Wan Choi Korea Advanced Institute of Science and Technology (KAIST), Korea Bruno Clerckx Samsung Electronics, Korea Jamie Evans University of Melbourne, Australia Gerhard Fettweis Technische Universität Dresden, Germany Gerard J. Foschini Bell Laboratories, USA Zhu Han University of Houston, USA

List of contributors

Stephen Hanly National University of Singapore, Singapore Wibowo Hardjawana University of Sydney, Australia Ahmadreza Hedayat CISCO Systems, USA Are Hjørungnes UNIK – University of Oslo, Norway Ekram Hossain University of Manitoba, Canada Praveen Kaligineedi The University of British Columbia, Canada Farooq Khan Samsung Electronics, Korea Byoung-Hoon Kim LG Electronics, Inc., Korea Dong In Kim Sungkyunkwan University (SKKU), Korea Young-Jo Ko Electronic Telecommunication and Research Institute (ETRI), Korea Taesoo Kwon Samsung Electronics, Korea Baochun Li University of Toronto, Canada Yonghui Li University of Sydney, Australia Shankhanaad Mallick The University of British Columbia, Canada Narayan B. Mandayam Rutgers University, USA

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Ninoslav Marina Princeton University, USA Mohammad Moghaddari University of Manitoba, Canada Hichan Moon Samsung Electronics, Korea Derrick Wing Kwan Ng The University of British Columbia, Canada Aria Nosratinia University of Texas at Dallas, USA Chandrasekharan Raman Rutgers University, USA Mohammad M. Rashid The University of British Columbia, Canada Daryl Reynolds West Virginia University, USA Walid Saad UNIK – University of Oslo, Norway Robert Schober The University of British Columbia, Canada Hanbyul Seo LG Electronics, Inc., Korea Changyong Shin Samsung Electronics, Korea Matthew C. Valenti West Virginia University, USA Reinaldo A. Valenzuela Bell Laboratories, USA Peter Rost NEC Euro Labs, Germany


Branka Vucetic University of Sydney, Australia Li-Chun Wang National Chiao Tung University, Taiwan Hong Xu University of Toronto, Canada Roy D. Yates Rutgers University, USA Chu-Jung Yeh National Chiao Tung University, Taiwan Wei Yu University of Toronto, Canada

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Preface

Cooperative communications and networking represent a new paradigm which uses both transmission and distributed processing to significantly increase the capacity in wireless communication networks. Current wireless networks face challenges in fulfilling users’ ever-increasing expectations and needs. This is mainly due to the following reasons: lack of available radio spectrum, the unreliable wireless radio link, and the limited battery capacity of wireless devices. The evolving cooperative wireless networking paradigm can tackle these challenges. The basic idea of cooperative wireless networking is that wireless devices work together to achieve their individual goals or one common goal following a common strategy. Wireless devices share their resources (i.e., radio link, antenna, etc.) during cooperation using short-range communications. The advantages of cooperation are as follows: first, the communications capability, reliability, coverage, and quality-of-service (QoS) of wireless devices can be enhanced by cooperation; second, the cost of information exchange (i.e., transmission power, transmission time, spectrum, etc.) can be reduced. Cooperative communication and networking will be a key component in next generation wireless networks. In this book we particularly focus on cooperative transmission techniques in cellular wireless networks. Although cellular wireless systems are regarded as a highly successful technology, their potential in throughput and network coverage has not been fully realized. Cooperative communication is a key technique to harness the potential throughput and coverage gains in these networks. Cooperation is possible among mobile stations (MSs) inside a cell as well as among base stations (BSs). In addition, specialized relay stations (RSs) can be installed in the network to facilitate cooperative communications. In addition to improving throughput and coverage, cooperative communication can improve the energy saving performance at the mobile devices, increase reliability in transmission, and decrease the overall interference in the network. However, successful deployment and operation of a cooperative cellular wireless network hinges on the development of advanced radio transmission and resource management techniques and optimization of these techniques considering the different network parameters. This has spurred a vibrant flurry of research on different aspects of cooperative communication during the last few years.

Preface

xxi

With BS cooperation, neighboring cells can exchange information aiming at mitigating intercell interference by coordinating the multicell transmission to a mobile or reception from a mobile. In a relay-based cooperative cellular wireless network, an MS may communicate with a BS via potential relays, and similarly, a BS can send data to distant nodes through relays. The potential relays could be either preinstalled fixed RSs or relay-capable MSs. The RSs are much cheaper than conventional BSs because they have far fewer functionalities compared to BSs. If the relay is positioned suitably, it is possible to increase the data rate (especially at the cell boundaries) and the reliability of the system. Similar to multiantenna transceivers, relays provide diversity by creating multiple replicas of the signal of interest. By properly coordinating different spatially distributed nodes in the system, a virtual antenna array can be synthesized that emulates the operation of a multiantenna transceiver. With cooperation at all layers of the protocol stack, the network can achieve higher throughput, higher system reliability, higher energy efficiency, a lower bit-error rate, and a smaller packet loss rate. For cooperation at physical, medium access control (MAC), network, and application layers, various cooperative signaling methods are being widely explored and many new mechanisms are under development with respect to medium access, routing, location management, scheduling, energy management, etc. This book provides a comprehensive treatment of the state-of-the-art of cooperative communications and networking techniques for cellular systems (e.g., Beyond 3G, Long-Term evolution systems). It consists of chapters covering different aspects of cooperative cellular wireless network design which include the following: architectures and protocols for cooperative cellular wireless networks; cooperative BS techniques (e.g., cooperative beamforming technique); radio resource management protocol design and network planning for relay-based cooperative cellular wireless systems (e.g., relaying strategies and protocols, resource allocation, energy management, network coding, and cross-layer issues); and the latest IEEE standardization activities pertaining to cooperative cellular wireless systems. The chapters are written by the distinguished researchers in these areas. This book is targeted at graduate students, or researchers working in the area of cellular wireless networks. It can also be used for self-study to become familiar with the state-of-the-art in cooperative communications for cellular wireless systems. This book contains 17 chapters which have been organized into five parts. A brief account of each chapter in each of these parts is given next. Part I: Introduction In Chapter 1, Nosratinia and Hedayat outline the trends in research into cooperative cellular wireless networks, as well as some of the outstanding problems in this area. In particular, the issues related to BS cooperation (for both

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Preface

downlink and uplink transmission) and cooperation through dedicated wireless relays (fixed and mobile) are discussed from the physical layer perspective. In Chapter 2, Moghaddari and Hossain focus on the resource allocation problem for cooperative communications in relay-based orthogonal frequency-division multiple access (OFDMA) and multiple-input multiple-output (MIMO) wireless networks. Starting with the basics of cooperative relay networks and strategies for relay-assisted transmission, a survey on the different approaches for radio resource allocation in OFDMA relay networks is provided. To this end, research issues on resource allocation in multihop MIMO relay networks and some related work in the literature are discussed. Part II: Cooperative base station techniques In Chapter 3, Hardjawana, Vucetic, and Li focus on BS cooperation for interference cancelation where each BS transmitter uses the transmitted signal information from other BS and channel state information to precode its own signal. A spectrally efficient cooperative downlink transmission scheme is designed by employing precoding and beamforming. The proposed scheme achieves fairness among different users in terms of symbol error rate. In Chapter 4, Aktas et al. focus on an approach for implementing BS cooperation in a distributed manner via message passing in network MIMO systems. This approach is based on a graphical model (in particular, a factor graph) of the network MIMO communication processes. Both uplink and downlink transmissions are considered. As an example, a graph-based approach for distributed beamforming and power allocation is discussed. In Chapter 5, Wang and Yeh discuss the antenna architectures for the network MIMO schemes based on BS cooperation in a multicellular system. One fundamental question when applying the network MIMO technique in such a high interference environment is: how many BSs should cooperate together to provide satisfactory signal-to-interference-plus-noise ratio (SINR) performance? Considering the interferences from the other cooperating groups, it is found that on top of the tri-sector directional antenna and fractional frequency reuse (FFR), the network MIMO based on the three-cell coordination strategy can outperform seven-cell-based network MIMO with omni-directional antenna. The authors also consider the effect of different cell sectorizations by using 120◦ and 60◦ beamwidths directional antennas. Part III: Relay-based cooperative cellular wireless networks In Chapter 6, Valenti and Reynolds focus on space-time block coding (STBC) strategies in a cooperative system to forward signals efficiently from multiple relays to the destination by exploiting the spatial diversity present in a multirelay network. Both decode-and-forward distributed STBC and

Preface

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amplify-and-forward distributed STBC are considered for a two-phase transmission protocol in a network with one source node, one destination node, and a set of relay nodes. The end-to-end outage probability, coding gain, and achievable diversity as well as the optimal ratio of the power used in the two phases of transmission are analyzed for different space-time codes. Unlike conventional space-time codes, the distributed space-time codes have to deal with the synchronization problem at the destination receiver. Delay diversity, delay-tolerant distributed space-time codes, and space-time spreading are some effective methods of dealing with this problem. In Chapter 7, Raman et al. present a simulation study of the downlink of a cellular system with relays in order to evaluate peak and average power savings for a given target common rate requirement for users. In particular, three schemes, namely, the collaborative power addition (CPA) scheme, the power control-based collaborative power addition (PC-CPA) scheme, and an orthogonal relaying scheme are simulated. In the CPA scheme, when a relay receives the complete message, it collaborates with the BS to transmit the complete message to the user using its peak power. In the PC-CPA scheme, power control is performed jointly at the BS and RS. In the orthogonal relaying scheme, the BSs and the RSs transmit in orthogonal time slots. The peak power savings (at the BSs) are rate gains (for the users) and are observed to be better with the PC-CPA scheme. In Chapter 8, Mallick et al. study the radio resource (i.e., bandwidth, transmit power) allocation problem in relay-based cooperative cellular wireless networks. For the different relaying schemes (i.e., amplify-and-forward, decodeand-forward) in single- and multiuser network scenarios, different optimization models for resource allocation and their solution approaches are described. Also, the problem of relay selection for individual communication between source and destination nodes is discussed. The problem of joint optimization of resource allocation and relay selection is an open research issue. In Chapter 9, Yu, Kwon, and Shin study the resource (i.e., power, spectrum, and rate) allocation problem for OFDMA-based cooperative cellular wireless networks. Two types of cooperative networks are considered: the multicell network with BS cooperation where multiple BS cooperatively allocate power to the different frequency subchannels, and networks with RSs. With a view to maximizing the sum of utilities of multiple uses in a multicell network, a network utility maximization (NUM) framework is used to solve the scheduling, and the power, frequency, and rate allocation problem. A key observation here is that, with OFDMA, the network utility maximization problem often decomposes into a tone-by-tone optimization problem, which is easier to solve. In Chapter 10, Ng and Schober focus on the problem of cross-layer scheduling design for two-way half-duplex amplify-and-forward relay-assisted OFDMA cellular networks. Such a scheduling scheme has to satisfy the different data rate and outage probability requirements of different users. Starting with the basics of cross-layer scheduling design and the related implementation challenges, the

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Preface

problem considered is formulated as a mixed combinatorial and non-convex optimization problem. In the problem formulation, the objective is to obtain the optimal power, rate, and subcarrier allocation policies while taking the imperfect channel state information (CSI) as well as heterogeneous QoS requirements of the users into account. The problem is then solved by dual decomposition. Also, a distributed iterative algorithm is designed to reduce the computational load at the relays. In Chapter 11, Rost and Fettweis focus on the system-wide energy consumption in cooperative cellular networks. Two deployment scenarios are considered, namely, a macrocellular deployment and a microcellular deployment, both of which use OFDMA air interface for uplink/dowlink transmission in time-division duplex (TDD) mode. The system performance is simulated considering multicell MIMO transmission only (nonrelaying protocol), a relay only protocol, and an integrated approach (which supports both multicell MIMO and relaying). The achievable throughput performance, the energy saving potentials, and the deployment costs are compared. In addition, performance comparison is carried out between femto-cells and relaying. In Chapter 12, Xu and Li study the potential application of network coding and the related issues in relay-based networks. Also, the idea of physical-layer network coding is discussed; this has the potential to improve the throughput performance of relay-based networks significantly. One key observation is that, since network coding is mostly applied at the lower layers of the protocol stack, the scheduling and resource allocation at the upper layers have to be codingaware. Such a cross-layer approach for network coded cooperation may reap the benefits of network coding, however, at the expense of increased complexity. Part IV: Game theoretic models for cooperative cellular wireless networks In Chapter 13, Saad, Han, and Hjørungnes explore the application of coalitional game theory to model the various aspects of cooperative behavior in cellular wireless networks. For example, cooperation among the BSs can be modeled by a class of coalitional games, known as coalition formation games, and thereby, algorithms can be derived which help in analyzing the groups of cooperating BSs that will emerge in a given network scenario. As another example, network formation games, a class of coalitional graph games, can be used to model the interactions among RSs. The key message is that coalitional game theory provides a rich framework to design efficient, fair, and robust models for resource allocation and sharing in cooperative cellular wireless networks. In Chapter 14, Marina et al. use game theory to analyze the secrecy capacity in cooperative networks in the presence of malicious users (e.g., eavesdroppers). The secrecy capacity refers to the maximum reliable data rate at which a perfectly secret communication is possible between a sender and a receiver. Three

Preface

xxv

different communications scenarios are considered. In the first scenario, several friendly jammers help the source in transmitting data to a destination by jamming the eavesdropper. The interaction between the source and the friendly jammers is analyzed using a Stockholder type of game. In the second scenario, several relay nodes help the source by relaying the transmitted data in the presence of a malicious node, and this cooperation improves the secrecy capacity. In this cooperative system, the number and locations of the relay nodes determine the secrecy region, i.e., the geometric area in which the secrecy capacity is positive. In the last scenario, the eavesdroppers cooperate to improve their reception performance. A coalitional game-based model is proposed for forming cooperative groups among the eavesdroppers. This modeling will be useful to develop defense mechanisms against the eavesdroppers’ cooperation. Part V: Standardization activities In Chapter 15, Moon, Clerckx, and Khan discuss the standard trends on cooperative communications in the Third Generation Partnership Project (3GPP) LongTerm Evolution Advanced (LTE-Advanced) system. In particular, an overview of the key technical features of LTE-Advanced Release 10 including carrier aggregation, cooperative multipoint transmission/reception (CoMP), extended multiantenna systems, and wireless relays is provided. Carrier aggregation provides wider transmission bandwidth and makes full use of the existing fractional spectrum bands. The other techniques provide higher cell spectrum efficiency, better coverage, and lower handover interruption time. CoMP transmission refers to a new class of intercell interference mitigation technique, which is also called multicell MIMO, collaborative MIMO (Co-MIMO), or network MIMO. The basic idea is to extend the conventional single-cell-to-multiple-user transmission to a multiple-cell-to-multiple-user transmission through BS cooperation. In Chapter 16, Kim et al. develop methods for partial information relaying in multiantenna decode-and-forward relay networks. These methods use a twophase transmission strategy and exploit the asymmetric link conditions in cellular networks, where the source–relay link and the relay–destination link are relatively better than the source–destination link. With multiple antennas available at source, relay, and destination, multiple parallel data streams are transmitted which consist of basic data streams and superposition coded (SC) data streams. The relay forwards only the SC streams (i.e., partial information in the second hop). Two methods, namely, per-antenna superposition coding (PASC) and multilayer superposition coding (MLSC), are proposed for power allocation among basic and superposed layers, and across the spatial layers. It is observed that partial information relaying results in significant capacity gain over full information relaying. To this end, the authors summarize the issues, discussions, and current conclusions on relaying in the LTE-Advanced standard.

xxvi

Preface

In Chapter 17, Cho et al. discuss the proposals and current conclusions on the CoMP technique in the 3GPP LTE-Advanced standard. Many companies and research groups are confident that CoMP systems are feasible in real systems and have put forth effort to find and evaluate what type of cooperation scheme should be standardized. The authors outline the issues discussed in the LTE-Advanced study group, for downlink CoMP, and present related simulation methodologies.

Part I Introduction

1

Network architectures and research issues in cooperative cellular wireless networks Aria Nosratinia and Ahmadreza Hedayat

1.1

Introduction The systematic study of relaying and cooperation in the context of digital communication goes back to the work of Van der Meulen [1] and Cover and El Gamal [2]. The basic relay channel of [1, 2] consists of a source, a destination, and a relay node. The system models in [1, 2] are either discrete memoryless channels (DMC), or continuous-valued channels which are characterized by constant (nonrandom) links and additive white Gaussian noise. The study of cooperative wireless communication is a more recent activity that started in the late 1990s, and since then has seen explosive growth in many directions. Our focus is specifically on aspects of cooperative communication related to cellular radio. Aside from the fading model, the defining aspects of a cellular system are base stations that are connected to an infrastructure known as the backhaul, which has a much higher capacity and better reliability than the wireless links. The endpoints of the system are mobiles that operate subject to energy constraints (battery) as well as constraints driven by the physical size of the device that lead to bounds on computational complexity and the number of antennas, among other considerations. There are multiple mobiles in each cell as well as frequency reuse, leading to intracell interference and intercell interference, respectively. The exponential path-loss laws lead to significant variations in signal power at various points in the cell. In this chapter we are concerned with cooperative radio communication that specifically engages one or more of these defining aspects. Within the context of cellular radio, cooperative communication may be used to enhance capacity, improve reliability, or increase coverage. It may be used in the uplink or the downlink. In the communication between a base station and a mobile, the cooperating entity may be another base station, another mobile, or a dedicated (often stationary) wireless relay node. The cooperating entity may have various amounts of information about the source data and channel state information. Cooperation may happen in the physical layer, data link layer, network layer, transport layer, or even higher layers. The large number of different Cooperative Cellular Wireless Networks, eds. Ekram Hossain, Dong In Kim, and Vijay K. Bhargava. Published by Cambridge University Press. C Cambridge University Press, 2011.

4

Network architectures and research issues

ways that cooperation may be exploited to improve the quality of service in cellular radio has given rise to much research and a rich and expanding literature. There are many questions that remain unanswered, among them the relation between the various forms of cooperation and their relative merits are in general not fully known. In this chapter, we aim to catalog some of the directions of research in this area, and outline some of the open questions.

1.2

Base station cooperation Base station cooperation can take multiple forms. The simplest form of base station cooperation, especially with multiantenna base stations, involves the exchange of information among neighboring cells regarding their cell-edge nodes and remote-cell aware processing at each of the base stations. Then, each of the base stations can put a null on the channel gain vector of the nodes that generate and/or are harmed by the most cochannel interference. This and other simple scenarios like it are in the realm of interference management, and are possible without fully coordinated action from base stations. Specifically, this form of action does not require the base stations to know the traffic for other base stations (therefore the issue of a wideband backbone and its delay does not come into play), nor is it required to know the codebooks used by the other base station, and nor does it require the base stations to be synchronized.

1.2.1

Downlink cooperation For downlink base station cooperation, base stations can generate a virtual multiantenna array with zero-forcing beamforming. There are a variety of ways to exploit this general idea. Somekh et al. [3] used the circular Wyner cellular model [4] to find expressions for downlink (and uplink) capacities with base station cooperation, which is also sometimes called multicell processing. In [5] the same model and a zero-forcing beamforming approach were used for data transmission in multiple cells. In particular, the approach is to transmit to the best user in each cell, and the high-load asymptotics are derived in an information theoretic approach. Mundarath et al. [6] considered the scheduling aspects of distributed downlink zero-forcing beamformers under finite loads. Such downlink strategies require certain assumptions about sharing of information among cells. To begin with, the data must be shared among the base stations. Secondly, the base station transmitters must be synchronized. Finally, the channel state information of the users must be shared among the base stations, and must be kept up-to-date, so that beamforming vectors can be reliably determined. The nascent area of distributed beamforming has seen much activity; we briefly mention a representative sample of the results.

1.2 Base station cooperation

5

The effect of channel state statistics on distributed beamforming was investigated in [7]. Ng et al. [8] developed a distributed method of beamforming by message passing between adjacent base stations instead of sharing the data between many base stations. Mudumbai et al. [9] investigated the feasibility of distributed beamforming from the viewpoint of local oscillator phase errors, showing encouraging results. However, the results were tempered by the fact that in this study it was assumed that the frequency of the oscillators is stable. Brown and Poor [10] proposed a method of carrier synchronization for distributed beamforming. Other works in this area include [11–18]. A tutorial on the challenges and progress in distributed beamforming is given in [19]. There is a key difficulty that limits the usefulness of conventional beamforming techniques in the distributed scenario: because the antennas are not colocated, the difference of propagation delay from different antennas to a node will become a relevant parameter. For beamforming to a single node (single-beam solution) any difference in delays can be absorbed into the beamforming coefficients. Multiple beams may also be generated in the same manner, but only as long as the target nodes are close to each other, i.e., the delay vectors for various nodes must be approximately similar. If the target nodes are far from each other and the transmit antennas are also far from each other, then the conventional methods of beamforming may not work. The degradation of distributed beamforming systems due to the distribution of the antennas and the target nodes is a subject that, to our knowledge, has not been systematically investigated. Also, the design of new optimization techniques to develop beamforming vectors in the presence of different delays remains an open problem. To study this issue further, it is useful to separate the two difficulties raised by this delay variance. The first one is the induced change in phase, which can be addressed via, e.g., systems of equations that impose the constraints at various nodes. The second, more challenging, problem is due to the variance in the time of arrival of the leading edge of each symbol at various nodes. Assuming that the arrival of symbols from the distributed antennas is calibrated to be cotimed at node A, the leading edge of the symbols may not arrive cotimed at node B. To our knowledge, no comprehensive method is known to address this problem. Intuitively, if the symbol duration is much larger than the differences in time of arrival, then there is a chance that if the phases can be appropriately adjusted, the overall effect can be brought under control. This also suggests the use of systems with longer symbol duration, e.g., OFDM. It would be interesting to investigate whether variations of techniques used in OFDM, such as cyclic prefix, can be used to “collect” the various components of the distributed beamforming that may be out of phase and out of time. Aside from the above-mentioned fundamental issue, there are also practical issues that require careful consideration and design. In particular, distributed beamforming requires delicate accounting for various types of delay, not just

6


in the channel but also within the base station and signal delivery path. Any unaccounted for delay, or delay variation anywhere within the transmit or receive path, would cause transmitted signals to arrive at the mobile station unaligned, causing loss in beamforming gain. These are requirements that often do not appear in theoretical studies, but in fact play an important role in any practical implementation. To summarize, base station cooperation offers the opportunity for improvent in two opposing directions: incorporating more theoretical results and addressing practical issues. Among various aspects that call for further investigation, one may name:

r possibilities with multiantenna mobiles, among them the extension of results r r r r 1.2.2

from multiple-input multiple output (MIMO) broadcast channels to the distributed MIMO case; the effect of partial channel state information or partially outdated channel state information; quantized channel-state feedback for distributed beamforming has been addressed in [16], but there is room for much more work in this area; the effect of uneven channel state information across a set of heterogeneous mobiles; investigation of limits on the backbone, e.g., limits on sharing of traffic data.

Uplink cooperation The problem of uplink cooperation is rather different from its downlink counterpart. In the uplink cooperation scenario, a mobile might be in a situation where no single base station can decode its data alone. However, the signals received at two or more base stations may be sufficient to decode the mobile data. The collection of information at various base stations and their combination present new issues. In particular, since each of the base stations cannot decode the received signal alone, these signals must be sampled and exchanged among base stations, which requires significantly larger bandwidth than the data do. Thus, considering the effect of base station cooperation on the backhaul capacity becomes an important issue. The capacity of the uplink linear cellular networks with base station cooperation via finite capacity links was broached in [20], and bounds on the rate of the system under the Wyner model were obtained from an information theoretic viewpoint. This work generated broad insights into the general capabilities of uplink base station cooperation, but the specifics of coding and signal design for such systems remain open problems. Thankfully, the uplink does not suffer in quite the same way from the timing problem that plagues the downlink distributed beamforming (see Section 1.2.1). The varying propagation times from the mobiles to base stations can be compensated in the algorithm that combines the data from multiple base stations, since the signal of each of the mobiles can be extracted separately. However, the

1.3 Dedicated wireless relays

7

problem will remain if we wish to listen to mobile A while simultaneously nulling the interference from mobile B, and these two mobiles have significantly different delay vectors to the set of base stations participating in multicell processing. The scope for future work in the area of uplink multicell processing is in two directions: incorporation of communication theoretic results into uplink cooperation and addressing issues related to practical limitations. The potential areas of work include:

r practical implications of the restrictions on the backhaul capacity and delay; r iterative methods based on belief propagation; r compute-and-forward (hashing) methods to reduce the cooperation bandwidth requirement between the base stations;

r analysis of nonideal conditions, including uncertainties in channel state information;

r the effect of nonideal synchronization and sampling; r investigating possibilities presented by multiantenna mobiles. 1.3

Dedicated wireless relays Traditional cellular networks provide fixed throughput for all subscribers where a basic voice service can be supported. Unlike such networks, broadband wireless cellular networks promise a high data rate throughout the coverage area. While such promise is feasible for the inner coverage area, at the cell-edge data rates are limited for various reasons. Decreasing the cell-size is one way to satisfy the required data rate; however, it is a costly solution because it requires the installation of additional base stations. In contrast, deploying relay stations provides a cost-effective solution. Compared with a full-scale base station, a dedicated relay can save on equipment costs, backhaul link, and deployment. A relay station assists the main base station to improve its coverage or throughput. A relay station can be used to extend the coverage area of a base station, or to provide coverage in so-called holes.1 In addition, thanks to the advances in antenna array techniques, relays can also be used to improve throughput and capacity. Due to above facts, the IEEE 802.16 Working Group has developed the IEEE 802.16j standard with techniques that are compatible with the WiMAX standard.

1.3.1

IEEE 802.16j The IEEE 802.16j standard was created to be backward compatible with the 802.16e standard known as WiMAX. Various modes of operation of 802.16j fit within the WiMAX OFDMA frame. In all the various modes of 802.16j, the base 1

For example, in tunnels or in certain areas inside a building.

8


station allocates part of its uplink and downlinks subframes for communicating with the relay station(s). It is envisioned that legacy mobile nodes are able to integrate seamlessly into 802.16j, therefore the mobiles are oblivious to the relays, i.e., they cannot distinguish between the relay and base station. Two of the modes of operation considered in the IEEE 802.16j standard are transparent and nontransparent modes. The usage of these modes depends on whether it is intended to increase throughput for cell-edge mobile stations, or to extend coverage to the mobile stations unreachable by base station. The transparent mode allows for one-time relaying while the nontransparent mode allows for multiple-time relaying. The transparent mode can be used, e.g., for in-building coverage, while the nontransparent mode can be used to access remote areas which might possibly require multiple relaying. There are also differences within the downlink and uplink frames of these two modes. In transparent mode only the traffic portion is exchanged between relay and mobile stations, while in nontransparent mode in addition to the traffic portion other signals such as synchronization, downlink and uplink maps, and ranging need to be exchanged as well. Both the transparent and nontransparent modes are multihop modes, i.e., the relay intervenes between the source and destination, and the data portions of source–relay and relay–destination communications are performed separately in time. Another mode of operation in the IEEE 802.16j standard is cooperative relaying, where the base station and relay transmit the same signal, or two copies of the same signal, to the mobile simultaneously. As long as the timing difference between the signal of the base and relay stations as seen by mobile stations is within the acceptable range, the mobile station sees the combined signals as a signal with high diversity. Operational cooperative relaying has multiple requirements. First, traffic data need to be exchanged between the relay and base stations. Second, the deployment of the relays needs to be such that the time difference seen by the mobile station does not cause OFDMA intersymbol interference. With these practical requirements fulfilled, research efforts have been focused on the various MIMO techniques that can be used to achieve cooperation between base and relay stations. The IEEE 802.16j standard says very little about the techniques for implementing cooperative relaying, therefore there is significant room for innovation by the wireless industry within the context of the standard. It must be noted that other broadband wireless standards, such as Long-Term Evolution (LTE) and LTE-Advanced, consider the use of relay stations. For details, the readers are referred to Chapters 15 and 16 of this book.

1.3.2

High-spectral-efficiency relay channels One of the main drawbacks of relaying is that in effect it requires duplicate transmissions (e.g., base station to relay and relay to mobile), unlike standard single-hop transmission. For instance, in both transparent and nontransparent

1.3 Dedicated wireless relays

9

modes of the IEEE 802.16j there are multiple zones of uplink and downlink subframes that are assigned for the exchange of traffic between base station and relay stations. The loss of time and/or bandwidth is more pronounced for multihop relaying. However, the advantages of relaying often more than offset the loss of bandwidth. The obvious advantages are the reduction of path loss and shadowing, as well as providing path diversity, but the advantages of relaying go beyond the obvious. For example, both the base station and the relay are stationary (nonmoving) and the base station is often elevated, so it is possible to estimate the channel gains between the base station and the relay with a very high degree of accuracy and stability, far beyond what is possible with mobiles. In addition, it is possible to use antenna arrays in both the base station and the relay, which combined with the accurate channel state information leads to a higher spectral efficiency as well as more efficient frequency reuse. More specifically, the base station can employ space-division multiple access (SDMA) techniques to transmit traffic to several relay stations using the same bandwidth. For efficient implementation of SDMA, the channel state information of each relay must be known by the base station with high precision. In fact, the more precise the channel state information, the larger the number of relay stations that can be served within the same bandwidth. Thanks to the fixed location of relay and base stations, it is possible to obtain a high-quality channel state information of each relay station. Likewise, it is possible to use a similar technique in the uplink to increase uplink spectral efficiency. For instance, collaborative spatial multiplexing, which is also introduced in the IEEE 802.16e and other wireless broadband standards, allows multiple relay stations to transmit uplink traffic utilizing the same burst location, i.e., the same bandwidth. If relay stations are equipped with antenna arrays, other MIMO techniques such as spatial multiplexing can also be used to further enhance spectral efficiency of downlink and uplink. Improving spectral efficiency of relay channels can further increase the utilization of relays in broadband cellular networks, and therefore is one of the important research topics in this area. For instance, the design of adaptive MIMO precoding techniques that can provide robustness as well as higher throughput can facilitate cellular relays. This could lead to precoding weights that adapt to spatial multiplexing, beamforming, or nulling. The various costs related to the backhaul channel constitute a big portion of the cost of cellular network deployment, operation, and maintenance. Increased utilization of wireless resources will result in shrinking cell sizes and an increase in the number of base stations, therefore it is expected that backhaul link expenses will be in future broadband networks, generating interest in backhaul links that are cheaper than laying cable or dedicated microwave links. It has been noted that one can use the same family of broadband wireless technologies that are servicing end-users to connect to some base stations. The similarity of operation and use of wireless backhaul links and relaying technologies suggests a potential

10


unification of these two applications. Thus, spectrally efficient relay channels could eventually also pave the way to less-expensive and easily deployable backhaul links, and might even lead to unified technologies or standards for both.

1.4

Mobile relays In the previous two sections, we considered the outlook for base station cooperation and dedicated relays. It has been noted that there is nothing in principle that precludes the possibility of mobile relays, although technologically their implementation is much more difficult. In this section, we give a brief overview of mobile relays. We begin by considering the distinguishing characteristics of mobile relaying. One of the fundamental differences between mobile and fixed relays is the limitations on power/energy in the mobile nodes. Fixed relays can be connected to the power grid, while the mobiles are dependent on resident energy storage, which with the present-day technologies is a severe limiting factor. This situation seems a fairly stable one, since neither energy storage devices with orders-ofmagnitude higher energy densities, nor an efficient means of tetherless delivery of energy to mobiles, is visible on the technological horizon. Another distinguishing factor of most mobile nodes, compared to fixed relays, is one of size. Mobile nodes are no more than several centimeters in each dimension, and this puts fundamental restrictions on the number of antennas that can be deployed on a mobile. Polarization diversity antennas offer some improvement, but a fixed relay has much more flexibility in the number of antennas. An aspect of mobile relaying, which is not unrelated to size and energy, is computational complexity. However, unlike size, this is less of a fundamental limitation. In the past, advances in computational power, measured in MIPS/mm3 , have been much more rapid than, e.g., advances in battery technology measured in terms of energy density (joules/mm3 ). Thus it is not unreasonable to assume that near-future technologies in mobiles will become ever more computationally complex, while the power available to them will grow at a much slower pace. Due to limited resources, any mobile relay must balance the needs of the node itself with relaying for other nodes. This includes not only power and computation, but also the total spectral efficiency available to a node. The fundamental tradeoff between a node’s own communications and relayed bandwidth was addressed in [21], which showed that the competition between its own bandwidth and the relayed bandwidth does not constitute a zero-sum game. However, there will still be questions of the motivation of a relay node to use local resources for other nodes. The specific aspects of network-wide management of resources, and the development of network control algorithms that guide the action of mobile relay nodes that also have individual incoming/outgoing traffic, have attracted some attention but a complete understanding of these algorithms has still not been achieved. Some interesting advances have been made using game theory and pricing analysis. However, a good part of the work in this area is not relevant

1.5 Conclusion

11

to the design of cooperative cellular networks, because the nodes in a cellular network are not autonomous agents and most decisions are, in fact, made in a centralized manner. Resource allocation and network control for mobile cooperative nodes (including aspects such as local rate splitting) are interesting problems that, under the practical conditions that are of interest to the designers of cellular systems, remain for the most part unsolved.

1.5

Conclusion Cooperative communication is one of the promising wireless technologies that has been reintroduced in the last decade, and it has promising applications in the context of cellular networks. This chapter has presented a brief overview of some of the aspects of research in cooperative cellular networks. To summarize, several important directions of future work seem to beckon wireless researchers. One direction points to the more sophisticated algorithms and harnessing the full power of the coding and signaling methods that are emerging from information theory. Another direction is to refine the models in order to get a more realistic grip on the practical aspects of operation in a cellular network. Finally, most systematic study and analysis of cooperation has concentrated on the physical layer. However, cooperative action at other layers of the communication hierarchy is also possible, but has not been studied quite as much, and this may present a host of opportunities to future wireless engineers.

References [1] E. C. Van der Meulen, “Three terminal communication channels,” Adv. Appl. Probab., 3, 1971, 120–154. [2] T. Cover and A. El Gamal, “Capacity theorems for the relay channel,” IEEE Trans. Inform. Theory, 25, 1979, 572–584. [3] O. Somekh, B. Zaidel, and S. Shamai, “Sum rate characterization of joint multiple cell-site processing,” IEEE Trans. Inform. Theory, 53, 2007, 4473– 4497. [4] A. Wyner, “Shannon-theoretic approach to a Gaussian cellular multipleaccess channel,” IEEE Trans. Inform. Theory, 40, 1994, 1713–1727. [5] O. Somekh, O. Simeone, Y. Bar-Ness, A. M. Haimovich, and S. Shamai, “Cooperative multicell zero-forcing beamforming in cellular downlink channels,” IEEE Trans. Inform. Theory, 55, 2009, 3206–3219. [6] J. Mundarath, P. Ramanathan, and B. Van Veen, “A distributed downlink scheduling method for multi-user communication with zero-forcing beamforming,” IEEE Trans. Wireless Commun., 7, 2008, 4508–4521. [7] V. H. Nassab, S. Shahbazpanahi, A. Grami, and Z.-Q. Luo, “Distributed beamforming for relay networks based on second-order statistics of the channel state information,” IEEE Trans. Signal Processing, 56, 2008, 4306–4316.

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[8] B. L. Ng, J. Evans, S. Hanly, and D. Aktas, “Distributed downlink beamforming with cooperative base stations,” IEEE Trans. Inform. Theory, 54, 2008, 5491–5499. [9] R. Mudumbai, G. Barriac, and U. Madhow, “On the feasibility of distributed beamforming in wireless networks,” IEEE Trans. Wireless Commun., 6, 2007, 1754–1763. [10] D. Brown and H. Poor, “Time-slotted round-trip carrier synchronization for distributed beamforming,” IEEE Trans. Signal Processing, 56, 2008, 5630– 5643. [11] H. Ochiai, P. Mitran, H. Poor, and V. Tarokh, “Collaborative beamforming for distributed wireless ad hoc sensor networks,” IEEE Trans. Signal Processing, 53, 2005, 4110–4124. [12] V. H. Nassab, S. Shahbazpanahi, and A. Grami, “Optimal distributed beamforming for two-way relay networks,” IEEE Trans. Signal Processing, 58, 2010, 1238–1250. [13] H. Chen, A. B. Gershman, and S. Shahbazpanahi, “Filter-and-forward distributed beamforming in relay networks with frequency selective fading,” IEEE Trans. Signal Processing, 58, 2010, 1251–1262. [14] K. Zarifi, A. Ghrayeb, and S. Affes, “Distributed beamforming for wireless sensor networks with improved graph connectivity and energy efficiency,” IEEE Trans. Signal Processing, 58, 2010, 1904–1921. [15] Z. Ding, W. H. Chin, and K. Leung, “Distributed beamforming and power allocation for cooperative networks,” IEEE Trans. Wireless Commun., 7, 2008, 1817–1822. [16] E. Koyuncu, Y. Jing, and H. Jafarkhani, “Distributed beamforming in wireless relay networks with quantized feedback,” IEEE J. Select. Areas Commun., 26, 2008, 1429–1439. [17] M. Ahmed and S. Vorobyov, “Collaborative beamforming for wireless sensor networks with Gaussian distributed sensor nodes,” IEEE Trans. Wireless Commun., 8, 2009, 638–643. [18] E. Zacarias, S. Werner, and R. Wichman, “Distributed Jacobi eigenbeamforming for closed-loop MIMO systems,” IEEE Commun. Lett., 10, 2006, 825–827. [19] R. Mudumbai, D. Brown, U. Madhow, and H. Poor, “Distributed transmit beamforming: challenges and recent progress,” IEEE Commun. Mag., 47, 2009, 102–110. [20] O. Simeone, O. Somekh, H. V. Poor, and S. Shamai, “Local base station cooperation via finite-capacity links for the uplink of linear cellular networks,” IEEE Trans. Inform. Theory, 55, 2009, 190–204. [21] R. Tannious and A. Nosratinia, “Relay channel with private messages,” IEEE Trans. Inform. Theory, 53, 2007, 3777–3785.

2

Cooperative communications in OFDM and MIMO cellular relay networks: issues and approaches Mohammad Moghaddari and Ekram Hossain

2.1

Introduction The continually increasing number of users and the rise of resource-demanding services require a higher link data rate than the one that can be achieved in current wireless networks [1]. Wireless cellular networks, in particular, have to be designed and deployed with unavoidable constraints on the limited radio resources such as bandwidth and transmit power [2]. As the number of new users increases, finding a solution to meet the rising demand for high data rate services with the available resources has became a challenging research problem. The primary objective of such research is to find solutions that can improve the capacity and utilization of the radio resources available to the service providers [3]. While in traditional infrastructure networks the upper limit of the source– destination (S–D) link’s data capacity is determined by the Shannon capacity [4], advances in radio transceiver techniques such as multiple-input multiple-output (MIMO) architectures and cooperative or relay-assisted communications have led an enhancement in the capacity of contemporary systems. In the MIMO technique the diversity relies on uncorrelated channels, and is achieved by employing multiple antennas at the receiver side, the transmitter side, or both, and by sufficiently separating the multiple antennas (of same polarization) [5]. The MIMO technique can be used to increase the robustness of a link as well as the link’s throughput. Unfortunately, the implementation of multiple antennas in most modern mobile devices may be challenging due to their small sizes [3]. Cooperative diversity or relay-assisted communication has been proposed as an alternative solution where several distributed terminals cooperate to transmit/receive their intended signals. In this scheme, the source wishes to transmit a message to the destination, but obstacles degrade the S–D link quality. The message is also received by the relay terminals, which can retransmit it to a desired destination, if needed. The destination may combine the transmissions received by the source and relays in order to decode the message.

Cooperative Cellular Wireless Networks, eds. Ekram Hossain, Dong In Kim, and Vijay K. Bhargava. Published by Cambridge University Press. C Cambridge University Press, 2011.

14

Cooperative communications in OFDM and MIMO cellular relay networks

The limited power and bandwidth resources of the cellular networks and the multipath fading nature of the wireless channels have also made the idea of cooperation particularly attractive for wireless cellular networks [6]. Moreover, the desired ubiquitous coverage demands that the service reaches the users in the most unfavorable channel conditions (e.g., cell-edge users) by efficient distribution of the high data rate (capacity) across the network [7, 8]. In conventional cellular architectures (without relay assistance) increasing capacity along with coverage extension dictates dense deployment of base stations (BSs) which turns out to be a cost-wise inefficient solution for service providers [9]. A relay station (RS), which has less cost and functionality than the BS, is able to extend the high data rate coverage to remote areas in the cell under power and spectral constraints [10–13]. By allowing different nodes to cooperate and relay each other’s messages to the destination, cooperative communication also improves the transmission quality [14]. This architecture exhibits some properties of MIMO systems; in fact a virtual antenna array is formed by distributed wireless nodes each with one antenna. Since channel impairments are assumed to be statistically independent, in contrast to conventional MIMO systems, the relay-assisted transmission is able to combat these impairments caused by shadowing and path loss in S–D and relay–destination (R–D) links. To this end, an innovative system has been proposed in which the communication between transmitter and receiver is done in multiple hops through a group of relay stations. This cooperative MIMO relaying scheme creates a virtual antenna array (VAA) [15] by using the antennas of a group of RSs. These RSs transmit the signal received from the BS (or previous hops) cooperatively on different channels to the receiving terminal (downlink case) or the signal that the transmitting terminal wants to send to the BS (uplink case). This system can be modeled as a MIMO system although the real receiver (downlink) or transmitter (uplink) only has one antenna. Since the relaying mobile stations (MSs) introduce additional noise and there is a double Rayleigh channel effect, the scheme is expected to perform below the corresponding MIMO diversity gain when used for spatial multiplexing. The combination of relaying and orthogonal frequency-division multiple access (OFDMA) techniques also has the potential to provide high data rate to user terminals everywhere, anytime [7, 8, 16]. Interest in orthogonal frequency-division multiplexing (OFDM) is therefore growing steadily, as it appears to be a promising air-interface for the next generation of wireless systems due, primarily, to its inherent resistance to frequency-selective multipath fading and the flexibility it offers in radio resource allocations. Likewise, the use of multiple antennas at both ends of a wireless link has been shown to offer significant improvements in the quality of communication in terms of both higher data rates and better reliability at no additional cost of spectrum or power [17]. These essential properties of OFDMA and MIMO, along with the effectiveness of cooperative relaying in combating large-scale fading and enhancing system capacity immediately motivate the integration of these technologies into one network architecture.

2.2 Cooperative relay networks

15

Figure 2.1. Example of a traditional infrastructure network.

However, adequate and practical radio resource allocation (RRA) strategies have to be developed to exploit the potential gain in capacity and coverage improvement in the integration of relaying, OFDMA, and MIMO techniques [18]. This chapter surveys algorithms proposed in the literature to adaptively allocate the available resources in a relay-enhanced OFDMA-based and MIMO wireless networks. We also briefly review resource management approaches in distributed-MIMO multihop systems.

2.2

Cooperative relay networks Wireless networks can be classified into two major categories: traditional infrastructure networks and multihop networks. In traditional networks the communication is performed directly between the BS and the MS and vice versa, so, there is only one hop. Though obstacles may degrade the line-of-sight (LoS) S–D link quality in this scheme, the source makes no use of the cooperation potential of other terminals in the network to compensate for the impairments (Figure 2.1).

2.2.1

Cooperative communication The method of relaying, which was introduced by Van der Meulen in 1971 [19], was studied from an information theoretical point of view by Cover and El

16


R S

D

Figure 2.2. The relay channel, source (S), relay (R), and destination (D).

Gamal in [20]. In these contributions, a source MS communicates with a target MS directly and via a relaying MS. In [20], the capacity of such a relaying configuration was shown to exceed the capacity of a simple direct link. In later studies, a very simple but effective user cooperation protocol was suggested to boost the uplink capacity and lower the uplink outage probability for a given rate [21]. The designed protocol stipulates an MS to broadcast its data frame to the BS and to a spatially adjacent MS, which then retransmits the frame to the BS. Such a protocol certainly yields a higher degree of diversity because the channels from both MSs to the BS can be considered uncorrelated. Cooperative communication was introduced in [10] using the scenario depicted in Figure 2.2 but with the relay terminal being another source. Both sources (associated partners) are also responsible for transmitting the information of their partners. It was assumed that the sources are working in full-duplex mode, so that both sources are transmitting to the destination and receiving a noisy version of the partner’s transmission. Results in terms of ergodic achievable rate regions and outage probability of the cooperative and noncooperative transmission show the benefits of this scheme.

2.2.2

Relay channel The relay channel was introduced in [19]. It assumes that there is a source that wants to transmit information to a single destination. However, there is a relay terminal that is able to help the destination (relay-assisted transmission). Based on the previously received symbols, it can transmit an additional message to the destination if needed. Figure 2.2 illustrates the channel model. When the channel to relay terminal is in a better condition than the LoS channel, this scheme is able to improve the S–D transmission. In general, it is assumed that the relay works in full-duplex mode, i.e., receiving and transmitting simultaneously. The duplex communication problem can be solved by assuming that the frequency bands for the main link (S–D) and the relaying links (R–D) differ. Since full duplex terminals are currently unrealistic in practical systems, relays are forced to work in half-duplex mode. However, the half-duplex constraint impacts negatively on the theoretical spectral efficiency provided by an ideal full-duplex assisting relay. Multiplexing gains are not possible in half-duplex relaying, although significant additive capacity gains are still possible [15, 22].

17

2.2 Cooperative relay networks

S

Protocol I

Protocol II

Protocol III

R

R

R

D

S

D

S

Figure 2.3. Half-duplex relay protocols. Solid lines correspond to the transmission during the relay-receive phase and dashed lines to the transmission during the relay-transmit phase.

2.2.3

Overview of relay protocols In the half-duplex mode there is an orthogonal duplexing (in time or frequency) between the phase that the relay is receiving (relay-receive phase) and the one it is transmitting in (relay-transmit phase). This phase separation allows the definition of several half-duplex relay protocols with various degrees of broadcasting and receiving collision in each relay-receive and relay-transmit phase among the three terminals (source, destination, and relay). The number of options leads to the four protocol definitions presented in Figure 2.3, (called protocols I, II, and III) and in Figure 2.4 (called forwarding) [23, 24]. In protocol I, the source communicates with the relay and destination during the relay-receive phase (solid lines in Figure 2.3). Then, in the relay-transmit phase, the relay terminal communicates with the destination (dashed line in Figure 2.3). On the other hand, in protocol II, during the relay-receive phase the source only transmits to the relay (solid line in Figure 2.3). It is assumed that the destination is not able to receive the message from the source in that phase. In the relay-transmit phase, the source and relay transmit simultaneously to the destination (dashed lines in Figure 2.3). Hence in the relay-transmit phase the channel becomes a multiple access channel. Protocol III can be seen as a combination of protocols I and II. The source transmits to the relay and the destination (solid lines in Figure 2.3) in the relayreceive phase. Then, in the relay-transmit phase, the source and the relay transmit to the destination (dashed lines in Figure 2.3). Notice that the relay is transmitting during the second phase, so that it cannot be aware of the signal transmitted by the source in the second phase. This protocol can achieve a better spectral efficiency than the previous ones. For example, this protocol was considered for obtaining the achievable rates of the relay channel in [22]. The traditional forwarding protocol consists of a transmission from the source to the relay during the relay-receive phase and a transmission from the relay to the destination in the relay-transmit phase, as in Figure 2.4. It should be

D

18


R S

D

Figure 2.4. Half-duplex forwarding protocol. emphasized that the half-duplex relay protocols defined in Figure 2.3 make good use of the S–D link in contrast to the forwarding protocol. Likewise, if that link presents very bad quality compared with the S–R and R–D links, the performance obtained by protocols I, II, and III converges to the forwarding one.

2.2.4

Strategies of relay-assisted transmission The paradigm of the conventional S–D communication is now changed to S–R–D, and the role played by the relay can be selected from different modes of operation influencing the total achievable rate of the system. Additionally, when there is a half-duplex relay, the resources allocated for each phase of the relay-assisted transmission also have an important impact on the achievable rate. Therefore, the strategies of relay-assisted transmission have to consider the decoding mode at the relay and the resource allocation. Basically, the three decoding modes analyzed in the literature are: amplify-and-forward (AF), decode-and-forward (DF), and compress-and-forward (CF).

Amplify-and-forward (AF) This is the simplest strategy that can be used at the relay. The relay amplifies the received signal from the source and transmits it to the destination without doing any decoding. For this reason, it is also called nonregenerative relaying. The main drawback of this strategy is that the relay terminal amplifies the received noise at the same time. Applying this strategy to cooperative communication leads to a better bit error rate (BER) than direct transmission [1]. The outage probability of the cooperative communication was derived in [1], demonstrating that a diversity order of 2 is obtained for two cooperative users. When the relay is equipped with multiple antennas and there is channel state information (CSI) available for the S–R/R–D links, the AF strategy can attain significant gains over the direct transmission by means of optimum linear filtering of the data to be forwarded [25].

Decode-and-forward (DF) In this strategy the complexity at the receiver increases in comparison to that in the AF strategy. Now the relay terminal has to estimate the message received

2.3 General system model of cellular relay networks

19

from the source, therefore the total performance depends on the success of this message decoding. Depending on the type of symbols retransmitted, the strategy at the relay is repetition coding (RC) or unconstrained coding (UC). In RC, the relay retransmits the same symbols previously estimated, while in UC the symbols transmitted are not the same as the received ones, but are related to the same information sent by the source (source and relay are using different codebooks). Hence, this protocol is also called regenerative relaying: the terms are used interchangeably in this chapter.

Compress-and-forward (CF) In this strategy, the relay does not decode the data but uses Wyner–Ziv lossy source coding [26] on the estimated symbols of the received signal. Then, the compressed signal is transmitted to the destination by the relay. This strategy was suggested in [20]. Depending on the channel gains of the different links, the CF strategy can be superior to the DF strategy. However, it adds more complexity to the system.

2.3

General system model of cellular relay networks A partial network in a multicellular relay network is shown in Figure 2.5, which is the general topology for reviewed algorithms and strategies in this chapter. It is assumed that the BS could continuously measure the quality of link, e.g., signalto-interference-plus-noise ratio (SINR) per subcarrier when OFDM is applied. Furthermore, for slowly varying channels, BSs and RSs can be assumed to have accurate estimates of the channel states. Despite being a common assumption in literature, this may not always be the case, especially for relay station to subscriber station (RS–SS) links. RRA based on partial CSI has been addressed in a number of references such as [27]. The BSs can optimize the resource allocation or they can involve a central network controller as shown in Figure 2.5. Consider a two-hop multiuser OFDM system with one BS at the center of each cell, K users, and N subcarriers, where each transceiver has only a single antenna. The RSs are assumed to be fixed and evenly distributed on a circle with a radius equal to one half of the cell radius in order to eliminate the effect of RS placements. The RS forwards the received signal to the BS (uplink) or SS (downlink) by employing either the amplify-and-forward (AF) or the decodeand-forward (DF) strategy on the same subcarrier. We consider a two-time-slot transmission pattern which is half-duplex in the sense that transmission and reception at any station do not occur simultaneously in the same frequency band. In the first time slot, the BS (SS) transmits while the RS and the SS (BS) receive. In the second time slot, only the RS transmits to the SS (BS). When the regenerated message is encoded to provide additional error protection for the original message, this is referred to as coded cooperation [2].

20


RS SS

SS

BS

RS RS

SS S SS SS RS

BS

Network controller

RS

SS

SS

BS RS

Subscriber station SS

RS

Relay station SS Back-bone link

Figure 2.5. A partial network in a multicellular relay network.

2.4

General system model for virtual antenna arrays (VAAs) The underlying principle for cellular deployment of VAAs is depicted in Figure 2.6. A BS array, consisting of several antenna elements, transmits a space-time encoded data stream to the associated mobile terminals which can form several independent VAA groups. Each mobile station within a group receives the entire data stream, extracts its own information, and concurrently relays further information to the other mobile terminals. It then receives more of its own information from the surrounding mobile terminals and, finally, processes the entire data stream. The wired links within a traditional receiving antenna array are thus replaced by wireless links. The same principle is applicable to the uplink [15]. In this situation, the VAA accomplishes a special type of network which bridges cellular and ad-hoc concepts to establish a heterogeneous network with increased capacity. It calls for intelligent synchronization, relaying, and data scheduling algorithms, the exact realization of which depends on the access scheme, the choice of main link technology, the choice of relaying technology, the technological limits, the number of antennas within a given geographical area, and other factors, e.g., the ability of the cellular system to synchronize users, etc. [15]. The deployment of VAAs creates various challenges which need to be addressed, for instance, how to enable the terminals to transmit and receive simultaneously and thus to operate in full-duplex mode. Of greater importance is the actual relaying process. Like in satellite transponders, the signal can be retransmitted using a transparent or regenerative relay. A transparent relay is generally

2.5 RRA in OFDMA-based relay systems

21

VAA MS

MS MS

MS

MS MS MS

MS

MS

MS BS

VAA

VAA cell

VAA

Figure 2.6. VAAs in cellular deployment.

easier to deploy since only a frequency translation is required. However, additions to the current standards are required. For a simple adaptation of VAA to current standards, regenerative relays should be deployed. This generally requires more computational power, but has been shown to increase the capacity of the network [28]. A generic realization of VAAs, which is henceforth referred to as distributedMIMO multihop relaying network was introduced in [29]. An example realization is depicted in Figure 2.7. Here, a source MS communicates with a target MS via a number of relaying MSs. Spatially adjacent relaying MSs form a VAA; each MS receives data from the previous VAA and relays data to the next VAA until the target MS is reached. Note that each of the terminals involved may have more than one antenna element. Furthermore, an arbitrary number of MSs of the same VAA may cooperate with each other. The suggested topology, depicted in Figure 2.7, encompasses a variety of communications scenarios. For instance, a cellular system operating on the downlink is obtained by replacing the source MS by the BS antenna array which communicates directly with the VAA containing the target MS. It may also represent a system where a BS array communicates with a VAA formed somewhere in the cell, which in turn relays the data to another VAA containing the target MS. This allows the coverage area of the BS to be extended. But as mentioned before, RRA algorithms should be designed to exploit the potential gains in all aforementioned wireless relay networks, by adaptively distributing scarce communication resources to either maximize or minimize some network performance metrics. We review the RRA algorithms proposed in the literature for relay-enhanced OFDMA-based and MIMO wireless networks as well as distributed-MIMO multihop systems.

2.5

RRA in OFDMA-based relay systems: general form In relay-enhanced OFDMA-based wireless networks, a typical resource allocation problem statement might be as follows [30]:

22


1st hop

2nd hop

Lth hop

D

S

Figure 2.7. Distributed-MIMO multistage communications system. How many information bits, how much transmit power (for SSs, RSs, or BSs), which and how many subcarriers (subcarrier assignment and allocation, respectively) should be assigned to SSs to either maximize or minimize a desired performance metric, e.g., system throughput (capacity) or total transmit power in the network, respectively?

Assume Ku = {1, 2, ..., K} and Nu = {1, 2, ..., N } are the sets of users and subcarriers respectively. The data rate of the kth user Rk is given by [30] Rk =

N B ck ,n log2 (1 + γk ,n ), N n =1

(2.1)

where B is the total bandwidth of the system and ck ,n is the subcarrier assignment index indicating whether the kth user occupies the nth subcarrier. ck ,n = 1 only if subcarrier n is allocated to user k; otherwise it is zero. The bandwidth of each subchannel is B/N = 1/T where T is the OFDM symbol duration. γk ,n is the signal-to-noise ratio (SNR) of the nth subcarrier for the kth user and is given by [30] γk ,n = pk ,n Hk ,n =

pk ,n h2k ,n , N0 B/N

(2.2)

where pk ,n is the power allocated for user k in subchannel n, and hk ,n and Hk ,n denote the channel gain and channel-to-noise ratio for user k in subchannel n, respectively. From (2.1), the total data rate RT of a zero margin system is given by N K B RT = ck ,n log2 (1 + γk ,n ). N n =1

(2.3)

k =1

Knowing the modulation scheme, γk ,n , the effective SNR, is adjusted accordingly to meet the BER requirements. The general form of the subcarrier and power allocation problem is [30]: max

c k , n ,p k , n

RT =

N K B ck ,n log2 (1 + γk ,n ) N n =1 k =1

(2.4)

2.6 Dynamic RA RRA in OFDMA relay networks

23

or min

c k , n ,p k , n

PT =

N K B ck ,n pk ,n , N n =1

(2.5)

k =1

subject to: C1: C2:

ck ,n ∈ {0, 1}, ∀k, n, K ck ,n = 1, ∀n, k =1

C4:

pk ,n ≥ 0, ∀k, n, N K ck ,n pk ,n ≤ Ptotal ,

C5:

user rate requirement.

C3:

(2.6)

k =1 n =1

The problem can be formulated with two possible objectives followed by various constraints (C1–C5). The first two constraints are on subcarrier allocation to ensure that each subchannel is assigned to only one user. C4 is only effective in problems where there is a power constraint Ptotal on the total transmit power of the system PT (e.g., rate adaptive algorithms). C5 determines the fixed or variable rate requirements of the users. In each class, the problem is formulated accordingly and the optimal solution is derived using different optimization techniques. Due to the high computational complexity of the optimal solutions, they may not be practical in real-time applications. As a result, suboptimal algorithms have been developed which differ mostly in the approach they choose to split the procedure into several (preferably independent) steps to make the problem tractable and, in their simplifying assumptions to reduce the complexity of the allocation process. The performance of each algorithm greatly depends on the formulation of the problem and the validity of these simplifying assumptions. Two major classes of dynamic resource allocation schemes have been reported in literature [30]: margin adaptive (MA) schemes [31–33], and rate adaptive (RA) schemes [34–36]. The optimization problem in MA allocation schemes is formulated with the objective of minimizing the total transmit power while providing each user with its required QoS in terms of data rate and BER. The objective of the RA scheme is to maximize the total data rate of the system with the constraint on the total transmit power. Both classes are overviewed and discussed in the following sections.

2.6

Dynamic RA RRA in OFDMA relay networks Different scenarios of centralized or distributed algorithms, along with single-cell and multicell network topologies have been considered in the literature for the RA RRA problem.

24


2.6.1

Centralized RA RRA schemes in single-cell OFDMA relay networks A downlink single-cell network with a single fixed RS was considered in [37], while such a network with multiple fixed RSs was studied in [38]. In both [37] and [38], time-division-based half-duplex transmission and adaptive modulation and coding (AMC) were assumed. In [37] two algorithms (fixed time-division and adaptive time-division) were proposed to improve the cell throughput and coverage while minimizing complexity and overhead requirements. However, the objective function in [38] was the total average throughput of both the direct and relayed links presented as a function of SNRs and some indicator (optimization) variables, with constraints as in [37]. In both the proposed algorithms, the BS transmission frame is followed by the transmission of an RS frame. The first algorithm performs subcarrier allocation with a predetermined equal power allocation (the same level for both BS and RS). The second algorithm achieves an optimal joint power and subcarrier allocation. Simulation results showed that as the number of RSs increases, the sum rate increases, while the joint allocation algorithm continues to outperform the fixed power allocation algorithm. In [39], the authors used the concept of utility functions to formulate the problem of RA in multiuser OFDM systems. Utility maps the network resources a user utilizes into a real number and is a function of the user’s data rate. The utility-based dynamic resource allocation problem is formulated as: max

c k , n ,p k , n

K

Uk (Rk ),

(2.7)

k =1

subject to: C1:

Si ∩ Sj = ∅, ∀i, j ∈ Ku , i = j,

C2:

∪k Sk ⊆ {1, 2, ..., N },

C3:

pk ,n ≥ 0, ∀k, n,

C4:

N K

ck ,n pk ,n ≤ Ptotal ,

(2.8)

k =1 n =1

where Uk (Rk ) is the utility function for the kth user. Rk is defined as in (2.1), Sk is the set of subcarriers assigned to user k for which ck ,n = 1. In [39] the extreme case of an infinite number of orthogonal subcarriers each with an infinitesimal bandwidth was investigated by introducing two theorems: theorem I gave the optimal subcarrier allocation assuming a fixed power allocation on all the subcarriers and theorem II gave the optimal power allocation given a fixed subcarrier allocation. Combining the results of the two theorems, the optimal frequency set and the power allocation for the extreme case were obtained. It is obvious from (2.7) and (2.8) that fairness among users was not considered. For RA schemes for OFDMA without relaying, it has been shown in literature, e.g., [40], that optimization can be achieved when a subcarrier is assigned to only one user who has the best channel gain for that subcarrier, and also that


25

equal power allocation among subcarriers has almost the same performance as waterfilling transmit power adaptation but with less complexity. In [34], the authors imposed proportional rate constraints in the OFDMA relaying network to ensure that each user could achieve the required data rate. However, all the transmitters, including the BS and RSs, are limited to one fixed transmitting power, which is not flexible and this is not practical in a relaying network. To tackle the mixed integer and continuous variable optimization problem in (2.7)–(2.8) with Uk (Rk ) = Rk , the authors of [41] proposed a greedy subcarrier and power coallocation algorithm based on a new theorem. The theorem states that in general situations, i.e., when all link gains between RSs and SSs are different from each other, for each SS and subcarrier allocated, there is only one RS among all RSs that has pk ,n = 0. In other words, for each symbol transmitted from the BS to the SS, only one RS needs to relay this symbol, given the power constraint on each RS. This also suggests that using subcarrier allocation without considering power allocation may not work well because many subcarriers at each RS may not have been allocated power even though they have been chosen [41]. The centralized subcarrier and power allocation algorithm which maximizes system capacity with a constraint on the overall transmission power when there is an LoS between the BS and the SS was studied in [42]. Hence, the aggregate system throughput was defined as RT =

i∈D

Ri +

K

Rk ,

(2.9)

k =1

where D represents the set of direct links. Similar to the approach taken in [34], the problem was broken down into two steps. In the first step, a heuristic algorithm was proposed to assign the subcarriers to each link based on the channel condition. In the second step, an iterative power allocation algorithm was proposed to balance the two-hop links for maximizing the end-to-end capacity of two-hop SSs. In the proposed algorithm, firstly, the subcarriers are allocated to the links with the best channel gain as an initialization. The overall capacity of each transmission slot is maximized in this step. In the next step, the subcarriers are reallocated to improve the system capacity by iteration. In other words, the basic idea is to take out the worst subcarrier allocated to the first-hop (second-hop) link of the richest (poorest) RS and to reassign it to the first-hop (second-hop) link of the poorest (richest) RS. Two cases are compared and the one that can achieve more gain is exploited. The subcarrier reassigning procedure is repeated until no improvement can be achieved [42]. Another interesting technique to deal with the mixed integer optimization problem in (2.7)–(2.8) was proposed in [18]: an OFDMA relay network with multiple sources, multiple relays, and a single destination was investigated and resource allocation was considered with fairness (load balancing) constraints on relay nodes. The authors’ approach was to transform the integer optimization problem into a linear distribution problem in a directed graph to allow the use of

26


Relay (multihop) region

Inner (single-hop) region

S1

S1

S2

S2

BS

Figure 2.8. Network layout and spatial reuse pattern.

the linear optimal distribution algorithms available in the literature. The required information is collected at the central unit for allocation decisions (Figure 2.5). It was assumed that the subcarriers allocated in the first hop (S–R) are the same as those in the second hop (R–D). This reduction in available frequency diversity gain results in a potential system performance loss. To address this issue, the concept of subcarrier pairing was employed in [43] to attain extra gain in the average system rate. It was shown that a higher performance in terms of mutual information can be achieved if the subchannels of both links, S–R and R–D, are paired according to the actual magnitude of the link gains, i.e., a strong first hop subchannel is coupled with a strong second hop subchannel and not with a weak one.

2.6.2

Centralized RA RRA schemes in multicell OFDMA relay networks A centralized downlink OFDMA scenario in a multicellular network enhanced with six fixed relays per cell was considered in [44] and [45]. The proposed scheme allows efficient use of subcarriers via opportunistic spatial reuse within the same cell, as shown in Figure 2.8 (i.e., a set of subcarriers used in a BS–RS link (S1) can be reused after 180-degree angular spacing in a RS–SS link), even when no directional antennas are employed. These are probably among the first papers to consider such spatial reuse in a multicell environment, although, with a greatly simplified model. Fading was not considered except for independent log-normal shadowing on links, which means that subcarriers are similar on any particular link. Consequently, the problem was formulated as the minimum number of subcarriers required to satisfy a SS’s QoS. This was used in the transmit scheme selection algorithm (TSSA) that switches among single-hop, multihop, and multihop with spatial reuse [7].


27

In the TSSA, the only scheme allowed in the interior hexagon is the single hop directly from the BS, whereas outside this region (relay region), the TSSA can choose the multihop with spatial reuse scheme or the multihop scheme, which requires fewer subcarriers to satisfy the QoS requirements. With this strategy, an integer programming optimization problem is formulated to maximize the number of SSs with satisfied QoS requirements. It was observed that a significant increase in the number of supported SSs is achieved when applying the TSSA compared with the case where the transmission scheme is restricted in the cell region to a particular scheme, regardless of the channel conditions. This suboptimal scheme potentially reduces the performance gains. By considering latency, overhead and system, and computational complexity, it may be seen that centralized RRA schemes are not the best option for future wireless networks. This has led to the importance of distributed schemes being recognized. However, there has not been much progress on this front.

2.6.3

Distributed RA RRA schemes in OFDMA relay networks A semi-distributed downlink OFDMA scheme in the form of two algorithms of separate and sequential allocation (SSA) and separate and reuse allocation (SRA), in a single cell enhanced by M half-duplex fixed relays was considered in [46]. The scheme divides the SSs into disjoint sets located in the neighborhoods of the BS and RSs, an approach that is common in the literature. The SSs attached to the BS and relays are referred to as the BS–SS and RS–SS clusters, respectively. The BS allocates some resources to the BS–SS cluster directly and to the RS–SS clusters through the RS. Implicitly, it is assumed that all routes have been established prior to resource allocation, regardless of the channel conditions, and that the same subcarrier is used on the two hops, BS–RS and RS–SS. The starting point of both the two-step SSA and the SRA algorithm allocation schemes is basically the same. In the first step, each RS, along with its SS cluster, is treated as a large SS with a required minimum rate equal to the sum of all the minimum required rates of the SSs in its cluster. The BS allocates the resources among its own SSs and these virtual large SSs. In the second step, the RS allocates resources to the SSs in its cluster based on one of two allocation schemes:

r Resources assigned to that BS-RS link in the first step are allocated among the connected SSs (SSA).

r The RS reallocates all the N subcarriers to its connected SSs regardless of the BS assignments (SRA). Simulation results for a single cell with one relay showed that the semidistributed scheme, SSA in particular, has a comparable capacity and outage probability performance to the centralized scheme [7]. The SSA algorithm showed significant performance stability over the SRA. Since both RS and BS may

28


assign the same subcarriers to their respective SSs in the SRA algorithm, intracell interference may occur, which results in a considerable increase in outage probability. In general, the proposed semi-distributed schemes reduce the amount of overhead required to feedback the CSI and minimum rates to the BS. However, in the case of SRA, there is no need to communicate such information to the BS. These schemes fail to exploit the interference avoidance and traffic diversity gains. In addition, there is an inherent loss in performance due to the decoupling of routing and scheduling processes.

2.6.4

RA RRA schemes with fairness in OFDMA relay networks Looking back at utility-function-based optimizations, such as in [39], one way to accomplish both efficiency and fairness is to use utility functions that are both increasing and marginally decreasing. As a result, the slope of the utility curve decreases with an increase in the data rate. Choosing a marginally decreasing utility function also guarantees its strict concavity which ensures global optimality as well as the uniqueness of the optimal solution. A logarithmic utility function U (R) = ln(R) is both increasing and marginally decreasing. Therefore, a resource allocation policy using a logarithmic utility function is said to be proportionally fair. Different types of utility functions were proposed in [36], [47], and [48], depending on the type of application. A utility function that ensures both efficiency and fairness is better obtained through subjective survey than by applying theory. For the general resource allocation problem formulated in (2.4)–(2.6), the optimization with variable rate constraints is given in (2.10)–(2.11), in which the objective is to maximize the total rate within the total power constraint of the system while maintaining rate proportionality among the users indicated in C5: K N pk ,n h2k ,n B , (2.10) RT = ck ,n log2 1 + max B c k , n ,p k , n N N0 N n =1 k =1

subject to: C1: C2:

ck ,n ∈ {0, 1}, ∀k, n, K

ck ,n = 1, ∀n,

k =1

C3: C4:

pk ,n ≥ 0, ∀k, n, N K


k =1 n =1

C5:

R1 : R2 : . . . : RK = α1 : α2 : . . . : αK .

(2.11)


29

Here {α1 , α2 , . . . , αK } is a set of predetermined proportional constraints in which αk is a positive real number with αm in = 1 for the user with the lowest required proportional rate. When all αk terms are equal, the objective function in (2.10) is similar to the objective function of the max–min problem introduced in [49]. The authors of [49] studied the max–min problem, where by maximizing the worst user’s capacity, it was ensured that all users achieve the same data rate. It was reported that in a single-user waterfilling solution the total data rate of a zero margin system is close to capacity, even with flat transmit power spectral density (PSD), as long as the energy is poured only into subchannels with good channel gains. Hence, in a system with N subchannels, a flat transmit power over all the subcarriers would always give close to optimum performance. Though acceptable fairness amongst users is achieved in [49] by allocating power uniformly across all subcarriers, the frequency selective nature of a user’s channel is not fully exploited. To improve its performance, Shen et al. [34] added a second adaptive power allocation step to further enforce the rate proportionality among the users. The two-step approach adopted in [34] is as follows: in the first step, the modified version of the algorithm outlined in [49] is employed for subcarrier allocation to achieve coarse proportional fairness. Hence, instead of giving priority to the user with the lowest achieved data rate Rk , priority is given to the user with the lowest achieved proportional data rate, i.e., Rk /αk . In this step, the achieved rate is calculated assuming equal power on all the subcarriers. After subcarrier allocation is carried out, the problem is simplified into maximization over continuous variables of power. In the second step, the power is reallocated among the users and then among the subcarriers through the use of waterfilling to enforce the rate proportionality among the users. Another suboptimal algorithm to solve RA RRA was formulated in [50] as a binary integer programming problem to maximize the Nash product of all users r eq in the form K k =1 (Rk − Rk ) and, at the same time, satisfy users’ minimum rate requirements. It was demonstrated in [51] that the solution achieves a Nash bargaining solution (NBS) fairness, which is a generalization of the well-known proportional fairness. The algorithm can be divided into two steps. In the first step, a subcarrier is randomly selected and then allocated to the user whose required minimum rate is not satisfied and whose achievable rate on this subcarrier is the largest, either by direct or by relayed transmission. The process loops until all users achieve their required rates. In the second step, the NBS algorithm assigns the remaining subcarriers to users in such a way that the Nash product for each assignment is maximized. While this scheme is fair in the sense that the user’s rate is determined only by its own channel condition, and not by other competing users’ conditions, it was also shown that the algorithm provides a good tradeoff between the overall system performance and the fairness among users.

30


2.7

Dynamic centralized margin adaptive RRA schemes in OFDMA relay networks In deriving this group of algorithms, a given set of user data rates is assumed with a fixed QoS requirement. The optimization problem can then be formulated as [30]: min

c k , n ,p k , n

PT =

N K

ck ,n pk ,n ,

(2.12)

k =1 n =1

subject to: C1: C2:

ck ,n ∈ {0, 1}, ∀k, n, K

ck ,n = 1, ∀n,

k =1

C3: C4:

pk ,n ≥ 0, ∀k, n, K N


k =1 n =1

C5:

Rk ≥ Rk ,m in , k = 1, 2, . . . , K

(2.13)

with the rate requirements indicated in C5. This problem was first addressed in [52], where the focus was only on subcarrier allocation, and further in [32], where adaptive power allocation was also considered. With the help of constraint relaxation and to make the problem tractable, the authors of [31] introduced a new parameter to the cost function, taking values within the interval [0,1], which can be interpreted as the sharing factor for each subcarrier; the same technique was also used in [3] and [53] to simplify the optimization problem. With the help of the new parameter, it was shown that the optimization problem can be reformulated as a convex minimization problem over a convex set [30]. Using the standard optimization techniques, the Lagrangian of the new problem is obtained along with the necessary conditions under which not only the minimum total transmit power occurs but also the data rate constraint of each user is satisfied. Lagrange multipliers which satisfy the individual data rate constraints can be found using an iterative search algorithm. Each subcarrier is then assigned to only the user that has the largest sharing factor on that subcarrier, using the set obtained in the previous step. However, the iterative computation and search for this algorithm make it prohibitively expensive and highly complex. One solution to simplify the algorithm is to assume that the channel is flat for a certain number of subcarriers, as in [54]. Adaptive resource allocation methods have been shown to offer higher user data rates due to the additional degree of freedom provided by multichannel systems [30]. One way to create multiple channels in a frequency domain is to

2.8 MIMO communications systems

31

use multiple carrier frequencies with the methods and algorithms discussed in this chapter. The other way is with multiple transmit and receive antennas in the spatial domain. The latter is also referred to as MIMO.

2.8

MIMO communications systems MIMO systems have been shown to hold the promise of providing capacity and data rates far exceeding those offered by conventional single-input single-output (SISO) communications systems, and hence are being widely studied for use in wireless systems. MIMO channels have a number of advantages over traditional SISO channels such as beamforming (or array) gain, diversity gain, and multiplexing gain. The beamforming and diversity gains are not exclusive for MIMO channels and also exist in single-input multiple-output (SIMO) and multipleinput single-output (MISO) channels. The multiplexing gain, however, is a unique characteristic of MIMO channels. Some gains can be simultaneously achieved, while others compete and establish a tradeoff. An excellent overview of the gains of MIMO channels is avaiable in [55]. In a nutshell, the use of multiple dimensions at both ends of a communication link offers significant improvements in terms of spectral efficiency and link reliability.

2.8.1

RRA in MIMO relay networks The main challenge in point-to-multipoint fixed relaying is to provide a highcapacity link between the BS and the RS, while at the same time providing multiple data links to multiple users [56]. A natural solution to this problem is to exploit the advantages of MIMO systems. A wireless MIMO relay can be regenerative or nonregenerative. It was suggested in [57] that a nonregenerative MIMO relay has the following potential advantages over a regenerative MIMO relay. First, a nonregenerative relay can relay signals faster than a regenerative relay if separate frequency channels are used for the relay’s input and output. Second, deployment of a nonregenerative relay can have little effect on the operations at the source and the destination as there is no handshaking requirement for each packet going through the nonregenerative relay using two frequency channels. Third, a nonregenerative relay contains virtually no information for decoding the source and hence exposes no security information even if it is stolen by an enemy. There has been much research into nonregenerative MIMO relay systems [56– 61]. The focus in the literature has been on the optimal design and power allocation of these systems. In the context of MIMO relays, the power allocation problem is to determine the source covariance matrix and the relay matrix that maximize the system performance. Here we present a review of work on two main categories of MIMO-enhanced relaying systems, single-user single-relay MIMO

32


1

Source

Relay

HSR

HRd

2

2 Encode

1

(Decode /encode

Q

Destination

F

M

N

Figure 2.9. DF MIMO relaying system. and multiuser single-relay MIMO systems as well as distributed-MIMO multihop systems.

2.8.2

Optimal design and power allocation in single-user single-relay systems For a single-user two-hop MIMO relay system, an optimal structure of the relay matrix that maximizes the S–D mutual information was presented in [57] and [58], and an optimal structure for both the source precoder matrix and the relay matrix was established in [59]. Optimal designs of beamforming and forwarding matrices for both the DF and the AF relaying protocols are presented in the following subsections.

DF relay system We first consider a single-user DF MIMO downlink relay system as illustrated in Figure 2.9, where s ∈ CM ×1 denotes the signal transmitted from the source equipped with M antennas, Q ∈ CM ×M the source precoder (beamforming) matrix, and HS R ∈ CM ×M the S–R channel matrix. Then the signal received at the relay, yR , is given by yR = HS R Qs + nR , where nR is the zero-mean Gaussian noise at the relay. The achievable rate at the first hop (S–R) can be represented as [62] (2.14) R1 (Q) = 12 log det σR2 IM + HS R QE[ssH ]QH HH SR 2 1 H H (2.15) = 2 log det σR IM + HS R QQ HS R , 1 2 where E[ssH ] = IM , and E[nR nH R ] = σR IM . The 2 represents the rate loss due to transmission in two hops. In the second phase, the relay decodes data (with the assumption of no outage) and forwards them to the destination using the forwarding matrix F. The received signal at the destination is given by yD = HR D Fs + nD . The achievable rate at the second hop (R–D) can be represented as 2 (2.16) R2 (F) = 12 log det σD IN + HR D FFH HH RD .

Finally, the achievable rate of the relay system is bounded by the minimum of R1 and R2 , i.e., R(Q, F) =min(R1 (Q), R2 (F)). Similarly to Section 2.6, the RA optimization problem can be formulated as max Q ,F

R(Q, F),

(2.17)


33

subject to: C1:

tr(QQH ) ≤ PS ,

C2:

tr(FFH ) ≤ PR ,

(2.18)

where PS and PR are the total power constraints at the source and relay, respectively and tr(·) represents the trace of the matrix. From (2.15) and (2.17), we note that the optimization problem can be divided into two MIMO channel rate maximization problems as: max Q

R1 (Q)

max F

R2 (F)

subject to: tr(QQH ) ≤ PS

tr(FFH ) ≤ PR .

(2.19)

It is well known that the optimal solution of (2.19) is singular value decomposition (SVD) with waterfilling power allocation.

AF relay system Consider the single-user AF MIMO downlink relay system as illustrated in Figure 2.10. The achievable rate at the first hop (S–R) can be obtained as [62] R1 (Q) =

1 2

log det σR2 IM + HS R QQH HH SR .

(2.20)

In the second phase, the relay simply amplifies its received data and forwards the data to the destination using the forwarding matrix F. The received signal at the destination is given by yD = HR D FyR + nD

(2.21)

= HR D F(HS R Qs + nR ) + nD

(2.22)

= HR D FHS R Qs + HR D FnR + nD .

(2.23)

From (2.23), it is obvious that relay amplifies not only data vector s, but the noise of the first hop nR . Though amplifying the noise causes rate loss in the AF relay protocol, the implementation is easy and delay is much smaller than in DF. The achievable rate of the second phase can be derived as H H H H −1 . R2 (Q, F)= 12 log det I+HR D FHS R QQH HH F H (I+H FF H ) RD SR RD RD (2.24) As with DF, the achievable rate of the relay system is bounded by the minimum of R1 and R2 , i.e., R(Q, F) =min(R1 (Q), R2 (Q, F)). Hence, the RA optimization

34


1

Source

Relay

HSR

HSR

2

2 Encode

1

Destination

F

Q M

N

Channel state information

Figure 2.10. AF MIMO relaying system.

problem can be formulated as max Q ,F

R(Q, F),

subject to: C1: C2:

tr(QQH ) ≤ PS , 2 H tr F(HS R QQH HH ≤ PR . S R + σR I)F

(2.25)

This is more complex than the problem for the DF case and cannot be divided into individual optimization problems. To tackle (2.25), the authors in [57–59] proposed different approaches though with the same basic idea. In [57] it was proved that for a relay system without a direct S–D link the optimal relay matrix is given by F = V2 ΛF UH 1 ,

(2.26)

H H H where ΛF is a diagonal matrix, and H1 HH 1 = U1 Σ1 U1 and H2 H2 = V2 Σ2 V2 are the eigenvalue decomposition (EVD) of channel matrices H1 = HS R and H2 = HR D . Hence, F can be considered as a matched filter along the singular vectors of the channel matrices. When the weighting matrix F obeys a set of canonical coordinates given by (2.26), the MIMO relay channel is decomposed into several parallel SISO channels. If we substitute (2.26) into (2.23) with Q = IM , the signal received at the destination is

˜D , ˜R + n ˜ D = Λ2 ΛF Λ1 ˜s + Λ2 ΛF n y

(2.27)

˜D = where we used the SVD of H1 = U1 Λ1 V1H and H2 = U2 Λ2 V2H . Also, y H H H ˜ ˜ ˜ y , s = U s, n = U n , n = U n . UH D R 2 D 1 2 D 1 R Since the MIMO channel is decomposed into (orthogonal) parallel SISO subchannels, the problem now is how to allocate the total power to those subchannels. The optimization objective is now concave and since the constraint is convex, the problem is easily transformed into a standard convex optimization problem.


2.8.3

35

Optimal design and power allocation in single-relay multiuser systems A generalized convex optimization problem was introduced in [63] as J = − log | I + HQHH |,

min Q ≥0

tr(Bi QBH i ) ≤ Pi ,

subject to:

∀i ∈ {1, . . . , m},

(2.28)

(2.29)

where H and Bi are complex matrices, Q is a complex positive semidefinite matrix, and Pi are positive numbers. If m = 1, the solution to the above problem can be found by a well-known waterfilling algorithm. It can be proved that the solution of (2.28)–(2.29) is given by Q = W−H V(I − Σ−2 )+ VH W−1 , where W =

m i=1

µi BH i Bi

12

(2.30)

(assumed to be nonsingular), V and Σ are deter-

−H

mined by the SVD HW = UΣVH , (.)+ replaces all negative diagonal elements by zeros and leaves all nonnegative diagonal elements unchanged, and µ = (µ1 , . . . , µm ) is the solution to the following dual problem: min µ≥0

− log | I + HQHH | +

subject to:

m

µi (tr(Bi QBH i ) − Pi ),

(2.31)

i=1

Q = W−H V(I − Σ−2 )+ VH W−1 .

(2.32)

A multiuser MIMO relay downlink/uplink system was treated in [63], where rate adaptive and margin adaptive algorithms were presented to maximize the system throughput (i.e., sum rate) under a power constraint, and to minimize the system power consumption under individual user rate constraints, respectively. Similarly, the problem of maximizing the sum rate for all users under a power constraint for the downlink case was considered in [56] where each user has a single antenna. In [56] and [63], the authors showed that with the use of zero-forcing dirty paper coding (ZFDPC) [64] the multiuser interference could be eliminated in a consecutive way, so the problem could eventually be reformulated as (2.28)– (2.29) and solved using (2.30). In other words, with dirty paper coding and QR decomposition, the interference from the first stream to the second stream can be virtually eliminated, and so forth. In this way, the source covariance matrix is matched to the right singular vectors of the S–R channel matrix [63], the optimality of which for a single-user relay system was shown in [59]. Also, the relay matrix is matched to the left singular vectors of the S–R channel matrix.

36


2.9

RRA in MIMO multihop networks In this section we review the resource allocation strategies in a wireless multihop network, where a source communicates with the destination via a number of relays. In order to avoid interference between the relaying hops, orthogonal access schemes such as frequency-division multiple access (FDMA) or time-division multiple access (TDMA) are usually used. However, it can be shown that both access schemes achieve the same capacities [15]. At each relaying node the DF relaying protocol is applied, whereby the data are first detected and decoded completely, then reencoded and transmitted to the next relaying nodes [65]. The end-to-end connection is therefore accomplished through a number of topologically imposed VAAs. In [66], a suboptimal bandwidth and power allocation algorithm was proposed to maximize the ergodic end-to-end link capacity for FDMA-based multihop networks. However, its allocated bandwidth was assumed to be consecutive, which makes it impractical in an OFDMA-based system. In each hop, the capacity can be considered as parallel narrowband subchannels. So the capacity of the ith hop is

βi P γi , i = 1, . . . , L, (2.33) Ci = αi BEγ i log2 1 + αi σR2 B where L is the number of hops (Figure 2.7), αi and βi are the ith hop bandwidth and power fractions, respectively, and P is the source transmit power. Also since the statistics of channel gain do not depend on the frequency, we use γi to denote the channel gain of the ith hop. The capacity of the end-to-end link is dictated by the smallest Ci and the goal is to find the fractional bandwidth and power allocations for given γi for all i, such as to maximize the minimum capacity. In other words, an optimal resource allocation strategy should assign fractional power and bandwidth to each hop in such a way that the end-to-end capacity is maximized: C = max min{C1 , . . . , CL }, α i ,β i

subject to:

L i=1

αi = 1,

L

βi = 1.

(2.34)

i=1

The strategy was shown to be of low complexity and to achieve near-maximum end-to-end ergodic capacity [66]. Similar resource allocation strategies were introduced in [28] to maximize the end-to-end data throughput over ergodic fading channels under the assumption of fixed total transmit power. For the same power constraint, an allocation strategy for minimizing the error rate was given in [67], where a power allocation solution to reduce pair-wise error probability (PEP) for a two-hop wireless network with an AF relaying protocol was introduced. It was shown that the optimal power allocation assigns half the total power to the source and the other half is shared

2.9 RRA in MIMO multihop networks

37

between the relays. However, as the majority of today’s wireless communications happen over slow-fading channels, i.e., nonergodic in the capacity sense, the consideration of the end-to-end outage probability is of greater practical relevance. Outage probability can be expressed as the probability that the channel cannot support an error-free transmission at a specific data rate. In addition, approaches for minimizing the transmit power are desired. The task of minimizing the total power while meeting a given end-to-end outage probability constraint was analyzed in [68] and [69]. In [68], the authors introduced an efficient near-optimal power allocation strategy for symmetric distributed MIMO networks by solving a high-order equation in one variable. For the case of a large number of relaying nodes per VAA, a closed-form solution was proposed by approximating the high-order equation to a quadratic equation. Based on these results an efficient closed-form solution for an arbitrary number of nodes per VAA was presented in [69]. According to the capacity of a MIMO channel determined in [4], the capacity of a MISO system is given by Ck ,j = αk B log2

tk 1 Pk ,i 1+ | hk ,i,j |2 αi σR2 B i=1 dk ,i,j

(2.35)

where Pk ,i is the transmission power of the ith node at the kth hop. The channel from the tk transmit nodes to the jth receive node at the kth hop is expressed as hk ,j and its elements hk ,i,j obey the same uncorrelated Rayleigh fading statistics. It is assumed that the relaying nodes belonging to the same VAA are spatially sufficiently close to justify a common path-loss between the two VAAs; this path-loss is given by dk ,i,j , where dk is the distance between two nodes and is the path-loss exponent, which is within the range of 2–5 for most wireless channels. The outage probability Pou t,k ,j can be expressed as Pou t,k ,j = Pr{R > Ck ,j }. If all of the receiving nodes of a hop cannot decode the message, the corresponding hop is in outage. Consequently, the end-to-end connection is in outage if any hop is broken, and the end-to-end outage probability corresponds to [70] Pe2e = 1 −

rk L

(1 − Pou t,k ,j ),

(2.36)

k =1 j =1

where rk is the number of successful receivers at the kth hop. Therefore, the optimization task could be defined as min

Ptotal =

L

Pk (1 − Pou t,k ,j ),

k =1

subject to: Pe2e ≤ e,

L k =1

αk = 1.

(2.37)

38


The assumption that should be noted and modified here is that the number of nodes at each VAA is considered constant and equal to tk . Optimally assigning resources in terms of fractional time and transmission power to the hops on the basis of network geometry, i.e., the number of nodes per VAA and the distances of the hops was considered in [70] and [71]. A power allocation problem and a joint power and time allocation (JPTA) problem were formulated. As shown in [70], the optimization problems are convex and can therefore be solved by common optimization tools. All of the resource allocation schemes require the solution of the optimization task at a central position and the distribution of the time fractions and power allocations to the different nodes. However, if the geometry changes, i.e., the number of nodes per VAA or the hop distance changes, the resource allocation solution has to be adapted.

2.10

Conclusion In this chapter, we have first presented a brief overview of relaying and its basic protocols, and introduced the concept of VAA as the main idea behind the MIMO multihop systems. This has been followed by a survey of algorithms in the literature which adaptively allocate the available resources in a singleuser/multiuser relay-enhanced OFDMA-based, MIMO, and distributed MIMO wireless networks. Different classes of algorithms consider different objectives and attempt to obtain a solution that is close to optimum but at the same time simple enough to be implemented. Numerous publications have highlighted the need for efficient resource management in such networks. Although RRA in OFDMA-based relay networks has begun to attract attention, only a few papers have investigated OFDMA-based relay networks in multicellular environments. Some of the proposed algorithms are designed to reduce the required signaling overhead compared with the optimal solution, when the optimal solution involves prohibitive complexity. There are ongoing research efforts towards finding more efficient centralized RRA algorithms, since most of those proposed in the literature are overly complex. Furthermore, significant savings in overhead and system complexity can be obtained through distributed resource allocation schemes. Therefore, research into distributed RRA algorithms in OFDMA-based relay networks has begun to attract attention.

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[60] Y. Fan and J. Thompson, “MIMO configurations for relay channels: Theory and practice,” IEEE Trans. Wireless Commun., vol. 6, pp. 1774–1786, May 2007. [61] Y. Rong, X. Tang, and Y. Hua, “A unified framework for optimizing linear non-regenerative multicarrier MIMO relay communication systems,” IEEE Trans. Signal Process., vol. 57, no. 12, pp. 4837–4852, Dec. 2009. [62] N. Varanese, O. Simeone, Y. Bar-Ness, and U. Spagnolini, “Achievable rates of multi-hop and cooperative MIMO amplify-and-forward relay systems with full CSI,” in Proc. of Signal Processing Advances in Wireless Communications (SPAWC’06), July 2006. IEEE, 2006. [63] Y. Yu and Y. Hua, “Power allocation for a MIMO relay system with multiple-antenna users,” IEEE Trans. Signal Process., vol. 58, no. 5, May 2010. [64] H. Weingarten, Y. Steinberg, and S. Shamai, “The capacity region of the Gaussian multiple-input multiple-output broadcast channel,” IEEE Trans. Inform. Theory, vol. 52, pp. 3936–3964, Sept. 2006. [65] Y. Lang, D. Wubben, C. Bockelmann, and K. D. Kammeyer, “A closed power allocation solution for outage restricted distributed MIMO multihop networks,” in Proc. of Workshop on Resource Allocation in Wireless Networks (RAWNET), Berlin, Germany, Mar. 2008, pp. 65–70. IEEE, 2008. [66] M. Dohler, “Resource allocation for FDMA-based regenerative multi-hop links,” IEEE Trans. Wireless Commun., vol. 3, no. 6, pp. 1989–1993, Nov. 2004. [67] Y. Jing and B. Hassibi, “Distributed space-time coding in wireless relay networks,” IEEE Trans. Wireless Commun., vol. 5, no. 12, pp. 3524–3536, Dec. 2006. [68] Y. Lang, D. Wubben, and K. D. Kammeyer, “Efficient power allocation for outage restricted asymmetric distributed MIMO multi-hop networks,” in Proc. of IEEE International. Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), Cannes, France, Sept. 2008, IEEE, 2008. [69] D. Wubben and Y. Lang, “Near-optimum power allocation solutions for outage restricted distributed MIMO multi-hop networks,” in Proc. of IEEE Global Communications Conf. (GLOBECOM), New Orleans, LA, Nov. 2008. IEEE, 2008. [70] Y. Lang, D. Wubben, and K. D. Kammeyer, “Joint power and time allocations for adaptive distributed MIMO multi-hop networks,” in Proc. of IEEE Vehicular Technology Conference (VTC), Spring, Barcelona, Spain, Apr. 2009. IEEE, 2009. [71] D. Wubben, “High quality end-to-end-link performance,” IEEE Vehicular Technology Magazine, vol. 4, no. 3, pp. 26–32, Sept. 2009.

Part II Cooperative base station techniques

3

Cooperative base station techniques for cellular wireless networks Wibowo Hardjawana, Branka Vucetic, and Yonghui Li

3.1

Introduction The spectral efficiency of existing cellular networks [1] is limited by interference. In cellular mobile networks, the dominant interference comes from adjacent cells [2]. This is especially true when the users are located near the cell edges where the interference from the adjacent cells is very strong. By getting the adjacent base stations (BS) to cooperate, spatial antenna diversity in each BS can be utilized to cancel the interference. To obtain BS cooperation, multiple BSs share information about the transmitted messages to their respective users and wireless channels via a backbone network. Each BS can transmit either a single symbol stream or multiple symbol streams to its respective mobile station (MS). Individual BSs and MSs are equipped with multiple transmit and receive antennas, respectively. Each BS transmitter uses the transmitted signal information from other BSs and wireless channel conditions to precode its own signal. The precoded signal for each BS is broadcast through all BS transmit antennas in the same frequency band and time slots. The precoding operation and transmit– receive antenna coefficients are chosen in such a way as to minimize the interference coming from other BS transmissions. The calculated receive antenna coefficients are then sent from the transmitter to the receiver through a wireless channel prior to the data transmission. In this chapter, we consider the use of a cooperative BS system to eliminate the interference in cellular networks. We will first start by reviewing related work in the literature, and follow this by presenting first a system model, and then a cooperative BS system design and its advantages over other existing schemes. Lastly, numerical results and conclusions are presented.

3.1.1

Related work Most of the published papers in this area consider only a downlink multiuser multiple-input single-output (MISO) broadcast channel. A variety of methods to suppress interference from other users have been developed. In [3], a method to Cooperative Cellular Wireless Networks, eds. Ekram Hossain, Dong In Kim, and Vijay K. Bhargava. Published by Cambridge University Press. C Cambridge University Press, 2011.

48

Cooperative base station techniques for cellular wireless networks

maximize individual signal-to-interference-plus-noise ratios (SINRs) by jointly adjusting the transmit weights and transmission powers was developed. A different approach was proposed in [4] where a combination of a zero-forcing (ZF) method, which determines transmit weights by forcing part of the interference to zero, and dirty paper coding (DPC) [5] was used to suppress interference from other users. A more practical approach than the one in [4] was considered in [6] by replacing DPC with Tomlinson–Harashima precoding (THP) [7, 8]. These algorithms, however, only consider single receive antenna scenarios, which are not directly applicable to multiple-input multiple-output (MIMO) systems. These works on downlink multiuser MISO systems have been extended to incorporate multiple receive antennas. In [9], the authors showed how a ZF method can be used to exploit the availability of multiple receive antennas. Here transmit– receive antenna weights are first jointly optimized by a ZF diagonalization technique and then a waterfilling power allocation method is applied to allocate power to each user. The scheme in [9] was further improved by using an iterative method in [10]. Nonlinear methods, utilizing a combination of a ZF method with DPC and a combination of a ZF method with THP [7, 8] for a multiuser MIMO system were considered in [11, 12], respectively. The authors use the ZF method to eliminate part of the interlink interference. DPC or THP is then used to cancel the remaining interference. These schemes, however, are not practical for cooperative MIMO systems, since their symbol error rate (SER) performance varies from user to user. In particular, this SER variation is not desirable since the MIMO systems can be deployed by different operators and they expect the systems to have a similar performance.

3.1.2

Description of the proposed scheme In this chapter, we propose a cooperative transmission scheme employing precoding and beamforming for the downlink of a MIMO system. In this algorithm, the THP cancels part of the interference while the transmit–receive antenna weights cancel the remaining interference. A novel iterative method based on [13] is used to generate the transmit–receive antenna weights. The receive and transmit weights are optimized iteratively until the SINR for each user converges to a fixed value. In addition to the iterative joint transmit–receive antenna weights optimization and THP above, we also employ SINR equalization, and an adaptive precoding ordering (APO) in the algorithm. The SINR equalization process [3] is used to allocate power to users in such a way that all users have the same SINRs. This ensures SER fairness among all users. We consider two types of power constraints. The first one is a total BS power constraint, where the total power for all BSs is constrained to a particular value. The second one is a per BS power constraint where the power for each BS is constrained to a particular value. We derive expressions for optimum power allocation under these two power constraints. The APO is then used to improve the performance of MIMO systems further by maximizing the minimum SINR for each user [14]. The proposed method offers a significant improvement over a nonlinear cooperative precoding

3.2 System model

49

algorithm presented in [9–12]. The improvements are a significant enhancement of the SER performance and a significant computational complexity reduction. These features allow the proposed algorithm to be applied to a wider range of scenarios than the schemes in [9–12], while providing a capacity-approaching performance in cellular mobile systems.

3.1.3

Notation The notation used in this chapter is as follows. We use boldface lower case letters to denote vectors and boldface upper case letters to denote matrices. The superscripts .H , .T , I and Diag() denote the conjugate transpose, transpose, an identity matrix, and a diagonal matrix, respectively. C a×b indicates a complex matrix with a rows and b columns. x , · and | · | are the greatest integer smaller than x, the Euclidean distance, and the absolute value, respectively. LoT(A) is defined as the operation to extract the lower triangular components of A and to set the other components to zero. UpT(A) is defined as the operation to extract the upper triangular components of A and to set the other components to zero. DiT(A) is defined as the operation to extract the diagonal components of A and to set the other components to zero. Lastly, we define 1 as a column vector with all entries equal to 1.

3.2

System model In this chapter, we consider a multiuser MIMO system, where K BSs transmit to K MSs. Each BS and MS is equipped with NB S k and NM S k antennas, for k = 1, ..., K, respectively. All BSs cooperate with each other to transmit S sym K bol streams to their respective MSs via N B S = kk = =1 NB S k antennas. Each of these transmissions is defined as a link. In a practical cellular wireless network, if frequency-division multiple access (FDMA) or orthogonal frequency-division multiple access (OFDMA) is used, a frequency or time slot can only be allocated to one user at a given time instant. Therefore, only one user can be served by a BS at any one time or frequency slot. Thus, to simplify the analysis, we consider a scenario where each BS transmits at a given time slot to a single mobile station. In a practical system, the proposed scheme enables a BS to communicate with multiple MSs through FDMA and time-division multiple access (TDMA). The proposed method aims to enable K such base stations deployed by different network operators in the same location to communicate simultaneously with K respective mobile stations, using the same frequency band at a given time slot.

3.2.1

Transmitter structure The proposed transmitter structure with joint precoding and beamforming is shown in Figure 3.1.

50


Cooperative transmitter for K BSs

BS 1

x1

y1

NR

1

u1

–

+

v1

n1

1 R1

x2

u2

+

–

modM' (•)

ˆ1 u

MS 1

n2

1

BS 2

y1

H1

NBS

d1

+

1

y2

v2 NBS

1 NR

H2

R2

+

y2

modM' (•)

ˆ2 u

MS 2

2

Mperm

d2

P

T K non cooperative MSs

BS K

dK

uK –

xK

+

vK

1 NBS

K

HK

nK

1 NR

RK

+

yK

modM' (•)

ˆK u

MS K

MTHP APO

THP precoding

(a)

Power allocation

Transmit–receive antenna weights optimization

THP decoding

(b)

Figure 3.1. (a) Nonlinear cooperative precoding transmitter structure; c 2009 IEEE). (b) receiver structure (adapted from [27] Let xk = [x1,k · · · xs,k · · · xS,k ]T represent the modulated signal vector, consisting of K M -ary quadrature amplitude modulation (M-QAM) modulated symbols, where xs,k is the sth modulated symbol stream from BS k intended for MS k. Thus, we have a multistream transmission where S symbol streams are transmitted from BS k to MS k simultaneously. The constellation √points for √ M -QAM are drawn from the signal set A = {±1 ± j, ... ± M ± j M }. The modulated symbols for K MSs can then be written as x = [xT1 · · · xTk · · · xTK ]T . The transmitted symbols for each user are first permuted by a block diagonal permutation matrix Mper m = [m1 ...mK ], where mi = [0...1S (i−1)+i ...1iS ...0]T , i = 1, ..., K, is a KS × 1 vector with its elements S(i − 1) + i to iS set to 1 and its other elements set to 0. The permutation operation is done by changing the location of mi in Mper m . By doing this, we have K! possible Mper m . The operation of selecting Mper m is referred to as the APO. The APO adaptively selects the precoding order of x that maximizes the minimum SINR of K users. It selects a suitable permutation matrix Mper m to permute x. Let u = Mper m x = [uT1 · · · uTj · · · uTK ]T be the permutated transmitted symbol vector, where uj = [u1,j · · · us,j · · · uS,K ]T . Thus, after the APO, xk for MS k is permuted into uj , which will be transmitted in link j. We will explain the APO in more detail later in Section 3.6. Let us first assume that we do not use the THP scheme at the BS transmitter. Thus, we omit THP precoding and decoding in Figure 3.1. The SINR equalization module then allocates powers to each symbol in u in such a way that the received SINRs for all KS symbols are equal. This is done by multiplying u with √ √ the matrix P = Diag(P1 , ..., PK ), Pj = Diag( p1,j , ..., pS,j ) where ps,j is the downlink power allocated to the sth symbol in link j, denoted by us,j . The signal for K links is then given as Pu.

3.2 System model

51

The interference in each link needs to be suppressed by multiplying the signal from each link by the transmit antenna weights of all BSs, T ∈ C N B S ×K S , and by the receive antenna weights matrix at the receiver of link j, Rj ∈ C N M S j ×S . The transmitted signal is thus given as xT = TPu. The receiver for each link is shown in Figure 3.1(b). Note that there is no cooperation among the receivers. Let yj ∈ C N M S j represent the received signal matrix for link j. The received signal matrix for K links, denoted by y, y = T T ] , can be written as [y1T ...yK y = HTPu + N,

(3.1)

where H = [H1 ...Hj ...HK ]T in which Hj ∈ C N M S j ×N B S is the channel matrix for link j. N = [nT1 , ..., nTK ]T and T = [T1 , ..., TK ]. nj ∈ C N M S j ×1 is the noise vector for link j. The transmit weight for link j is defined as Tj = [t1,j ...tS,j ] ∈ C N B S ×S , where ts,j is the transmit weight vector for the sth symbol transmitted in link j. After multiplying y by the receive weights matrix R, the received signal vector becomes y = RHTPu + RN,

(3.2)

H H H where R = Diag(RH 1 , ..., RK ) is a block diagonal matrix with R1 , ..., RK as its block diagonal components. Rj is the receive signal matrix for link j and is defined as Rj = [r1,j ...rS,j ], where ri,j is the receive weight vector for stream i in link j. The signal received at MSs is defined as y = [y1 ...yj ...yK ]T ,yj =

[y 1,j , ..., y S,j ]T , where y s,j is the received signal at the input of the THP decoder for sth symbol transmitted in link j. The received signal y, can be further written as y = RHTPu + RN = (D + F + B)Pu + RN,

(3.3)

where D = DiT(RHT), B = UpT(RHT), and F = LoT(RHT); DPu is a vector of scaled replicas of the transmitted symbols for K links. We define interlink interference as the interference between symbol streams in different links and interstream interference as the interference between symbol streams in the same link. FP is defined as the front-channel interference matrix, since the rows j = 1, ..., KS of FP represent the interlink interference caused by links 1, ..., j − 1 and interstream interference caused by symbol streams 1, ..., s − 1 transmitted in link j to symbol stream s in link j. Similarly, BP is defined as the rear-channel interference matrix, since the rows j = 1, ..., KS of BP represent the interlink interference caused by rear links j + 1, ..., K and the interstream interference caused by symbols s + 1, ..., S in link j to symbol stream s in link j.

3.2.2

THP precoding structure To further improve system performance, we presubtract some of the interference prior to transmission instead of using the transmit–receive weights for symbol

52


stream s in link j to cancel front-channel and rear-channel interference. Because of this, the transmit–receive weight matrix needs to suppress less interference. We will use the THP scheme proposed in [7, 8] and choose to presubtract the front-channel interference FP. Thus, prior to the power allocation module, THP precodes u into v = [v1 · · · vj · · · vK ]T ∈ C K S , where vj = [v1,j · · · vS,j ]T . The front-channel interference is then subtracted from u as in [15], v = u + d − (DP)−1 FP v, v ˜

MT

(3.4)

HP

where (DP)−1 is used to normalize√the front-channel interference with respect to u, d = [d1,1 , ..., dS,K ]T , ds,j = 2 M ∆, and ∆ is a complex number whose real and imaginary parts are suitable integers√selected √ to ensure the real and imaginary parts of vs,j are constrained into ( M , M ]. Here, the integers for ∆ can be found by an exhaustive search across √all integers [15]. d is an offset √ to ensure the energy of v lies between (− M , M ], since the value of v after presubtraction of the front-channel interference can be very large and exceed √ √ ( M , M ]. Note that if ds,j is selected as above, adding ds,j to us,j is equivalent to performing a modulo operation on ds,j +us,j [1, 12, 15]: us,j = mod√M (˜ vs,j ) = mod√M (ds,j + us,j ), s = 1, ..., S,j = 1, ..., K, where the modulo operation is defined as [6] √ √ √ M √ M us,j + mod M (us,j ) = us,j − M 2

(3.5)

(3.6)

for s = 1, ..., S and j = 1, ..., K. In addition, if we apply √ to (3.4), the oper√ (3.6) ation in (3.6) actually maps v into the interval of (− M , M ] [15]. Thus, by using the modulo operations, we implicitly find d that forces the THP precoded symbols v to lie within this interval. In addition as mentioned √ in [15], √ the variance 2 ] = 2M/3 and it is distributed uniformly in (− M , M ]. Note that of v is E[vs,j E[x2s,j ] is 2(M − 1)/3. Thus, there is a power enhancement of M/(M − 1) due to THP. This enhancement needs to be taken into consideration when designing the transmit–receive weights and power allocation. In general, the transmit 2 ] = 1. To ensure this, we scale down the symbol energy is normalized, i.e., E[vs,j ds,j and xs,j by 3/2M . This is discussed in detail in [15]. By taking this into consideration, the operation of the THP precoder in (3.4) can be rewritten as ⎧ 3 ⎪ ⎪ [u]j , j = 1, ⎨ (2M − 1) [v]j = (3.7) ⎪ 3 ⎪ ⎩ modM ( [u]j − aj ), j = 2, .., KS, 2M √ j −1 [MT H P ]j,l [v]j and M = 3/2M M . [MT H P ]j,l denotes the where aj = l=1 (j, l)t component of MT H P and [a]l is the lth component of vector a. Note that the first line of (3.7) comes from the fact that, when precoding [v]1 , there is no

3.3 Cooperative BS transmission optimization

53

front-channel interference to be canceled. Thus, we can simply set [v]1 as the normalized u1,1 . Since now we are using the THP scheme, we are transmitting THP precoded symbol streams v instead of u. After THP precoding, the received signal y in (3.3) can be rewritten by replacing u by v. By using (3.4) and (3.3), the received signal now becomes v + BPv + RN. y = (D + F)Pv + BPv + RN = DP˜

(3.8)

ˆj = The estimates of the transmitted symbols for link j, denoted by u uS,j ]T , can be recovered from yj , by applying an element-wise modulo [ˆ u1,j ...ˆ operator in (3.6) to each ys,j , as u ˆs,j =

y s,j , s = 1, j = 1, modM (y s,j ) , otherwise,

(3.9)

where u ˆs,j is the estimate of us,j . Here, the effect of offset vector d on the desired transmitted signal is removed at the MS receiver by applying the modulo operation in (3.6) to each y s,j in (3.8). This is shown in (3.5) and in Figure 3.1(b). In the proposed scheme, THP cancels the interference caused by the front-channel, while the interference caused by the rear-channel is eliminated by the transmit–receive antenna weight optimization process. Note that no modulo operation is performed on the first stream to be transmitted in link 1. Thus, MSs need to know which one of them will be scheduled in the first link. This information can be appended in the signal preamble of wireless systems such as cellular networks, WiMax or WLANs. However, if high modulation rates are used, (e.g., M = 16, 64), the power enhancement of THP is negligible. The THP performance loss is given as M/(M − 1) [15] and decreases as the modulation rate increases. Thus the THP performance loss for M = 16 and M = 64 is 0.28 and 0.07 dB, respectively. Thus, if a higher modulation rate is used, we could apply the modulo operation to the first stream of the first link in (3.7) and (3.9).

3.3

Cooperative BS transmission optimization In this section, we propose a joint iterative transmit–receive antenna weight optimization and power allocation method based on ZF to cancel the rear-channel interference, while maximizing the SINR for each link and maintaining the same SER for all links. The transmitted signal estimate of stream s in link j at each

54


receiver, y s,j , can be obtained from (3.8) and expressed as y s,j =

K S √ √ ps,j rH H t v ˜ + pl,i rH s,j j s,j s,j s,j Hj tl,i vl,i l=1 i= j +1

+

S

√

H pl,j rH s,j Hj tl,j vl,j + rs,j nj .

(3.10)

l= s+1

By using the fact that the effect of vector d on the received signal is completely removed by the THP decoder modulo operator, the SINR for the sth transmitted symbol in link j, can be written as SIN Rs,j =

H ps,j rH s,j Hj ts,j (Hj ts,j ) rs,j

rH s,j Rs,j rs,j

,

(3.11)

where Rs,j =

K S

pl,i Hj tl,i (Hj tl,i )H +

l=1 i= j +1

S

pl,j Hj tl,j (Hj tl,j )H + σ 2 I

(3.12)

l= s+1

is the interference in link j. Maximizing the minimum SINR for each link, while maintaining its equality for all links, can be formulated as follows: max

min

R,T,P 1≤i≤K ,1≤s≤S

subject to:

SIN Rs,i T (1) TH T = I, (2) rH s,j rs,j = 1, (3) 1 p = Pm ax H (4) rH s,j Hj ts,i = 0, (5) rs,j Hj ts ,j = 0

(3.13)

for j = 1, ..., K, i = j + 1, ..., K, s = 1, ..., S, s = s + 1, ..., S, where Pm ax and p = [p1,1 , ..., pS,K ]T = P2 1 are the power constraint at the cooperative transmitter and the set of powers assigned to each link, respectively. Here the objective of (3.13) is to maximize the minimum SINR for each link. The first, second, and third constraints in (3.13) are to ensure that the transmit–receive weight vectors are unitary vectors and the sum of the power allocated to each link does not exceed the maximum power available at the transmitter (total BSs power constraint). These constraints bound the possible solution for R, T, and P and ensure the convergence of (3.13) to a solution. Finally, the fourth and fifth constraints are the ZF constraints which ensure the interlink interference from links j + 1, ..., K to link j and the interstream interference from symbol stream s + 1, ..., S in link j are fully canceled. Here, to maximize the minimum SINR in (3.13), we reduce the SINR of the best symbol streams until the SINRs of all links are equal. Thus, the optimal solution is reached when all symbol streams attain the same SINR [3]. This optimization problem, however, is difficult to solve as it is not jointly convex in variables R,T, and p. To solve (3.13), we propose a suboptimal solution that splits the problem into a two-step optimization. The first step is to solve R and T iteratively, when p is fixed. Hence in this step we simply ignore the equalization of SINRs among all links. The second step is to


55

R(i)

R(0)

f1(R(i–1))

T(i)

gj(T(i))

(i) (i) R ,T

MTHP = (DP)–1FP

SINR equalization

p,R(i),T(i)

Feedback matrix

Figure 3.2. Iterative weight optimization, SINR equalization, and feedback c 2009 IEEE). matrix process (adapted from [26] solve p in a way that equalizes SINRs for all links under fixed R and T. Once R, T, and p are obtained, MT H P = DP−1 FP is computed. The process is described in Figure 3.2, where i, f1 (·) and gs,j (·) are the iteration number, a function to generate transmit antenna weights for K links, and a function to generate the receive antenna weights vector for symbol stream s in link j, respectively.

3.3.1

Iterative weight optimization (first step) In the first step, we assume an equal power allocation for each link by setting P = I. Then (3.13) can be simplified as max R,T

SIN Rs,i ,

subject to: (1) TH T = I, (2) rH s,j rs,j = 1, H (3) rH s,j Hj ts,i = 0, (4) rs,j Hj ts ,j = 0

(3.14)

for j = 1, ..., K, i = j + 1, ..., K, s = 1, ..., S, s = s + 1, ..., S. To solve (3.14), we propose to alternately optimize R and T until they converge, under the ZF constraints in (3.14). We first assign the initial value of the receive antenna (0) weights for K links. The initial receive weights of K links are given as rs,j = vsv d (Hj ) , j = 1, ..., K, s = 1, ..., S, where vsv d (·) is the singular value decomposition operation (SVD) [16], to select the S left singular vectors of Hj , corresponding to the Sth largest singular value. We then transform the system into (0) H

a downlink multi-link MISO system by fixing R = Diag(R1 (3.3) can be written as y = RHTv + RN = He Tv + N.

(0) H

, ..., RK

). Then

(3.15)

Here, we know from (3.8) that the interference from the front-channel does not exist at the receiver. The remaining interference at symbol stream s in link j that needs to be canceled is the rear-channel interference, coming from links j + 1, ..., K to links j = 1, ..., K and stream s + 1, ..., S in link j, respectively. At each iteration, we apply a QR decomposition [16] to HH e to find T that forces

56


this interference to zero: T = f1 (R) , f1 (R) = [Q|QR(HH e )].

(3.16)

We choose the unitary matrix Q obtained from the QR decomposition of HH e in (3.16) as T. We need to compute R that gives a maximum SIN Rs,j for each link for the derived T. This can be calculated as rs,j = gs,j (T),

(3.17)

where j = 1, ..., K. gs,j (T) is a function that generates the receive weight vector rj for the derived T such that the gain SIN Rs,j for each link is maximized. We now describe how gs,j (T) operates. By using (3.11), the SINR maximization for the sth symbol in link j can be written as max rs , j

˜ ˜H ps,j rH s,j hs,j hs,j rs,j rH s,j Rs,j rs,j

,

(3.18)

˜ s,j = Hj ts,j and Rs,j is the interference in link j as given in (3.12). To where h obtain rs,j that maximizes SINR in (3.18) we use the spectral/eigenvalue decomposition [16]. Thus the functions to generate r1,1 , ..., rS,K , gs=1,...,S,j =1,...,K (T) can now be written as −1 ˜ s,j h ˜ H ) , s = 1, ..., S, j = 1, ..., K, gs,j (T) = vE V D (ps,j Rs,j h s,j

(3.19)

where vE V D (·) is the spectral/eigenvalue decomposition operation [16] to select −1 ˜ s,j h ˜ H , corresponding to the largest singular the left singular vector of ps,j Rs,j h s,j value. We can obtain a simpler expression for rs,j that gives the same maximum SINR, as in (3.18), by using the following fact: max rs , j

˜ ˜H rH s,j hs,j hs,j rs,j rH s,j Rs,j rs,j

= max rs , j

˜ rH s,j hs,j rH s,j Rs,j rs,j

.

(3.20)

Here we state that the optimum SIN Rs,j obtained by using the term on the left hand side of (3.20) is equal to the optimum SIN Rj obtained by using the term on the right hand side of (3.20). The proof of SINR equivalence is shown in the Appendix. By solving the term on the right hand side of (3.20), the normalized receive antenna weight vector for stream s in link j can be obtained as [17] −1

rs,j = gs,j (T) =

Rs,j Hj ts,j Rs,j Hj ts,j

.

(3.21)

It is straightforward to show that the SIN Rs,j generated by using the receive antenna weight vector from (3.21) yields the optimum SIN Rj given in (3.20). We can conclude from this fact and (3.20) that the normalization process of the receive weight vector in (3.21) will not affect the SINR. Note that this receiver design is also known in the literature as the minimum variance distortionless response (MVDR) design [18]. The iterative calculations of R and T continue


57

by fixing one and optimizing the other one, until they converge to a fixed solution. The proof of convergence of the proposed iterative method is shown in the Appendix.

3.3.2

Power allocation (second step) In the second step, we use the R and T obtained in the first step to find p. By using the fact that at the optimal solution all links will attain equal SINR, (3.11) can be written as S K

|rs ,j Hj ts ,i |2 ps ,i +

s =1 i= j +1

S

|rs ,j Hj ts ,j |2 ps ,j + σ 2 =

s = s+1

ps,j |rs,j Hj ts,j |2 SIN R

(3.22) for s = 1, ..., S, j = 1, ..., K. Equation (3.22) can be represented in a matrix format as p , (3.23) A−1 Bp + σA−1 1 = SIN R where A = DiT(M), B = UpT(M), and M is a KS by KS matrix with entries |rs,j Hj ts ,j |2 , s = s = 1, ..., S, j = j = 1, ..., K in row S(j − 1) + s and column S(j − 1) + s . By multiplying both sides of (3.23) with 1T , we obtain [3] 1 Pm ax

(1T A−1 Bp + σ1T A−1 1) =

1 . SIN R

(3.24)

By defining the extended power vector pe = [pT 1]T , we can then combine (3.23) and (3.24) to obtain [3]

pe σA−1 1 A−1 B . (3.25) pe = 1T A−1 B/Pm ax σ1T A−1 1/Pm ax SIN R Hence the optimum p can be obtained by selecting the pe that corresponds to the maximum eigenvalue of Ψ. This is the only possible solution of (3.25) satisfying ps,j ≥ 0 for j = 1, ..., K and SINR ≥ 0. The proof is described in detail in Theorems 1 and 2 of [19]. The above SINR equalization process can be further simplified. By using the proof of SINR convergence in the Appendix, we can assume that after i iterations, we are very close to the local optima (i.e., the rear-channel interference is zero, UpT(M) = 0). The solution for (3.25) can be given as ps,j =

Pm ax , s = 1, ..., S, j = 1, ..., K. K |rs,j Hj ts,j |2 s =1 i=1 |rs ,i Hi ts ,i |2

S

(3.26)

Even though the power constraint used above allocates the power to each link in an optimal manner, it is not very practical. This power constraint does not take into account the power constraint for each BS in a real system. A more practical power allocation that takes into account the power constraint for each BS can also be derived. We refer to this power constraint as the per BS power

58


constraint. We denote the maximum power available at each BS j as Pm ax,j and the modified transmit weights ti,s,j ∈ C N B S ×1 as the entries of ti,s,j used as antenna weights by BS i. A power allocation formulation that takes into account the power constraint for each BS can be derived as σ 2 SIN R,

max p

subject to: (1) σ 2 SIN R ≤ pj |rs,j Hj ts,j |2 , K S tj,s ,i 2 ps ,i ≤ Pm ax,j (2)

(3.27)

s =1 i=1

for j = 1, ..., K, s = 1, ..., S. After some manipulations, the solution for (3.27) can be given as |rs,j Hj ts,j |2 ps,j =

min

j =1,...,K ,s=1,...,S

Pm ax,j K |tj,s ,i |2 s =1 i=1 |rs ,i Hi ts ,i |2

S

(3.28)

for j = 1, ..., K, s = 1, ..., S.

3.4

Modification of the design of R In this section, we modify the receive antenna weight calculations in (3.21) to speed up the convergence to the local maxima and improve the SINR during the (i) (i) iteration process. We define rs,j and ts,j as the receive and transmit antenna weights found in step 1 in Section 3.3.1 at the ith iteration, for link j. The entries of the rear-channel interference matrix BP at the ith step of the iterative (i) process, εl,k can be written as follows: (i)

εl,k =

√

(i)

(i)

H ps ,j (HH j rs,j ) ts ,j ,

(3.29)

where l = jS + s − S, k = j S + s − S. The interlink and interstream components of the rear-channel interference in stream s in link j correspond to row l and column k of BP when s = 1, ..., S, j = j + 1, ..., K and when s = s + 1, ..., S, respectively. Similarly, the diagonal entries of matrix D at the ith step of the iterative pro(i) cess, denoted by βl= j S + s−S , represent the signal gain for stream s in link j. This (i)

(i)

(i)

H can be written as βl= j S + s−S = (HH j rs,j ) ts,j , s = 1, ..., S, j = 1, ..., K at the ith iteration. In the Appendix, we show the proof of transmit–receive weight opti (i) (i) (i) H (i) mality. There we prove that l βl ≤ det(R∗ HT∗ ), where βl = (HH j rs,j ) ts,j and (R)∗ and (T)∗ are the optimal transmit–receive antenna weight vectors for K links satisfying the proof of convergence in the Appendix. From the proof of convergence and transmit–receive weight optimality in the (i) appendix, we know that at the local maximum: (1) l βl achieves the maximum value equal to det(R∗ HT∗ ); (2) the front-channel interference BP converges to

3.5 Geometric mean decomposition

59

0 since (3.16) forces R∗ HT∗ to have a lower triangular structure. Hence, we (i) could simply maximize βl to achieve the local maxima. By using the Matrix (i) (i) Inversion Lemma [20], (3.12), and (3.21) in βl , we can rewrite βl= j S + s−S for stream s in link j as cβl= j S + s−S = (Hj ts,j )H (σ −1 I − (Z−1 + σI)−1 )Hj ts,j , (i)

(i)

(i)

(3.30)

Hj ts ,j (Hj ts ,j )H

(3.31)

where Z=

S K

(i)

(i)

Hj ts ,a (Hj ts ,a )H +

s =1 a= j +1

S

(i)

(i)

s = s+1

and c is a scaling/normalization factor given by c = Rs,j Hj ts,j . It is obvious (i) (i) (i) that (Hj ts,j )H (Z−1 + σI)−1 Hj ts,j in (3.30) reduces the value of βl . Therefore, if we omit this term in calculating the receive antenna weights, we can (i) reach the maximum βl faster. Thus, we can simply ignore this term to speed up the convergence of the iterative process. Therefore by omitting the term (i) (i) (Hj ts,j )H (Z−1 + σI)−1 Hj ts,j , we have βl= j S + s−S ∼ (Hj ts,j )H (σ −1 I)ts,j = σ −1 (rs,j )H Hj ts,j . (i)

(i)

(i)

The maximum βl

(i)

(i)

(i)

(i)

(3.32) (i)

can be obtained by aligning rs,j in the direction of Hj ts,j . (i)

The total power of the receive weight vector, rs,j is normalized to 1 to ensure it satisfies the second constraint in (3.13), (i)

(i) rs,j

=

Hj ts,j (i)

Hj ts,j

.

(3.33)

We refer to this receiver structure as a matched filter (MF) design.

3.5

Geometric mean decomposition In [22, 23], geometric mean decomposition (GMD) has been shown to give the best BER performance for multistream transmission while at the same time maintaining an equal SINR across S symbols within each link and the lower triangular structure required by THP [12]. We want to further maximize the channel gain for each stream in each link j by modifying the found iterative transmit and receive weights using GMD. We first define a new effective channel ¯ j as matrix for each link j H ¯ j = Hj Tj , H

(3.34)

where Tj is the transmit weight matrix for link j previously defined in Section ¯ j into a lower triangular matrix with 3.2.1. The GMD is used to decompose H ¯j an equal diagonal component. The process is as follows. We first decompose H

60


Algorithm 3.1. Cooperative transmission algorithm 1 2 3 4 5 6 7 8

Initialize receive weights and set Maxiteration For i=2 to Mit Find transmit weights using (3.16) Find receive weights using (3.21) or (3.33) end Use GMD to modify transmit–receive weights (3.37) and (3.38) Equalize SINR for all links using (3.28) or (3.26) or (3.25) THP precoding operation using (3.7)

by using the SVD [24] as follows: ¯ j Tj = [US U0 ] H

DS 0

0 D0

[VS V0 ]T ,

(3.35)

¯ j Tj where US and VS consist of the first S left and right singular vectors of H and DS is a diagonal matrix with entries that are the first S nonnegative square ¯ jH ¯ H . The GMD takes US , VS , and DS as inputs roots of the eigenvalues of H j j, V S , and D S . The GMD transforms DS into a lower triangular and produces U S , by rotating US and VS . This is given matrix with equal diagonal entries, D as ˜ jD ¯j = U ˜SV ˜H. ¯jT H S

(3.36)

The goal of our transmit–receive design is to create a lower triangular structure within each link. Thus, by using (3.36), the new transmit–receive weights denoted ¯ j and R ¯ j can be written as by T ˜ S , j = 1, ..., K ¯ j = Tj V T

(3.37)

j , j = 1, ..., K. ¯j = U R

(3.38)

and

The cooperative transmission algorithm is shown in Algorithm 3.1, where i represents the iteration number and Mit is the maximum number of iterations.

3.6

Adaptive precoding order (APO) In the algorithm in Table 3.1, we fix the order of uj , resulting in a fixed permutation matrix Mper m . The performance of the system, however, differs when a different Mper m is used. In addition, the performance of the system also depends on the weakest link. In this section we propose an APO scheme. APO arranges the order of links, x, by selecting on Mper m that maximizes the minimum SINR

3.7 Complexity comparison of the proposed and other known schemes

61

for each link. We formulate the optimization process to find a permutation matrix ˘ per m ∈ Mper m that gives the maximum SINR as M ˘ per m = argM max min(SIN R1 (Mper m ), ..., SIN RK (Mper m )), M perm

(3.39)

where SIN Rj (Mper m ) is the SINR of link j, given that the permutation matrix Mper m is used. Note that here, due to the use of GMD, the SINRs for each ˘ per m without searching K! possible stream in link j are equal. To find the M orderings, we use the idea of the myopic optimization method proposed in [14], which has been proven to be optimal. Using this idea we now only need to search K −1 i=0,i = 1 K − i possible orderings.

3.7

The complexity comparison of the proposed and other known schemes In this section, we discuss the advantages of the proposed scheme over other existing schemes. We first compare the proposed method with the scheme in [9] and the iterative scheme in [10] that work by finding transmit–receive weights that diagonalize the receive signal matrix of K users without the receiver noise in (3.3). To have a fair comparison with the proposed method, we replace the waterfilling power allocation in [9] with (3.26) and (3.28), which equalize the SINR for all links under total BS and per BS power constraints, respectively. This is required as the waterfilling power allocation used in [9] tends to assign more power to stronger links and less power to weaker links. Hence, the performance of a weaker link will decrease the overall SINR. The main differences between the methods in [9, 10] and the proposed method are (1) [9, 10] suppress both the front-channel and rear-channel interference using transmit–receive weights, while the proposed method suppresses the rearchannel and front-channel interference using THP and iterative transmit–receive weights, respectively. (2) Unlike [9, 10], the proposed scheme does not calculate null spaces. To compute these null spaces, the iterative scheme in [10] and the noniterative scheme in [9] perform K SVD operations per iteration and K SVD operations, respectively. (3) Within a single iteration, a QR decomposition [16] and K matched filter (MF) receiver calculations are required to find all transmit–receive antenna weights, while in [10] K SVD operations per iteration are required to find the transmit–receive weights of all links. Note that [9] requires K SVD operations to find the transmit–receive weights of all links. The complexity order requirements in terms of the number of floating point operations (flops), for the proposed method and the methods in [9, 10] are listed in Table 3.1, where Mit and Mit,P an denote the total number of iterations for the proposed method and the scheme in [10], respectively. Hence for K = 3, NM S = 2, and NB S = 2, the number of flops for the proposed method is approximately 93% less than the number of flops for [9] per iteration.

Proposed algorithm Pan et al. [10] Spencer et al. [9] Liu and Witold [12] Foschini et al. [11]

Schemes

O(K 3 SMit N B S ) 2 2 3 O(Mit,P an K(4KSN B S + 8(KS)2 N B S + 9N B S )) 2 2 3 O(K(4KSN B S + 8(KS)2 N B S + 9N B S )) 2 2 3 2 2 2 O(0.5K 2 (4KNM S N B S + 8KNM S N B S + 9KN B S + KNM S N B S (K − 1) + KNM S + KNM S N B S )) 2 2 3 2 2 O(0.5K 2 (4KNM S N B S + 8KNM S N B S + 9KN B S + KNM S N B S (K − 1)))

2

Computational complexity order (in flops)

Table 3.1. Computational complexity of linear and nonlinear precoding algorithms (in flops)

3.8 Numerical results and discussions

63

The second comparison is done using the nonlinear precoding methods in [11, 12]. Again to have a fair comparison with the proposed method, after the algorithm in [11, 12], we apply (3.25) to equalize the SINR, instead of using the original power allocation. Unlike [11, 12], we do not require the constraint of (K − 1)NM S < KNB S because we do not create null spaces. Thus, there is no relationship between the required number of transmit antennas and receive antennas. This is a definite advantage, since to support say five users with NM S = 4 receiving one stream each, the proposed method only needs five transmit antennas while [9] needs 12 transmit antennas. Another important difference is in the ZF condition definition. In our scheme when S = 1 for example we have rH 1,j Hj t1,i = 0 , j = 1, ..., K, i = j + 1, ..., K, while [11, 12] have Hj t1,i = 0 , j = 1, ..., K, i = j + 1, ..., K for the ZF condition. By using the ZF condition in our scheme, the proposed algorithm allows some interlink interference to be transmitted (e.g., Hj t1,i = 0), and cancels the interference by steering Hj t1,i to be perpendicular with the receive antenna weights vector r1,j . Hence the receive and the transmit antenna weights jointly cancel the interference. The ZF constraint in [11, 12], on the other hand, does not allow any interlink interference to be transmitted. Here, the receive antenna weights are not used at all to cancel the interference. The computational complexity required for the methods in [11, 12] is shown in Table 3.1. The complexity of the methods in [11, 12] for a system with K = 3, NM S = 2, S = 1 and NB S = 2, is approximately 47 628 and 47 844 flops, respectively.

3.8

Numerical results and discussions For convenience, in our simulations, we will use the notation (NB S , NM S , S, K) in all figures to denote a system with NB S transmit antennas per BS, NM S receive antennas per MS, S data streams transmitted in each link, and K BSs. Monte Carlo simulations have been carried out to assess the performance of the proposed method. We investigate its performance and compare it with [9, 11, 12] and with an interference-free performance. An interference-free performance is defined as the performance of any random single link i assuming there is no interference from other links at all. In this case, the received signal of the cooperative transmission system is given as yi = rH i (Hi ti xi + ni ), where ri and ti are the left and right eigenvectors associated with the maximum eigenvalue of Hi HH i . To generate an interference-free performance for multistream transmission with S symbols transmitted in each link, we use the left and right eigenvectors associated with the S largest eigenvalues of Hi HH i found by using the SVD. We then maximize the minimum SINR of S symbols by applying the power allocation method given in [25]. The comparison of the schemes is performed at SER = 10−4 . We use a fixed permutation matrix that orders MSs 1, ..., K as links K, ..., 1, when we are not using APO, for all the simulation results except when stated otherwise. Perfect

64


channel state information (CSI) is assumed to be available at both ends. Rectangular 64-QAM (M = 64) modulation is used for all transmissions. The wireless channel model we used is a Rayleigh fading channel. This channel model is commonly used for cellular networks or WLANs, since in most cases there is no lineof-sight path between the transmitter and receiver in these networks. In order to simulate the wireless channel, we set each entry of the Hj channel matrix as an independent and identically distributed (i.i.d.) complex Gaussian variable with a zero mean and unit variance. In all simulations, we fix the signal-to-noise ratio H H vs,j ]/2σ 2 , where E[vs,j vs,j ] of each THP precoded symbol to be SN R = E[vs,j is normalized to 1, Pm ax = K and Pm ax,i=1,...,K = Pm ax /K . In all simulation figures, the proposed method refers to the algorithm with THP, joint iterative transmit-receive weight optimization, SINR equalization (SINRE) under a total BS power constraint unless stated otherwise and APO.

3.8.1

Convergence study Figure 3.3 shows the convergence characteristics of the proposed method with a total BS power constraint for (2, 2, 1, 3) and (1, 2, 1, 4) systems. Note that here it does not matter whether total power or per BS constraints are used. This is because, as shown in Figure 3.2, the SINR equalization is not an iterative process. We plot the number of iterations versus the average error and scaled output SINR (after SINR equalization), while fixing the SNR at 21 dB. The average error is defined as the average of the maximum entries of the front(i) channel interference BP, ε(i) = maxj,l |εj,l | defined previously in (3.29) over all channel realizations. The output SINRs for (1, 2, 1, 4) and (2, 2, 1, 3) systems are scaled up by 4 dB and 0 dB to fit in one figure. The scaling does not matter here since we only want to observe the convergence rate. The figure also shows the convergence characteristics when the MF receiver design, represented by (3.33), and the MVDR receiver design, represented by (3.21) are used. An interesting observation is that during the first few iterations the MVDR design outperforms the MF design. This improvement is due to the smaller errors (i) obtained using MVDR and is not due to a higher signal gain βj . During the first few iterations, the second term of (3.30) for the MF receiver design is larger than for the MVDR receiver design, thus leading to a higher average error for the MF receiver. This happens because MF ignores the interference when calculating the receive antenna weights. However, its average error decreases rapidly. The average error for the (1,2,1,4) and (2,2,1,3) systems, denoted by (1,2,1,4)MF and (2,2,1,3)-MF in Figure 3.3, approaches the average error of the MVDR method. The SINR using the MF method from that point onwards is always greater than the SINR using the MVDR method. This is shown in the analysis in Section 3.4. This analysis is consistent with the results shown in Figure 3.3. MF converges much faster to the optimal SINR solution than MVDR. This is shown in Figure 3.3 and agrees with the proof of convergence in the Appendix. MF’s SINR reaches a plateau after eight iterations, since it almost converges


65

Figure 3.3. SINR and average error convergence comparison for proposed scheme c 2009 IEEE). (adapted from [26]

to the optimal solution while MVDR’s SINR is still rising. A similar conclusion is found for all other configurations. Not much performance improvement can be obtained by increasing the number of iterations further. In all simulations for SER comparison, we set the maximum iteration number for the proposed scheme to ten.

3.8.2

Performance of the individual links Figure 3.4 shows the SER of the worst user and the best user versus the SNR in a (2, 2, 1, 3) system. Note that it does not matter whether total power or per BS constraints are used to compare the performance of the individual links. This is because, as shown in Section 3.2.2, the SINR for all links is the same under both constraints. As shown in Figure 3.4, when the proposed method does not perform SINRE and APO (denoted by w/o in the figures), MS 3 has the best performance while MS 1 has the worst performance. The SER performance difference between links 1 and 3 exceeds 3 dB. When SINRE is used, the SER difference between links disappears. This is shown in Figure 3.4. Here, the performance of link 1 is improved at the expense of links 2 and 3. This results in a similar SER across all links. An interesting point here is that APO tends to equalize the performance of K users even without the use of SINRE. This is shown in Figure 3.4. Hence, it seems sufficient to use APO without SINR equalization to maximize the

66


Figure 3.4. SER performance comparison of individual links for the (2, 2, 1, 3) system when SINRE is not used and when SINRE and APO are used (adapted c 2009 IEEE). from [26] minimum SINR in the system. The performance of APO without SINRE, however, is still worse than when the proposed method does not perform APO. This is denoted as “Proposed w/o APO” in Figure 3.4. This suggests that SINR equalization plays a more important role than APO in performance improvement. In other words, using a good power allocation scheme might be more beneficial than searching for the best order of the users to achieve a higher diversity gain.

3.8.3

Overall system performance We first show the overall SER of the proposed scheme and compare it with other available methods [9–12]. Overall SER is defined as the average SER of K links. The overall SER performances for a (2, 2, 1, 3) system for both the proposed method with or without APO and for [9–12] are shown in Figure 3.5. The proposed method without APO outperforms the methods in [11, 12] and [9] by 5 dB and 3 dB, respectively, and is only 1 dB away from an interferencefree performance when SER = 10−4 . The large improvement in performance in the proposed scheme with respect to [11, 12] comes from an increase in the degree of freedom and the iteration process used in determining the transmit– receive antenna weights. In addition, the proposed method without APO is able to achieve much better performance with much less complexity (we only use


67

Figure 3.5. Average SER performance comparison for (2, 2, 1, 3) system using c 2009 IEEE). various non-linear precoding algorithms (adapted from [26] ten iterations). The computational complexity of the proposed method for a (2, 2, 1, 3) system is on average about 75% less than the complexity of methods in [10–12]. In essence, the proposed method fully utilizes THP, transmit antennas, and receive antennas in a more optimal way with much less complexity to create noninterfering spatial channels. Figure 3.5 also shows the performance of the proposed method with APO. APO moves the SER performance of the proposed method to within 0.25 dB of an interference-free transmission when SER = 10−4 . Thus, APO gives about 1 dB gain over the proposed method without APO. This gain, however, comes at the cost of complexity since now the proposed method −1 needs to do a search over K l=0,l = 1 K − l possible user orderings. As a result, −1 the complexity of the proposed method is K i=0,i = 1 K − i times more than the proposed method without APO. This is shown in the last column of Table 3.1. The performance of the iterative scheme in [10] depends on the number of iterations. To show that the proposed method performs better than the scheme in [10], we set the iteration number for the scheme in [10] to five, giving a computational complexity of around 74 520 flops for a (2, 2, 1, 3) system. The computational complexity of the proposed method using ten iterations is 4860 flops. The performance of [10] is shown in Figure 3.5. Here, we can see clearly that [10] is worse than the proposed method with or without APO. It is not possible to get much improvement in performance in [10] by raising the SNR above 21 dB. We refer to this SNR value, above which there is no further SER decrease, as the saturation point. Here, we must stress that the performance of [10] can be further improved by increasing the number of iterations. This is shown in Figure 3.5

68


Figure 3.6. Average SER performance comparison for a (2, 2, 2, 3) system using various nonlinear precoding algorithms.

when we increase the number of iterations to 11. However, the performance of the scheme in [10] is worse than the performance of the proposed method and the scheme in [10] is much more complex than the proposed method. Lastly, we also plot the performance of the proposed method under a per BS power constraint. There is only a 1 dB performance degradation by switching from total BS to per BS power constraints. The performance of the proposed method under a per BS power constraint is much better than the performance of other schemes under both total BS and per BS power constraints. In Figure 3.6, we illustrate how the proposed method performs under a different configuration. We show the performance when the number of users, K, the number of transmit antennas per BS, NB S , the number of streams per user, S, and the number of receive antennas per MS, NM S , are three, two, two, and two, respectively. Here, the total number of transmit antennas KNB S is equal to the number of MSs. Even when the proposed method does not perform APO, it still significantly outperforms the one in [10, 11]. This improvement is even greater than that shown in Figure 3.6 (>4 dB). Interestingly, the performance in [12] is exactly the same as the performance of the proposed method. Note that here, the complexity of the proposed scheme is 80% less than that in [12], making the proposed method most practical for implementation. We also plot the performance of the proposed method under per BS power constraints for a (2, 2, 2, 3) system. Its performance is still better than the

69


40 35 30

bps/Hz

25 Proposed (total power constraint) Scheme [10] 11 iterations (total BS constraint) Proposed (per BS constraint) Scheme [10] 11 iterations (per BS constraint) Interference free

20 15 10 5 0 12

14

16

18

20

22

24

26

28

30

SNR

Figure 3.7. Capacity performance comparison for a (2, 2, 1, 3) system using various nonlinear precoding algorithms.

performance of the other schemes under both the total BS and per BS power constraints. As the system has an error performance close to an interference-free system, its capacity should approach the capacity of individual interference-free links. In typical cellular networks, only one user signal can be transmitted in a frequency band at a given time slot. The proposed method enables K base stations in the same location to simultaneously transmit to K users using the same frequency band and time slots. By using the proposed method, instead of transmitting to one user at a time with a power of 1, we can simultaneously transmit to K users with a power of K with the performance of each user approaching an interference-free performance. For example, the capacity of cellular mobile networks for a (2, 2, 1, 3) system can be increased by up to K times, as shown in Figure 3.7, by using BS cooperation. Note that the capacity of the proposed method is higher than the capacity of its best competitor [10]. An interesting point here is that the capacity of a (2, 2, 2, 3) system using the method in [12] is the same as the capacity of the proposed method. Note that these two significantly outperform any other methods. This is shown in Figure 3.8. In a (2, 2, 2, 3) system, we have six cooperative transmit antennas at BSs transmitting to users each with two receive antennas. The maximum possible number of independent transmissions for each user is two. Thus, if the number of streams is two, we fully use the transmission space and it is not possible to use this transmission space for other users without violating the ZF constraint. On

70


60 Proposed (total power constraint)

55

Scheme [10] (11 iterations) (per BS constraint) Proposed (per BS constraint) Scheme [10] (11 iterations) (per BS constraint)

50

Scheme [11] (total power constraint) Scheme [11] (per BS constraint)

45

Scheme [12] (total power constraint) Scheme [12] (per BS constraint) Interference free

bps/Hz

40 35 30 25 20 15 10 12

14

16

18

20

22

24

26

28

30

SNR

Figure 3.8. Capacity performance comparison for a (2, 2, 2, 3) system using various nonlinear precoding algorithms.

the other hand, for a (3, 3, 2, 3) system, we have three receive antennas for each link and only use two out of three possible transmission spaces for each user. It is possible to use the remaining available transmission space without violating the ZF constraint. In our proposed method, we allow the transmission space for each user to overlap. Our proposed scheme will outperform that in [12] in this type of configuration. This is shown in Figure 3.9 where the capacity of the proposed scheme is 20% more than the capacity of its nearest competitor, i.e., that in [12].

3.9

Conclusion In this chapter, we have proposed a method to design a spectrally efficient cooperative downlink transmission scheme by employing precoding and beamforming. THP and iterative transmit–receive weight optimization have been used to cancel multiuser interference. A new method to generate transmit–receive antenna weights has been proposed. SINRE and APO have been used to achieve SER fairness among different users and further improve the system performance, respectively. The error performance for two sets of system parameters (NB S , NM S , S, K) has been shown. For a (2, 2, 1, 3) cooperative system, the proposed method outperforms existing schemes by at least 3 dB and is only 0.25 dB away from an interference-free performance when SER = 10−4 . For a (3, 3, 2, 3) system, the proposed method has a 20% higher spectral efficiency than existing

71

3.9 Conclusion

80 Proposed (total power constraint) Proposed (per BS constraint) Scheme [12] (total power constraint) Scheme [12] (per BS constraint) Interference free

70

bps/Hz

60

50

40

30

20

10 12

14

16

18

20

22

24

26

28

30

SNR

Figure 3.9. Capacity performance comparison for a (3,3,2,3) system using various nonlinear precoding algorithms. schemes. In addition, the proposed method eliminates the dependency between the numbers of transmit and receive antennas. The complexities of the proposed method have been shown to be on average 75% less than the complexities of the schemes in [9–12] with the same configurations. Thus, we can conclude that our proposed scheme has the best capacity, the lowest SER, and the lowest computational complexity compared to those in [9–12] in most cases. These features make the proposed method suitable for practical implementation.

Appendix

Proof of SINR equivalence We first calculate SIN Rs,j using the term on the left hand side of (3.20). We −1 ˜ s,j h ˜ H only has one eigenvalue. Let us assume first need to prove that Rs,j h s,j −1 H ˜ H by b, where a = [a1 ...aN ]T ∈ ˜ = 0. We denote R h ˜ s,j by a and h that h s,j

s,j

s,j

−1

M S

˜ s,j h ˜ H as C N M S ×1 and b = [b1 ...bN M S ] ∈ C 1×N M S . We then express Rs,j h j −1

˜ s,j h ˜ H = ab = [b1 a...bN a]. Rs,j h s,j M S

(3.40)

−1 ˜ s,j h ˜ H is a matrix that has NM S columns and rows. We can see that Here, Rj h s,j −1 ˜ s,j h ˜ H can be rewritten the vectors represented by each column of matrix R h j

s,j

using vector a as a basis. This indicates that the rank of this matrix is 1 and as a consequence, there is only one eigenvalue. The receive weight vector computation in (3.19) can be written as −1 ˜ s,j h ˜ H rs,j = λs,j rs,j , where λs,j is the eigenvalue for stream s in link j. Rs,j h s,j ˜ H , we have By multiplying both sides of this equation by h s,j ˜H ˜ ˜ H R−1 h (h s,j s,j s,j − λs,j )hs,j rs,j = 0.

(3.41)

−1 ˜ H R−1 h ˜ ˜ ˜H The eigenvalue of h s,j s,j s,j is the same as the eigenvalue of Rs,j hs,j hs,j . −1 ˜ ˜H R h As a consequence, h s,j s,j s,j only has one eigenvalue. This eigenvalue is the solution for the term on the left hand side of (3.20). Thus, the SIN Rs,j for it ˜ H R−1 h ˜ is given as SIN Rs,j = λs,j = h s,j s,j s,j . We now find the SIN Rs,j by solving the term on the right hand side of (3.20). The optimum receive weights vector −1 ˜ H R−1 h ˜ s,j /c where c = h ˜ is given by [17] as rs,j = Rs,j h s,j s,j s,j . By inserting this receive weights vector into (3.11) and replacing its numerator with rH s,j Rs,j rs,j , ˜ H R−1 h ˜ s,j . we obtain SIN Rs,j = h s,j

s,j

Proof of convergence In order to calculate SIN Rs,j in (3.11), we need to know the receive weight vector for stream s in link j, rs,j and all transmit weight vectors t1,1 ,...,tS,K , obtained

73

Appendix

by using (3.17) and (3.16), respectively. We write SIN Rs,j as SIN Rs,j (rs,j , T) since it is a function of rs,j and T. Since in the proposed scheme, we optimize one variable at a time, while fixing the other one, we have SIN Rs,j (gs,j (T), T) = max SIN Rs,j (a, T), gs,j (T) ∈ A1 , a∈A 1

(3.42)

where T is fixed while the best rs,j = gs,j (T) in the set A1 is searched and SIN Rs,j (rs,j , f1 (R)) = max SIN Rs,j (rs,j , a), f1 (R) ∈ A2 , a∈A 2

(3.43)

where rs,j is fixed while the transmit weight vectors for K links, T = f1 (R), in the solution set A2 are searched. To describe the proposed alternating optimization process, we denote the number of iterations by i, the receive weight (i) (0) vector by rs,j and transmit weight vectors by T(i) . First, rs,j , j = 1, ..., K, are arbitrarily chosen as initial vectors. T(1) is then calculated by using the (i) function in (3.16), f1 (R0 ). For i ≥ 1, we then have, rs,j = gs,j (T(i) ) , s = (i)

(i)

1, ..., S, j = 1, ..., K, where T(i) = [t1,1 ...tS,K ], and T(i) = f1 (R(i−1) ), where R(i) = Diag(rH 1,1 (0)

(i)

, ..., rH S,K

(i)

(i)

). Here, rs,j and T(i) are generated in the order

(1)

rs=1,...,S,j =1,...,K , T(1) , rs=1,...,S,j =1,...,K , T(2) and so on. From (3.42) and (3.43), and by using the fact that SIN Rs,j (rs,j , T) is nondecreasing and bounded from above by constraints in (3.14), we can write (i)

SIN Rj (rj , T(i) )

(i)

≥ SIN Rj (rj , T(i−1) ) (i−1)

≥ SIN Rj (rj

, T(i−1) ).

(3.44)

The terms on the right hand side of (3.44) come from the fact that since we are performing an alternate optimization of the transmit–receive weights by using (3.42) and (3.43), the SINR obtained at iteration i − 1 could only be either equal or less than the SINR obtained at iteration i. This shows that as the (i) number of iterations increases, the SIN Rs,j (rs,j , T(i) ) will converge to a local maximum and simultaneously satisfy (3.17) and (3.16). The former will also cause the remaining interference to converge to 0 as the number of iterations goes to ∞.

Proof of transmit–receive weight optimality We know from the proof of convergence in this Appendix that we can write the optimal solution as det(R∗ HT∗ ) = det(Z) = l |zl,l |, where Z and zi,i with i = S(j − 1) + s, are a lower triangular matrix and the entry of the diagonal of Z, respectively. Thus the channel gain for stream s in link j corresponds to the ith diagonal entry of Z. R∗ and T∗ indicate the optimal transmit–receive weight vectors for K links. We also need (3.16) to be satisfied for the optimal solution ∗ H ∗ for each stream s in link j, where (HH j rs,j ) ts,l = 0, s = 1, ..., S, l = j + 1, ..., K,

74


∗ H ∗ and (HH j rs,j ) ts ,j = 0, s = s + 1, ..., S. The vector created by multiplying the channel matrix by the receive antenna weight vector is perpendicular to the transmit weight vector for links j + 1, ..., K and stream s + 1, ..., S in link j. As a result, there is no interference at all at link j. This is so since the transmission spaces of link j + 1, ..., K and stream s + 1, ..., S in link j do not overlap with the transmission space of stream s in link j. The interference from link 1, ..., j − 1 and stream 1, ..., s − 1 in link j to stream s in link j is canceled by THP. However, prior to finding the optimal solution, the receiver design from (3.17) destroys the orthogonality created by QR decomposition in (3.16). As a (i) H (i) result at the ith iteration, for link j, we have (HH j rj ) tl = 0, l = j + 1, ..., K H and (HH j rs,j ) ts ,j = 0, s = s + 1, ..., S. This means the transmission space for stream s in link j intersects with the transmission spaces of link j + 1, ..., K and stream s + 1, ..., S in link j prior to convergence. In other words, the vector (i) generated by HH j rs,j also has components in other directions. This reduces the optimal signal gain for stream s in link j, zi,i where i = S(j − 1) + s. Thus, we (i) can then conclude that j |βs,j | ≤ j |zj,j |. (i)

(i)

References [1] D. Tse and P. Viswanath, Fundamentals of Wireless Communication. Cambridge University Press, 2003. [2] R. Morrow, Wireless Network Coexistence. The McGraw-Hill Companies Inc., 2004. [3] M. Schubert and H. Boche, “Solution of the multiuser downlink beamforming problem with individual SINR constraints,” IEEE Transactions on Vehicular Technology, 53, 2004, 18–28. [4] G. Caire and S. Shamai, “On the achievable throughput of a multiantenna Gaussian broadcast channel,” IEEE Transactions on Information Theory, 49, 2003, 1691–1706. [5] M. Costa, “Writing on dirty paper,” IEEE Transactions of Information Theory, 29, 1983, 439–441. [6] C. Windpassinger, R. F. H. Fischer, T. Vencel, and J. B. Huber, “Precoding in multiantenna and multiuser communications,” IEEE Transactions on Wireless Communications, 3, 2004, 1305–1316. [7] M. Tomlinson, “New automatic equalizer employing modulo arithmetic,” IEEE Electronics Letters, 7, 1971, 138–139. [8] M. Miyakawa and H. Harashima, “New automatic equalizer employing modulo arithmetic,” IECE Transactions, 52-A, 1971, 272–273. [9] Q. H. Spencer, A. L. Swindlehurst, and M. Haardt, “Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels,” IEEE Transactions on Signal Processing, 52, 2004, 461–471.

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[10] Z. Pan, K. Wong, and T. Ng, “Generalized multiuser orthogonal spacedivision multiplexing,” IEEE Transactions on Wireless Communications, 3, 2004, 1969–1973. [11] G. J. Foschini, K. Karakayali, R. A. Valenzuela, “Coordinating multiple antenna cellular networks to achieve enormous spectral efficiency,” IEE Proceedings on Communications, 153, 2006, 548–555. [12] J. Liu and A. K. Witold, “A novel nonlinear joint transmitter-receiver processing algorithm for the downlink of multi-user MIMO systems,” IEEE Transactions on Vehicular Technology, 57, 2008, 2189–2204. [13] J. C. Bezdek and R. J. Hathaway, “Some notes on alternating optimization,” Lecture Notes on Computer Science, 2275, 4, 2002, 187–195. [14] G. J. Foschini, G. D. and Golden, R. A. Valenzuela, and P. W. Wolniansky, “Solution of the multiuser downlink beamforming problem with individual SINR constraints,” IEEE Journal on Selected Areas in Communications, 17, 11, 1999, 1841–1852. [15] R. F. H. Fischer, Precoding and Signal Shaping for Digital Transmission. John Wiley and Sons Inc., 2002. [16] G. H. Golub and C. F. Van Loan, Matrix Computations. The John Hopkins University Press, 1996. [17] W. Hardjawana, B. Vucetic, and A. Jamalipour, “Adaptive beamforming and modulation for OFDM in co-working WLANs with ack eigen-steering,” in Proc. of IEEE PIMRC 2006, 1–5. IEEE, 2006. [18] L. C. Godara, “Application of antenna arrays to mobile communications. II. Beam-forming and direction-of-arrival considerations,” Proceedings of IEEE, 85, 8, 1997, 1195–1245. [19] W. Yang and G. Xu, “Optimal downlink power assignment for smart antenna systems,” in Proc. of IEEE ICASSP 1998, vol. 6. 3337–3340. IEEE, 1998. [20] S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice Hall Press, 1993. [21] Y. Jiang, J. Li, and W. Hager, “Uniform channel decomposition for MIMO communications,” IEEE Transactions on Signal Processing, 53, 11, 4283– 4294, 2005. [22] Y. Jiang, J. Li, and W. Hager, “Joint transreceiver design for MIMO communications using geometric mean decomposition,” IEEE Transactions on Signal Processing, 53, 10, 2005, 3791–3803. [23] Y. Jiang, J. Li, and W. Hager, “The geometric mean decomposition,” Linear Algebra and Its Applications, 396, 2005, 373–384. [24] J. R. Schott, Matrix Analysis for Statistics. John Wiley and Sons, Inc., 1997. [25] D. P. Palomar, J. M. Cioffi, and M. A. Lagunas, “Joint Tx-Rx beamforming design for multicarrier MIMO channels: A unified framework for convex optimization,” IEEE Transactions on Communications, 51, 9, 2003, 2381– 2401.

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[26] W. Hardjawana, B. Vucetic, Y. Li, and Z. Zhou, “Spectrally efficient wireless systems with cooperative precoding and beamforming,” IEEE Transactions on Wireless Communications, 8, 12, 2009, 5871–5882. [27] W. Hardjawana, B. Vucetic, Y. Li, and Z. Zhou, “Multi-user cooperative base station systems with joint precoding and beamforming,” IEEE Journal of Selected Topics in Signal Processing, 3, 6, 2009, 1079–1093.

4

Turbo base stations Emre Aktas, Defne Aktas, Stephen Hanly, and Jamie Evans

4.1

Introduction Cellular communication systems provide wireless coverage to mobile users across potentially large geographical areas, where base stations (BSs) provide service to users as interfaces to the public telephone network. Cellular communication is based on the principle of dividing a large geographical area into cells which are serviced by separate BSs. Rather than covering a large area by using a single, high-powered BS, cellular systems employ many lower-powered BSs each of which covers a small area. This allows for the reuse of the frequency bands in cells which are not too close to each other, increasing mobile user capacity with a limited spectrum allocation. Traditional narrowband cellular systems require the cochannel interference level to be low. Careful design of frequency reuse among cells is then crucial to maintain cochannel interference at the required low level. The price of low interference, however, is a low frequency reuse factor: only a small portion of the system frequency band can be used in each cell. More recent wideband approaches allow full frequency reuse in each cell, but the cost of that is increased intercell interference. In both approaches, the capacity of a cell in a cellular network, with six surrounding cells, is much less than that of a single cell operating in an intercell interference-free environment. In this chapter, we survey an approach that allows the cell with neighbors to achieve essentially the same capacity as the interference-free cell. In a conventional cellular system, each mobile user is serviced by a single BS, except for the soft-handoff case – a temporary mode of operation where the mobile is moving between cells and is serviced by two base stations. A contrasting idea is to require each mobile station to be serviced by all BSs that are within its reception range. In this approach all the BSs in the cellular network are components of a single transceiver with distributed antennas, an approach known as “network multiple-input multiple-output (MIMO).” Cooperative Cellular Wireless Networks, eds. Ekram Hossain, Dong In Kim, and Vijay K. Bhargava. Published by Cambridge University Press. C Cambridge University Press, 2011.

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Turbo base stations

Network MIMO requires cooperation between BSs. On the uplink, the BSs must cooperate to jointly decode the users, whilst on the downlink, the BSs must cooperate to jointly broadcast signals to all the users in the network. This approach may appear unrealistically complex, but information-theoretic studies have highlighted the potentially huge capacity gains from such an approach [23, 49, 59]. In a nutshell, these works (and others) have shown that such cooperation effectively eliminates intercell interference. In other words, the per-cell capacity of a network of interfering cells is roughly the same as a non-interfering system where the cells are isolated and do not interfere at all (in fact, there is a diversity advantage for the interfering system, which means its capacity is higher than the capacity of the isolated cell model). In the network of interfering cells there is no wasted interference: all received signals contain useful information. Crucially, to obtain this advantage, it is necessary for there to be intercell interference: it was shown in [23, 59] that full frequency reuse in each cell is required in order to achieve the full information-theoretic capacity. This is in contrast to the conventional cellular model with single cell processing which usually requires fractional frequency reuse. The question then arises: how can such cooperation be realized in practice? It is natural to conceive first a centralized system in which a central processor is connected to all the base stations, so that the network is operated as a single cell MIMO system, but with distributed antennas. Such an architecture is, however, expensive to build, has a single point of failure, and does not satisfactorily address issues of complexity and delay. A more feasible and desirable solution is to distribute the processing among the base stations. In this chapter we present distributed BS cooperation methods for joint reception and transmission, which allow the desired network MIMO behavior to emerge in a distributed manner. For distributed processing, communication among the BSs is mandatory. The desired properties of a feasible distributed method are: (1) communication should only be required between neighboring BSs, as opposed to message passing among all BSs, and (2) the processing per BS and message passing delay should remain constant with increasing network size. In this chapter, we survey an approach to BS cooperation (and provide new results for this approach) based on a graphical model of the network-MIMO communication processes. In essence, we show that both uplink and downlink modes of communication reduce to belief propagation on graphs derived from the way BSs are interconnected in the backhaul, and from the signal propagation between BSs and mobiles, and vice versa, across the air interface. To give a simple picture of what we mean by message passing between BSs, consider a cellular network where the BSs and the cells are placed on a line. In this model, every cell has two neighboring cells. Although this simple model is far from being realistic, it provides a framework where the main concepts of distributed processing with message passing can be developed and explained, and it can then be generalized to less restrictive models. The one-dimensional cellular array is illustrated in Figure 4.1.

79

4.1 Introduction

y1

y2

y3

yn

BS 1

BS 2

BS 3

BS n

x1

x2

x3

xn

MS 1

MS 2

MS 3

MS n

Figure 4.1. Linear cellular array. The cells are positioned on a line. Each cell has one active mobile station (MS). Dashed lines show boundaries between cells. At cell i, xi and yi represent the transmitted symbol and the received signal. Let xi denote the data symbol transmitted by mobile station (MS) i and yi denote the channel output observed at BS i. In the linear cellular array model, the relationship between the transmitted symbols and the received signals is yi = hi (−1)xi−1 + hi (0)xi + hi (1)xi+1 + zi ,

(4.1)

where hi (j) is the channel coefficient from MS i + j to BS i, and zi is the additive Gaussian noise with variance σ 2 . We assume that the channel coefficients hi (j) and the noise variance are known at BS i. For convenience, for the cells at the edges of the network, add dummy symbols x0 and xn +1 , and set the corresponding hi (j)s to zero. The signal model for the one-dimensional cellular array model is depicted in Figure 4.2.

xi−1

)

h

−1 i(

hi

−1 (1

hi (0)

zi−1

)

xi

zi

)

hi

1 (−

+1

hi

(1

)

xi+1

yi+2

zi+1

)

1 (−

2

h i+

hi

+1

(1

)

zi+2

hi+2 (0)

yi+1

hi+1 (0)

yi

hi−1 (0)

yi−1

xi+2

Figure 4.2. Linear cellular array signal model. The symbol transmitted in one cell is received at that cell, and also in the two neighboring cells (one neighboring cell if it is one of the two edge cells). In the traditional single-cell processing (SCP) approach, BS i tries to detect symbol xi based on yi alone. Using a frequency-reuse factor of 1/2 avoids the intercell interference, but this halves the capacity of the system. With full frequency reuse, MS i receives interference from MSs i − 1 and i + 1, as is clear in (4.1). One could treat this interference as Gaussian noise, and use a mis-matched decoder to decode the desired signal, but information theory tells us that intercell interference can be completely eliminated via multicell processing (MCP) [23, 49, 59].

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Turbo base stations

MCP requires cooperation between the BSs, but how much cooperation is required in the simple model we are considering here? At first sight, it might seem sufficient for BS i to use (yi−1 , yi , yi+1 ) in the detection of symbol xi , as these are the only outputs to which xi actively contributes. This is not the case, but it is certainly true that BS i can do a much better job of detecting xi in this scenario. The BS’s task is first to compute the conditional distribution p(xi |yi−1 , yi , yi+1 ) and then to pick the maximum a posteriori estimate for xi . One approach to realize this detection strategy would be for each BS to pass the observed channel output to its immediate neighbors: thus, BS i sends yi to BSs i − 1 and i + 1 respectively. This strategy involves one single message passing between adjacent BSs. Considering this further, however, we see that intercell interference has not been eliminated after a single message passing step. For example, yi−1 receives a contribution from data symbol xi−2 and the uncertainty in xi−2 must be accounted for in the above probabilistic model. Again, it could be treated as Gaussian noise, or it could be modeled more accurately than that, depending on what is measured or known by the BSs, and what information is passed from one to the other. For example, BS i may know the constellations from which the interfering symbols xi−2 and xi+2 have been chosen. The BS may also have phase information (the coherent case) or the phase may be unknown (incoherent). The exact model used by BS i depends on which particular assumptions best describe the real-world scenario, but in all these possible models, intercell interference remains after one message passing step in the effect of the unknown symbols xi−2 and xi+2 , which cannot be reliably detected. The above interference model may remind the reader of standard intersymbol interference (ISI) channels that arise in frequency-selective digital communication scenarios. Such models are linear, and if we assume in addition that the a priori distributions on the input symbols are Gaussian, then the optimal equalizer is to apply the matched filter (in this case, the linear minimum mean squared error (LMMSE) filter) to the observed symbols y1 , y2 , ..., yn . This makes it clear that it is not optimal for BS i to have access only to (yi−1 , yi , yi+1 ): to be optimal, BS i requires all the channel outputs y1 , y2 , ..., yn , as well as all the channel gains, and information about the a priori distributions on the symbols. With that information, it can apply the optimal filter, and obtain an optimal estimate of xi . In other words, there is a system-wide coupling of the interference between cells. This approach might be called centralized MCP . The problem with centralized MCP is that it requires a huge amount of message passing. All BSs require global channel knowledge in order to each apply the globally optimal filter. Note, however, that distributed methods can be used in ISI equalization. In the Gaussian case, the LMMSE estimates can be obtained by the recursive Kalman smoother . In the case of discrete input constellations, the maximum a posteriori (MAP) detector can be obtained by the forward– backward or BCJR algorithm [8] . Such methods are special cases of Bayesian estimation for graphical models. This suggests the idea of representing the

4.2 Review of message passing and belief propagation

81

cellular network by a graphical model, and obtaining distributed versions of MCP that do not require each BS to obtain the complete global channel state information (CSI). Further, these methods will allow us to investigate how well performance improves with the number of message passing steps. For example, in some scenarios, we will see that a single message passing step is sufficient to get most of the gains of MCP, whereas in other scenarios, many more message passing steps are required. The challenge in the area of turbo BSs is to distribute the computations of the conditional distributions of the xi s, so that they can be obtained by message passing between neighboring BSs only. We do this for the uplink in Sections 4.3, and 4.4. In Section 4.5, we apply similar ideas to the downlink broadcast channel problem in which the BSs are sending data symbols to the MSs. To initiate this study, our first step will be to review message passing and belief propagation methods in a more generic framework, and then to apply the results from this theory to the cellular models of interest in this chapter.

4.2

Review of message passing and belief propagation The distributed algorithms presented in this chapter are built on the key concepts of factor graphs and the sum-product algorithm. We begin with a brief review of these concepts. The use of iterative, or turbo, receiver methods defined on graphs has become an important focus of research in communications since the success of turbo codes and the rediscovery of low-density parity-check codes. Both the turbo decoder [38] and the low-density parity-check code decoder [20] are instances of belief propagation on associated graphs. A factor graph is a graphical representation on which message passing algorithms are defined. There are at least two other popular graphical representations employed in the communications literature. Firstly, there are graphs on which codes are defined. These graphs represent sets of constraints which describe a code and include Tanner graphs [51], Tanner–Wiberg–Loeliger (TWL) graphs [58], and Forney graphs [17]. These graphs also provide iterative decoding of the associated codes via message passing algorithms. Secondly, there are probabilistic structure graphs including Markov random fields [29] and Bayesian networks [44]. These graphs represent statistical dependencies among a set of random variables. Markov random fields are based on local Markov properties, whereas Bayesian networks are based on causal relationships among the variables and factoring the joint distribution into conditional and marginal probability distribution functions. The message passing algorithms defined on these structures provide methods of probabilistic inference: compute, estimate, and make decisions based on conditional probabilities given an observed subset of random variables.

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Turbo base stations

Factor graphs are not specifically based on describing code constraints or probabilistic structures. They indicate how a joint function of many variables factors into a product of functions of smaller sets of variables. They can be used, however, for describing codes and decoding codes, and in describing probabilistic models and statistical inference. In fact, factor graphs are more general than Tanner, TWL, and Forney graphs for describing codes [34], and they are more general than Markov random fields and Bayesian networks in terms of expressing factorization of a global distribution [19].

4.2.1

Factor graph review In this subsection, we provide just enough review for the uninitiated reader to be able to grasp the BS cooperation material presented in this chapter. For further information, the reader may refer to [30] and the excellent tutorials [32, 33]. The reader experienced in factor graphs may skip this section. Let g(x1 , x2 , . . . , xn ) be a function of variables x1 , . . . , xn , where for each i, xi takes on values in a set Ai .

Definition of marginal function and summary notation We are interested in a numerically efficient computation of the marginal function gi (xi ) = g(x1 , x2 , . . . , xn ) (4.2) ∼{x i }

for some i. The right hand side of (4.2) denotes the summation for xi of function g as defined in [30]: for each a ∈ Ai the value of gi (a) is obtained by summing the value of g(x1 , x2 , . . . , xn ) over all (x1 , . . . , xn ) ∈ A1 × · · · × An such that xi = a. For example, for n = 3, the summation for x2 of g is g2 (x2 ) = g(x1 , x2 , x3 ) = g(x1 , x2 , x3 ). ∼{x 2 }

x 1 ∈A 1 x 3 ∈A 3

Relationship to the APP For probabilistic models, the computation of the marginal in (4.2) is related to the computation of the a posteriori probability (APP), a quantity of particular interest to us in this chapter. Let (x1 , . . . , xn ) denote the realization of some random variables in a probabilistic model, let (y1 , . . . , ym ) denote some observed variables in the model, and let p(x1 , . . . , xn , y1 , . . . , ym ) denote the joint distribution. Taking a given (y1 , . . . , ym ) as fixed, (i.e., observed) define the global function g: g(x1 , . . . , xn ) = p(x1 , . . . , xn , y1 , . . . , ym ). Typically, g is factorized into two as g(x1 , . . . , xn ) = p(y1 , . . . , ym |x1 , . . . , xn )p(x1 , . . . , xn ),

(4.3)

83


where the first term is the likelihood function and the second term is the a priori distribution of (x1 , . . . , xn ). Depending on the probabilistic model, these two factors themselves are further factorized. The APP of xi for any desired i ∈ {1, . . . , n} is proportional to the marginal of g for xi : p(xi |y1 , . . . , ym ) ∝ gi (xi ),

(4.4)

where gi (xi ) is the marginal of the joint distribution in (4.3), and the notation “∝” means “proportional to”, i.e., the right hand side of “∝” is scaled by a constant to obtain the left side. If the left hand side is a probability function, this scaling constant can be found using the fact that this function adds up to unity over all possible values of its argument.

Definition of factor graph Suppose that g(x1 , . . . , xn ) is in the form of a product of local functions fj : g(x1 , . . . , xn ) =

J

fj (Xj ),

(4.5)

j =1

where Xj is a subset of {x1 , . . . , xn }, and the function fj (Xj ) has the elements of Xj as arguments. A factor graph represents the factorization of g(x1 , . . . , xn ) as in (4.5). The corresponding factor graph has two types of nodes: variable nodes and factor nodes. For each variable xi there is a variable node shown by a circled xi , and for each local function fj there is a factor node shown by a solid square in the graph. Thus there are n variable nodes and J factor nodes in the graph. There is an undirected edge connecting variable node xi to factor node fj if and only if xi is an argument of fj . Thus connections are only between variable and factor nodes; two factor nodes are never connected, and two variable nodes are never connected. We define the neighbors of a variable node to be those factor nodes to which it is directly connected in the graph. We correspondingly define the neighbors of a factor node to be those variable nodes in the graph to which it is directly connected.

Definition of sum–product algorithm The goal of the sum–product algorithm is to obtain the marginal function in (4.2) for some i ∈ {1, . . . , n}. This is done in a numerically efficient manner, based on the factorization in (4.5) using the distributive law to simplify the summation. The algorithm is defined in terms of messages between connected factor and variable nodes. A message from node a to node b is computed based on previously received messages at node a from all its neighbors except for node b. A message from variable node xi to factor node fj is a function with argument xi that can take on values in Ai . A message from factor node fj to variable node xi is also a function of xi . After the messages from all nodes propagate through the factor graph in a sequential manner, at termination, the incoming messages

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Turbo base stations

at desired variable nodes are combined in order to obtain the associated marginal function. The rules for message updates are given below. Message from variable node x to factor node f : µh−x (x). µx−f (x) =

(4.6)

h∈n (x)\{f }

Message from factor node f to variable node x: ⎛ ⎝f (n(f )) µf −x (x) = ∼{x}

⎞ µy −f (y)⎠ ,

(4.7)

y ∈n (f )\{x}

where n(x) : n(x)\{f } : n(f ) :

set of all factor node neighbors of variable node x in the factor graph, set of all neighbors of x except for f , set of all variable node neighbors of factor node f in the factor graph.

We make the following observations on the messages in the sum–product algorithm. The computations done by variable nodes in (4.6) are a simple multiplication of incoming messages, whereas the computations done by the factor nodes in (4.7) are more complex. A variable node of degree 2 (i.e., a node with two neighbors) simply replicates the message received on one edge onto the other edge. A factor node of degree 1 simply outputs the function of the variable that it is connected to as the message. The computation typically starts at the leaf nodes of the factor graph. Each leaf variable node sends a trivial identity function. If the leaf node is a factor node, it sends a description of f . If the computation is started from nonleaf nodes, it is assumed that it has received trivial identity messages during initiation. Each node remains idle until it receives all required messages based on which it can compute outgoing messages. To terminate the computations, the messages are combined at the desired variable nodes. The rule for combining messages at a variable node is to take the product of all incoming messages: µh−x (x). (4.8) µx (x) = h∈n (x)

Equivalently, µx (x) can be computed as the product of the two messages that were passed in opposite directions over any single edge incident on x: µx (x) = µf −x (x)µx−f (x)

for any f ∈ n(x).

(4.9)

If the factor graph is a tree, then µx (x) will be the marginal function g(x) defined in (4.2). If the factor graph has loops, then the message passings can be repeated, and at termination µx (x) will be an approximation of the marginal


85

function g(x). In many cases, scaled versions of the messages are computed, which results in a µx (x) scaled by a constant. Thus the final µx (x) is obtained after a proper normalization.

Definition of [P ] notation If P is a Boolean proposition involving some set of variables, then [P ] is the {0, 1}-valued truth function 1, if P is true, [P ] = (4.10) 0, if P is false.

4.2.2

Factor graph examples Example 1 Hidden Markov model Consider a probabilistic model where we have the states vector s = (s1 , s2 , . . . , sn ) and output variables vector u = (u1 , u2 , . . . , un ). The states s1 , . . . , sn form a Markov chain, and the transition from si−1 to si produces an output variable ui . The local function Ti computes the conditional probability of transitioning from si−1 to si , and the output ui : Ti (si−1 , ui , si ) = p(si |si−1 )p(ui |si , si−1 )

for i = 1, . . . , n.

(4.11)

In several examples, ui is a function of only si , so in those examples, Ti (si−1 , ui , si ) = p(si |si−1 )[ui = d(si )], where d is the function that determines ui . Corresponding to each output variable ui is the “noisy” observation yi , where the relationship between the output variable and its observation is characterized by the conditional distribution p(yi |ui ). The global function of (s, u) is g(s, u) = p(y|s, u)p(s, u) n n = p(yi |ui ) Ti (si−1 , ui , si ) . i=1

(4.12)

i=1

Note that y is fixed for any realization of observation, so we consider g(s, u) to be a function of (s, u) only, and regard y as a vector of parameters. The factor graph corresponding to the factorization in (4.12) is given in Figure 4.3 for n = 3. The dummy nodes added in this graph do not alter the function g nor the resulting algorithm, but they allow a convenient description of the algorithm. For T1 , the state transition from s0 to s1 is independent of s0 . During initialization, each pendant factor node sends the messages, which are their function descriptions to their corresponding variable nodes. Then, since the corresponding variable nodes are all of order 2, they replicate the messages at the other edge. Afterwards, forward (si−1 to si for i = 1, . . . , n) and backward (si to

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Turbo base stations

f (s0 ) = 1

s0

α(s0 ) T1 α(s1 ) β(s1 )

s1

α(s1 ) T2 α(s2 ) β(s1 )

β(s2 )

γ(u1 )

s2

α(s2 ) T3 α(s3 ) β(s2 )

β(s3 )

γ(u2 )

s3

f (s3 ) = 1

γ(u3 )

u1

u2

u3

f (y1 |u1 )

f (y2 |u2 )

f (y3 |u3 )

Figure 4.3. Factor graph for hidden Markov model for n = 3. Dummy nodes f (s0 ), s0 , and f (s3 ) are added to handle the initialization of the algorithm at the edges of the Markov chain. Since the variable nodes in this graph have degree 2, they simply replicate the message received on one edge on the other edge. si−1 for i = n, . . . , i + 1) message passing occurs along the chain. The resulting algorithm is known as the forward–backward or BCJR algorithm [8]. In the literature, the message µu i −T i (ui ) is denoted by γ(ui ), the message µT i −s i (si ) is denoted by α(si ), and the message µT i −s i −1 (si−1 ) is denoted by β(si−1 ). Using that notation, at initialization, we have γ(ui ) = p(yi |ui ) = f (yi |ui )

for i = 1, . . . , n,

α(s0 ) = 1, β(sn ) = 1. Then the forward recursion is computed as the message from Ti to si , using (4.7): Ti (si−1 , ui , si )α(si−1 )γ(ui ) for i = 1, . . . , n (4.13) α(si ) = ∼{s i }

and the backward recursion is computed as the message from Ti to si−1 β(si−1 ) = Ti (si−1 , ui , si )β(si )γ(ui ) for i = n, . . . , 2. (4.14) ∼{s i −1 }

This is the general form of the forward–backward algorithm. For different specific cases, the local functions are different but the general structure of the algorithm is the same, outlined by the forward and backward recursions in (4.13) and (4.14). After the forward and backward recursions are complete, at termination, for each state variable node si , the incoming messages are combined as µs i (si ) = α(si )β(si )

for i = 1, . . . , n.

(4.15)

Since the factor graph is a tree, µs i (si ) is, in fact, the true marginal gi (si ) and a scaled version of the APP p(si |y). This model is directly applicable to the uplink of the simple one-dimensional cellular network that we examine in Section 4.3. It is the simplest model of turbo BS cooperation that we encounter in this chapter.


p(x1 )

p(x2 )

p(x3 )

p(x4 )

p(x5 )

x1

x2

x3

x4

x5

87

µx1 −y1 (x1 ) µy1 −x1 (x1 ) p(y1 |·) p(y2 |·) p(y3 |·) p(y4 |·)

Figure 4.4. Factor graph for the interference channel model for n = 5, m = 4, ny 1 = {x1 , x2 }, ny 2 = {x1 , x3 }, ny 3 = {x2 , x3 , x4 , x5 }, and ny 4 = {x3 , x4 , x5 }. The notation p(yi |·) refers to the conditional distribution of yi given the neighbor variable nodes: p(yi |·) = p(yi |ny i ). In the following sections, the prior distribution factor nodes, p(xi ), will not be shown in the graphs.

Example 2 Interference channel Consider a channel with n input variables x = {x1 , . . . , xn } and m output variables y = {y1 , . . . , ym }. Each output variable is a noisy observation of a linear combination of the elements in a subset of the inputs, indexed by ni ⊂ {1, . . . , n}, hi,j xj + zi , (4.16) yi = j ∈n i

where hi,j is the complex channel coefficient of input xj at the channel output yi , and zi is the additive white circularly symmetric complex Gaussian noise. Suppose that the channel coefficients and the variance of zi (σ 2 ) are known. Let ny i denote the set of the input variables indexed by ni : {xj : j ∈ ni }. Then the distribution of yi conditioned on ny i is ⎧ " "2 ⎫ " " ⎬ ⎨ " " 1 1 " " exp − − h x . (4.17) p(yi |ny i ) = y i i,j j " " 2 2 ⎩ σ " πσ " ⎭ j ∈n i

Suppose that the inputs are independent, then the joint distribution of {x1 , . . . , xn } is g(x1 , . . . , xn ) = p(x1 , . . . , xn , y1 , . . . , ym ) m n p(yi |ny i ) p(xj ). = i=1

(4.18)

j =1

We can use the (loopy) factor graph corresponding to the factorization in (4.18) and the sum–product algorithm on that graph to compute (an approximation of) the APP p(xi |y1 , . . . , ym ) ∝ gi (xi ). The factor graph corresponding to (4.18) is given in Figure 4.4. There are two types of messages in Figure 4.4: x-to-y messages, and y-to-x messages. Let nx j denote the set of yi nodes such that yi is a neighboring factor node of the variable node xj in the graph. If yi ∈ nx j , the message from variable

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Turbo base stations

node xj to factor node yi is, from (4.6), µx j −y i (xj ) = p(xj )

µy k −x j (xj ).

(4.19)

y k ∈n x j \{y i }

If xj ∈ ny i , the message from factor node yi to variable node xj is, from (4.7), ⎛ ⎞ ⎝f (yi |ny i ) µx l −y i (xl )⎠ . (4.20) µy i −x j (xj ) = ∼{x j }

x l ∈n y i \{x j }

During initialization, the pendant factor nodes p(xj ) send their description to variable nodes xj . In addition, the factor nodes p(yj |·) send trivial messages to their neighboring variable nodes: µy i −x j (xj ) = 1 for i = 1, . . . , m, and xj ∈ ny i . Afterwards, we have an iterative algorithm, where at each iteration we compute (1) x-to-y messages for each j ∈ {1, . . . , n} and yi ∈ nx j in (4.19); (2) y-to-x messages for each i ∈ {1, . . . , m} and xj ∈ ny i in (4.20). Notice that the graph in Figure 4.4 is loopy, and this means that the algorithm will not terminate in a finite number of steps, nor will it be guaranteed to find the correct marginalizations. If the algorithm does converge, however, then it can be terminated after a sufficiently large number of steps, and then an approximation to the marginal distribution on the variable nodes can be obtained as follows. The messages at variable node xj for j ∈ {1, . . . , n} are combined as µy k −x j (xj ). (4.21) µx j (xj ) = p(xj ) y k ∈n x j

Models that lead to factor graphs with loops like this simple interference channel example will arise when we turn our attention to two-dimensional cellular network models in Section 4.4. First, however, we will look at one-dimensional cellular networks where the corresponding factor graphs are loop-free.

4.3

Distributed decoding in the uplink: one-dimensional cellular model Consider again the cellular network where the BSs and the cells are placed on a line, as depicted in Figure 4.1. In this model, every cell has two neighboring cells. Although this simple model is far from being realistic, it provides a framework in which the main concepts of distributed processing with message passing can be developed and explained, and it can then be generalized to less restrictive models. Let xi denote the symbol transmitted by MS i and yi denote the channel output observed at BS i, as depicted in Figure 4.2. In the linear cellular array model, the relationship between the transmitted symbols and the received signals is described by (4.1). As discussed in Section 4.1, the goal is to obtain optimal detection of any particular xi given all observations y1 , . . . , yn , in a distributed

4.3 Distributed decoding in the uplink: one-dimensional cellular model

89

manner with cooperating BSs, as an alternative to the traditional approach of SCP. In SCP, BS i has access to the channel output yi only. In contrast, we are interested here in distributed, message-passing algorithms to accomplish MCP, based on probabilistic graphical models.

4.3.1

Hidden Markov model and the factor graph The linear cellular array model is highly reminiscent of a standard linear ISI model in digital communications, and hence we expect to be able to apply the BCJR algorithm [8]. In [8], a state-based hidden Markov model is used, as described in Example 1 in Section 4.2.2. In a state-based model, several input variables are combined to form a state such that each channel output is only a function of that state, and the state sequence forms a Markov chain. The key idea in [21] is to treat the one-dimensional cellular model as an ISI channel. In fact, this idea goes back to [59]. The state for cell i is si = (xi−1 , xi , xi+1 ) and we assume the symbols from different mobiles are independent, taking values in some finite alphabet (which can be different for the different users). Thus, there are several possible values for the state si , so we will write (xi−1 (si ), xi (si ), xi+1 (si )) for the values of the data symbols corresponding to a particular state value si . It is clear that the state sequence is a Markov chain, with the following transition probabilities: p(s1 ) = p(x0 (s1 ))p(x1 (s1 ))p(x2 (s1 )), p(si+1 |si ) = [xi (si ) = xi (si+1 )][xi+1 (si ) = xi+1 (si+1 )]p(xi+2 (si+1 )), where the [P ] notation was defined in (4.10). Note that [xi (si ) = xi (si+1 )][xi+1 (si ) = xi+1 (si+1 )] indicates whether state si+1 conforms with state si , i.e., whether a transition from si to si+1 is possible. Note that each cell has one channel output, yi , which is dependent only on the state si , as in the hidden Markov model of Section 4.2.2. To complete the match with the model in that section, we define the output variable corresponding to the transition from si−1 to si to be ui , where ui = d(si ) := hi (−1)xi−1 (si ) + hi (0)xi (si ) + hi (+1)xi+1 (si ), and we note that the conditional distribution of the observation, yi , given ui , is f (yi |ui ) = N (yi ; σ 2 , ui ), where N (x; σ 2 , M ) denotes the Gaussian distribution with mean M and variance σ 2 . The corresponding factor graph is shown in Figure 4.5, where the function node Ti computes the function: Ti (si−1 , ui , si ) = p(si |si−1 )[ui = d(si )].

(4.22)

It follows that the forward–backward algorithm can be applied to obtain the APP p(si |y1 , . . . , yn ), which can be further marginalized to obtain p(xi |y1 , . . . , yn ), the APP of the mobile data symbols. The implementation of the forward–backward recursions is distributed among the BSs, where BS i performs the computations done by node Ti in the algorithm.

90

Turbo base stations

s0

f (s0 ) T1

s1

f (sn ) T2

s2

T3

s3

Tn

u1

u2

u3

un

f (y1 |u1 )

f (y2 |u2 )

f (y3 |u3 )

f (yn |un )

sn

Figure 4.5. Factor graph for the hidden Markov model for the linear cellular array. Dashed lines show boundaries between cells. The computations of the nodes within a cell are done by the BS of that cell. Any message passing through a cell boundary corresponds to actual message passing between corresponding BSs.

For example, upon receiving the message α(si−1 ) from cell i − 1, BS i computes α(si ) and forwards it to cell i + 1. Thus, α messages ripple across the BSs from left to right, and β messages ripple in the reverse direction. After the forward and backward recursion is complete, the APP p(si |y1 , . . . , yn ) is obtained as a scaled version of (4.15). In this formulation, the middle BS is the first to be able to decode its mobile. This serial formulation of the forward–backward algorithm is the natural one to use in solving an ISI equalization problem. It is not natural, however, in cellular radio networks to designate a leftmost or rightmost BS. In fact, we cannot do that at all for an infinite linear array model. Fortunately, the sum– product algorithm has flexibility in terms of node activation schedules [30]. Initial conditions can be arbitrary, and each node can operate in parallel. This allows all BSs to immediately begin computing their messages starting with the a priori distributions on the input symbols. At each iteration, a BS passes an α message to the right, and a β message to the left. In a finite linear array, this parallel version of the forward–backward algorithm converges to the same solution as obtained from the serial implementation, but an important point is that it can be terminated early giving a suboptimal estimate of the mobile’s data symbol at an earlier time. In the infinite linear array, the algorithm must be terminated at some point in time. This approach allows an investigation of estimation error versus delay, as can be found in [39]. The actual values that the variables can take have not been specified. In this section, we have in mind that each xi takes a value from a discrete constellation, and, as such, the BSs are engaged in the demodulation of the users’ data symbols. If the symbol xi is replaced by the transmitted codeword of mobile i and yi is replaced by the channel outputs corresponding to a codeword, i.e., if we include the time dimension, then we can use the described method for decoding as opposed to the detection of individual symbols, as considered in [21]. In the present section, the forward–backward algorithm is accomplishing joint


91

multiuser detection (MUD) of the users’ data symbols, prior to single-user decoding. After the detection of the symbols, each BS can decode its own user using a single-user decoder. Note that the complexity of MUD is typically exponential in the number of users [54], but it is known that in some special cases the complexity can be much reduced [47, 52], for example when the signature sequences have constant cross-correlation [48]. In the present section, we have a distributed MUD that is linear in the number of users, and this is due to the highly localized interference model: the cross-correlations of most signature sequences are zero. Indeed, the BCJR algorithm implements the optimal MAP detection of the users’ symbols, and this is known to have a complexity that is linear in time [8], i.e., in the number of symbols. To approach Shannon capacity at high SNR, it is required to send many bits per symbol, which requires a large alphabet size (large signal constellations), and the BCJR algorithm is exponential in the alphabet size. So even if the complexity is linear in the number of users, the overall complexity can be very high. This observation also applies to the decoding of codewords in the model considered in [21]. A standard approach to limit the complexity of MUD is to restrict attention to suboptimal linear techniques, which we consider further in Section 4.3.2. Unfortunately, this does not avoid the complexity of the overall decoding problem, but at least one can then focus attention on well-established techniques for decoding single-user codes.

4.3.2

Gaussian symbols A standard approach in MUD is first to estimate the individual symbols from different users using linear MUD techniques. Once the BS has estimated symbol xi from mobile i it then passes this soft estimate to a single-user decoder for mobile i. The decoder waits until it receives the estimates of all symbols in the codeword, and then it attempts to decode the codeword. This approach limits the complexity of the MUD component of the receiver. It is well known that optimal MUD is in fact linear if the underlying symbols being estimated are jointly Gaussian. In this section, we assume that the input symbols are drawn from joint Gaussian distributions (independent across mobiles) and then we apply the corresponding optimal linear filters, and the task of the present section is to show how these filters can be implemented via message passing between the BSs in the cellular network. Another motivation for this section is that the developed methods will prove useful in designing iterative message-passing algorithms to accomplish beamforming on the downlink of a cellular system, as we will see in Section 4.5. When the input symbols are modeled as Gaussian random variables, we can still employ factor graph methods. The global function is now a continuous function and the marginalization is done by integrating (as opposed to summing) with respect to unwanted variables. Since the messages are now continuous

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Turbo base stations

functions, each message in general corresponds to a continuum of values. However, if the message functions can be parameterized, they can be represented by a finite number of parameter values. For example, if a message function is the probability density function of a Gaussian vector, then it is characterized by a mean vector and covariance matrix pair, which is the case for the Gaussian input model. We will now describe the Kalman-smoothing-based distributed algorithm in [39] for the linear cellular array. The model is the same as in (4.1) except that now the xi s are independent zero-mean Gaussian distributed with variance p. We are going to use matrix-vector notation, so define the state for cell i to be the column vector si = [xi−1 , xi , xi+1 ]T . The states again form a Markov chain, but we now express the transition from state si to si+1 as si+1 = Af si + bf xi+2 , where ⎡

0 Af = ⎣0 0

1 0 0

⎤ 0 1⎦ , 0

⎡ ⎤ 0 bf = ⎣0⎦ . 1

Then the state transition is characterized by the conditional distribution T

f (si+1 |si ) = N (si+1 ; pbf bf , Af si ),

(4.23)

where we use the notation

* + 1 N (s; M, m) ∝ exp − (s − m)T M−1 (s − m) 2

to denote a Gaussian distribution, scaled by an arbitrary constant that is not a function of the argument of the function. Here, s is the argument of the function and M and m are parameters. Define the column vector -T , hi = hi (−1) hi (0) hi (1) , then the observation in cell i can be expressed in vector form as yi = hTi si + zi . The factorization of the joint distribution again has the form in (4.12). The corresponding factor graph is shown in Figure 4.6. Since the si s and yi s are jointly Gaussian, all of the messages turn out to be Gaussian distributions. Thus the actual messages will be the mean vector and covariance matrix pairs. Before deriving the messages, let us present some useful results for the Gaussian distribution. Remember that in our notation the distribution is scaled by

93


p1|0 (s1 ) f (s1 )

s1

p1|1 (s1 ) p2|1 (s2 ) f (s2 |s1 )

f (y1 |s1 )

s2

p2|2 (s2 ) p3|2 (s3 ) f (s3 |s2 )

f (y2 |s2 )

s3

p3|3 (s3 ) p4|3 (s4 ) f (s4 |s3 )

f (y3 |s3 )

s4

f (y4 |s4 )

Figure 4.6. Factor graph for a hidden Markov model for n = 4 used for the linear cellular array with Gaussian inputs. Dashed lines show boundaries between cells. The computations of the nodes within a cell are done by the base station of that cell. Any message passing through a cell boundary corresponds to an actual message passing between corresponding base stations. an arbitrary constant. N (s; M, m) = N (m; M, s), −1

(4.24) −1 T

−1

, A (m − s)),

(4.25)

−1 −1 −1 −1 M3 = (M−1 1 + M2 ) , m3 = M3 (M1 m1 + M2 m2 );

(4.26)

N (As + b; M, m) = N (s; A MA

N (s; M1 , m1 )N (s; M2 , m2 ) = N (s; M3 , m3 ), where −1

N (s; M1 , m1 )N (s; M2 , m2 )

= N (s; M4 , m4 ),

where .

−1 −1 −1 −1 M4 = (M−1 1 − M2 ) , m4 = M4 (M1 m1 − M2 m2 );

N (s; M1 , m1 )N (As; M2 , t) ds = N (t; AM1 AT + M2 , Am1 ).

(4.27) (4.28)

We know that the messages are going to be Gaussian. Denote them by pi|i−1 (si ) = N (si ; Mi|i−1 , ˆsi|i−1 ), pi|i (si ) = N (si ; Mi|i , ˆsi|i ).

(4.29) (4.30)

From the observation node, we have the message f (yi |si ) = N (yi ; σ 2 , hTi si ). From (4.6), the message from variable node si to factor node f (si+1 |si ) is pi|i (si ) = pi|i−1 (si )f (yi |si ) *

+ * 0+ 1/ 1 1 T 2 ˆ ∝ exp − (si − ˆsi|i−1 )T M−1 (s − s ) exp − (y − h s ) i i i i|i−1 i i|i−1 2 2 σ2 + * / 0 1 si|i ) , ∝ exp − (si − ˆsi|i )T M−1 i|i (si − ˆ 2

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Turbo base stations

where

Mi|i =

M−1 i|i−1

1 + 2 hi hTi σ

−1

ˆsi|i = Mi|i M−1 si|i−1 + i|i−1 ˆ

,

(4.31)

1 hi yi . σ2

Thus the pair (4.31)–(4.32) is the message from si to f (si+1 |si ). This equations is another form of the more familiar Kalman filter correction [27]: Mi|i = I − Ki hTi Mi|i−1 , ˆsi|i = ˆsi|i−1 + Ki yi − hTi ˆsi|i−1 ,

(4.32) pair of update (4.33) (4.34)

where Ki =

Mi|i−1 hi . σ 2 + hTi Mi|i−1 hi

The equivalence of (4.31)–(4.32) and (4.33)–(4.34) can be shown using inversion of matrix sum identities. Next, let us obtain the message function pi|i−1 (si ) using (4.7): . pi|i−1 (si ) = f (si |si−1 )pi−1|i−1 (si−1 ) dsi−1 . (4.35) Note that the summation in (4.7) becomes integration in (4.35) since we are dealing with continuous variables. From (4.23) and (4.30): . T pi|i−1 (si ) = N (si ; pbf bf , Af si−1 )N (si−1 , Mi−1|i−1 , ˆsi−1|i−1 ) dsi−1 ∝ N (si ; pbf bf

T

T

+ Af Mi−1|i−1 Af , Af ˆsi−1|i−1 ),

(4.36)

where (4.36) is due to (4.24) and (4.28). As a result, the message function pi|i−1 (si ) is represented by the mean-covariance pair: ˆsi|i−1 = Af ˆsi−1|i−1 , fT

Mi|i−1 = pbf b

(4.37)

+ Af Mi−1|i−1 A

fT

.

(4.38)

Equations (4.37)–(4.38) are Kalman filter prediction updates [27]. Note that the message pi|i (si ) is the posterior distribution of si given {y1 , . . . , yi }, and pi|i−1 (si ) = f (si |y1 , . . . , yi−1 ). We desire the posterior distribution of si given all observations: f (si |y1 , . . . , yn ). For that purpose, form a graph similar to Figure 4.6 but in the backward direction: states are ordered from sN to s1 and connected by the transition nodes f (si−1 |si ), where [39] T

f (si−1 |si ) = N (si−1 ; pbb bb , Ab si ), ⎡ ⎤ ⎡ ⎤ 0 0 0 1 Ab = ⎣1 0 0⎦ , bb = ⎣0⎦ . 0 1 0 0


95

For the backward graph, denote the message from factor node f (si |si+1 ) to variable node si by pi|i+1 (si ) = N (si ; Mi|i+1 , ˆsi|i+1 ), which will be the posterior distribution of si given {yi + 1, . . . , yn }. Combination of the backward message pi|i+1 (si ) with the forward message pi|i (si ) to obtain f (si |y1 , . . . , yn ) can be done as follows: f (si |y1 , . . . , yn ) ∝ f (si , y1 , . . . , yn ) = f (y1 , . . . , yi |si , yi+1 , . . . , yn )f (si , yi+1 , . . . , yn ) ∝ f (y1 , . . . , yi |si )f (si |yi+1 , . . . , yn )

(4.39) −1

∝ f (si |y1 , . . . , yi )f (si |yi+1 , . . . , yn )f (si ) = pi|i (si )pi|i+1 (si )f (si )−1

= N (si ; Mi|i , ˆsi|i )N (si ; Mi|i+1 , ˆsi|i+1 )N (si ; pI, 0)−1 −1

(4.40)

= N (si ; M3 , m3 )N (si ; pI, 0)

(4.41)

= N (si ; Mi , ˆsi ).

(4.42)

Equation (4.39) is due to the fact that given si , {y1 , . . . , yi } and {yi+1 , . . . , yn } become independent. In (4.40) the fact that the prior distribution of si is zeromean Gaussian with covariance pI is used. Equation (4.41) is from (4.26), where −1 −1 M3 = (M−1 i|i + Mi|i+1 ) ,

(4.43)

m3 = M3 (M−1 si|i + M−1 si|i+1 ). i|i ˆ i|i+1 ˆ

(4.44)

Equation (4.42) is from (4.27), where −1 −1 Mi = (M−1 3 − p I) ,

ˆsi =

(4.45)

Mi (M−1 3 m3 ).

(4.46)

Combining (4.43)–(4.46), we obtain the result Mi =

1 −1 M−1 i|i + Mi|i+1 − I p

−1 ,

ˆsi = Mi (M−1 si|i + M−1 si|i+1 ). i|i ˆ i|i+1 ˆ For the one-dimensional cellular network we have seen how message passing algorithms can be applied on the uplink to detect discrete data symbols and estimate Gaussian data symbols. The one-dimensional nature of these models leads to underlying factor graphs without loops and thus to guaranteed convergence of the sumproduct algorithm on these factor graphs. In the sequel, we will see that the situation is quite different when we move to two-dimensional cellular networks.

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Turbo base stations

BS 11

MS 11

BS 12

MS 12

BS 21

MS 21

BS 22

MS 22

BS 31

MS 31

BS 32

MS 32

BS 41

MS 41

BS 42

MS 42

BS 13

MS 13

BS 14

MS 14

BS 23

MS 23

BS 24

MS 24

BS 33

MS 33

BS 34

MS 34

BS 43

MS 43

BS 44

MS 44

Figure 4.7. Rectangular cellular array model. The cells are positioned on a rectangular grid. Each cell has one active MS. The signal transmitted in one cell is received at that cell, and also four neighboring cells (except for edge cells). Dashed lines show boundaries between cells.

4.4

Distributed decoding in the uplink: two-dimensional cellular array model

4.4.1

The rectangular model A model that is more general than the linear array model is the model where BSs are positioned on a two-dimensional grid. For example, consider the rectangular model where the BSs are on a rectangular grid. Again, assume flat fading and orthogonal multiple access channels within a cell. The received signal at the BS of any cell, in any channel, is the superposition of the signal from its own MS, and the signals of the four adjacent cell cochannel users. The positioning of the BSs and MSs is shown in Figure 4.7. For cell (i, j) in the rectangular grid, let xi,j denote the symbol transmitted by the MS, yi,j the signal received at the BS, hi,j (xm ,n ) the channel from mobile (m, n) to BS (i, j), and zi,j additive Gaussian noise. The relationship between the observations yi,j and the transmitted symbols xi,j is expressed as yi,j =

x m , n ∈n y i , j

hi,j (xm ,n )xm ,n + zi,j ,

(4.47)

4.4 Distributed decoding in the uplink: two-dimensional model

BCJR columns

y

APP

97

APP

BCJR rows

Figure 4.8. Iterative implementation of BCJR algorithm along the columns and c 2008 IEEE). rows of the rectangular array ( where ny i , j = {xi,j , xi−1,j , xi+1,j , xi,j −1 , xi,j +1 }

(4.48)

is the set of transmitted symbols that can be heard at BS (i, j). For the cells at the edges of the rectangular network, dummy symbols x0,j , xn +1,j , xi,0 , xi,n +1 are added and the corresponding hi,j (xm ,n ) are set to zero. The goal is again to obtain the global APP p(xi,j |y), where y = {y1,1 , . . . , y1,n , . . . , yn ,1 , . . . , yn ,n } is the set of all observations. It is still possible to obtain exact inference by forming a Markov chain via clustering (e.g., states obtained by clustering along the rows of the two-dimensional array) and then apply the BCJR algorithm, but the complexity grows exponentially with n (the number of columns or rows in the rectangular array) and is intractable as the network size grows. It is possible that the inherent complexity is only polynomial in the network size (we have not investigated this issue) but in any case, we are looking for distributed approaches using message passing between neighboring base stations. Encouraged by the elegance of the implementation of the BCJR algorithm for the one-dimensional array, one can be tempted to use this approach along the columns and rows of a rectangular array in an iterative manner. The APP outputs of the BCJR along one direction will be used as a priori probabilities for the BCJR along the other direction. Thus the global decoder is built as an iterative decoder where the two modules of the iterative decoder are the BCJR in each direction (Figure 4.8 from [5]). The details of this approach, and a discussion of its implementation are in [4]. The idea of running BCJR along the rows and columns of a rectangular cellular array was also proposed for two-dimensional ISI channels by Marrow and Wolf in [35]. Although applying the BCJR algorithm along the rows and columns of the rectangular array seems to work [5, 35], we see that it does not directly exploit the two-dimensional structure of the problem but instead imposes a one-dimensional structure on parts of it. As this is an ad-hoc iterative method, it will result in only an approximation to the desired APPs. However, if we are looking for an approximation of the APP, there is no need to impose the use of the BCJR algorithm which gives the optimum result only if the problem is one-dimensional.

98

Turbo base stations

Thus we can accept an approximate APP and form loopy graphs that reflect the true two-dimensional nature of the problem.

4.4.2

Earlier methods not based on graphs Research has considered distributed global demodulation in two-dimensional cellular channels [53, 57]. In [53], the authors considered BSs computing soft estimates of the symbols, and then sharing and combining them to obtain a final soft estimate. This strategy was compared with BSs sharing channel outputs and performing maximum-ratio combining of the channel outputs. In [57], a reduced complexity maximum-likelihood (ML) decoder was developed, which was motivated as an extension of the Viterbi algorithm which exploits the limited interference structure. Although the general large two-dimensional cellular structure was not treated, it seems that the algorithm, if applied to that structure, would result in increasing complexity per symbol with growing network size. Alternatively, graph-based iterative message passing methods for distributed detection for two-dimensional cellular networks were proposed in [3–5, 50].

4.4.3

State-based graph approach One way to model the two-dimensional case is to adapt the state-based graphical idea from the one-dimensional case. Remember that in a state-based graph, each channel output depends only on one state variable, and everything else in the system is modeled by the transitions among the states. For the one-dimensional case, the states form a Markov chain, but in the two-dimensional case they do not. For cell (i, j), define the state to be si,j = ny i , j ,

(4.49)

where ny i , j is the set of symbols defined in (4.48), upon which yi,j depends, as in yi,j = mi,j (si,j ) + zi,j , where the conditional mean mi,j (si,j ) is a deterministic function of si,j , hi,j (xm ,n )xm ,n . (4.50) mi,j (si,j ) = x m , n ∈n y i , j

It can be observed that the states form a Markov random field, a fact that we will exploit in (4.51). As in the one-dimensional model, the variables in the sum–product algorithm are not the channel input symbols xi,j , but the states si,j . The goal of BS (i, j) is to obtain the APP p(si,j |y), from the marginalization of which it can obtain the APP p(xi,j |y). Let s = {si,j } denote the set of all states. The global function


p(s22 |s12 , s21 ) s22

p(s23 |s13 , s22 )

p(s24 |s14 , s23 )

s23

p(y22 |·)

s24

p(y23 |·)

p(s32 |s22 , s31 ) s32

p(y24 |·)

p(s33 |s23 , s32 )

p(s34 |s24 , s33 )

s33

p(y32 |·)

s34

p(y33 |·)

p(s42 |s32 , s41 ) s42

p(y34 |·)

p(s43 |s33 , s42 )

p(s44 |s34 , s43 )

s43

p(y42 |·)

p(y43 |·)

99

s44 p(y44 |·)

Figure 4.9. Factor graph for the state-based probabilistic model for the rectangular cellular array. Dashed lines show boundaries between cells. The computations of the nodes within a cell are done by the BS of that cell. Any message passing through a cell boundary corresponds to actual message passing between corresponding BSs.

to be marginalized to compute the p(si,j |y) ∝ gi (si ) is g(s) = p(y, s) n n = p(yi,j |si,j )p(si,j |si−1,j , si,j −1 ),

(4.51)

i=1 j =1

where s0,j and si,0 are dummy states: p(s1,j |s0,j , s1,j −1 ) = p(s1,j |s1,j −1 ) and p(si,1 |si−1,1 , si,0 ) = p(si,1 |si−1,1 ). The factor graph for the factorization in (4.51) is depicted in Figure 4.9. Note that this is a loopy graph and hence the sum–product algorithm is not guaranteed to give the exact APP. Nevertheless, we now describe the algorithm which will be observed to provide good performance in practical settings. Uniform prior distributions p(xi,j ) are assumed on the input symbol constellations. Define the

100

Turbo base stations

set of states pi,j = {p1i,j , p2i,j }, where p1i,j = si−1,j , p2i,j = si,j −1 . The system is modeled by transitions from pi,j to si,j . Note that not every transition pi,j → si,j is possible. Similarly to the one-dimensional case, we say that si,j is conformable with pi,j if there is transition from pi,j to si,j , i.e., p(si,j |pi,j ) > 0 for some prior distribution on the xi,j s. The set of all configurations of pi,j that are conformable with si,j will be denoted by pi,j : si,j , and the set of all configurations of si,j that are conformable with pi,j will be denoted by si,j : pi,j . The message computations described next for cell (i, j) can be implemented at BS (i, j), simultaneously in parallel by all BSs. The message from p(yi,j |·) to si,j is µy i , j −s i , j (si,j ) = p(yi,j |si,j ) = CN (yi,j ; m(si,j ), σ 2 ), where CN (y; m, σ 2 ) is the distribution function of the complex Gaussian with mean m and variance σ 2 . This message is computed only once given an observation yi,j at BS (i, j). Next, for convenience, define the following factor nodes corresponding to the conditional distribution functions in the factorization in (4.51): c1i,j : factor node p(si,j +1 |si−1,j +1 , si,j ); c2i,j : factor node p(si+1,j |si,j , si+1,j −1 ); di,j : factor node p(si,j |si−1,j , si,j −1 ). The messages between nodes si,j and di,j are internal calculations in BS (i, j). The message from factor node di,j to variable node si,j , from (4.7), is

µd i , j −s i , j (si,j ) =

p(si,j |si−1,j , si,j −1 )

∼s i , j

=

∝

2 p i , j :s i , j k =1

µp ki, j −d i , j (pki,j )

k =1

p(si,j |pi,j )

pi , j

2

2


k =1


(4.52)


2 p 1i , j p 2i , j

=


101

(4.53)

:s i , j k =1 :s i , j

2

µ ¯p ki, j −d i , j (ski,j ),

(4.54)

k =1

where (4.52) is because p(si,j |pi,j ) is a constant if pi,j is conformable with si,j , as prior distribution of xi,j s is uniform, and in (4.54) µp ki, j −d i , j (pki,j ) µ ¯p ki, j −d i , j (ski,j ) = p ki, j :s i , j

can be considered as a preprocessed message from pki,j to di,j . Note that (4.52) and (4.53) are not, in general, equal because in (4.52) the summation is over p1i,j and p2i,j , which conform with each other as well as with si,j , whereas in (4.53) we also include p1i,j and p2i,j , which do not conform with each other. Specifically, xi−1,j −1 s in p1i,j and p2i,j should be the same for the summation in (4.52), but they may be different in (4.53). The additional terms in (4.53) lead to the simplification in (4.54), which results in a considerable saving in complexity. The message from variable node si,j to factor node di,j , from (4.6), is 2

µs i , j −d i , j (si,j ) = µy i , j −s i , j

µc ki, j −s i , j (si,j ).

(4.55)

k =1

The message from variable node si,j to factor node cki,j for k = 1, 2 is µs i , j −c mi, j (si,j ) = µd i , j −s i , j µy i , j −s i , j µc li , j −s i , j (si,j ),

(4.56)

where l = {1, 2}\k. The message in (4.56) is an actual message from BS (i, j) to the corresponding BS. Finally, we need the message from di,j to pki,j for k = 1, 2, which also should be implemented as an actual message from BS (i, j) to adjacent cells. Using (4.7), p(si,j |pki,j , sli,j )µs i , j −d i , j (si,j )µp li , j −d i , j (pli,j ) µd i , j −p ki, j (pki,j ) = ∼p ki, j

=

µs i , j −d i , j (si,j )

si , j

∝

p li , j

µs i , j −d i , j (si,j )

s i , j :p ki, j

α

p(si,j |pki,j , pli,j )µp li , j −d i , j (pli,j )

p li , j p li , j

µp li , j −d i , j (pli,j )

(4.57) (4.58)

:s i , j :p ki, j

µs i , j −d i , j (si,j )¯ µp li , j −d i , j (si,j ),

(4.59)

s i , j :p ki, j

where l = {1, 2}\k, (4.58) is due to the fact that p(si,j |pki,j , pli,j ) is a constant for all si,j : pki,j and pli,j : si,j . The approximation in (4.59) is similar to (4.53)

102

Turbo base stations

in that we have extra terms in the summation with nonconforming pki,j and pli,j . Combining everything, the approximation (due to loops) of the marginal function gi (si ) is, from (4.8), µs i (si ) = µy i , j −s i , j (si,j )µd i , j −s i , j (si,j )µc 1i , j −s i , j (si,j )µc 2i , j −s i , j (si,j ).

(4.60)

For some related work on state-based method for rectangular grids the reader is referred to [50].

4.4.4

Decomposed graph approach As an alternative to the state-based graph approach, let us remember the signal model in (4.47). It is seen that this model is the same as (4.16) in Example 2 of Section 4.2.2. Therefore, for each observation yi,j , the conditional distribution given the contributing symbols has the same form as (4.17). As the input symbols are independent, the joint distribution of all symbols and observations has the same form as (4.18). Thus, a factor graph, in the form of Figure 4.4 can be obtained for the purpose of obtaining APPs of the symbols. For the rectangular array model, corresponding to cell (i, j), there will be variable node xi,j and factor node yi,j in this graph, and each factor node yi,j will be connected to the variable nodes in the neighborhood: ny i , j defined as in (4.48). Such a graph for the rectangular model in Figure 4.7 is depicted in Figure 4.10. Having the factor graph in Figure 4.10, we can perform message passing as described in Example 2 in Section 4.2.2 in order to obtain estimates of the transmitted symbols (the graph clearly has loops). Equations (4.19) and (4.20) are the x-to-y and y-to-x messages, respectively, except that now we have two indices for each variable, denoting the two-dimensional location of the cell. Any time a message is passed along an edge that crosses a dashed line in Figure 4.10, an actual message passing among corresponding BS is required. At termination, the posterior probability of the transmitted symbol xi,j at cell (i, j) is computed by combining all incoming messages, using (4.21). In addition to its conceptual simplicity, the decomposed graph approach has the advantage that it does not require the regular positioning of the cells. The method can be applied to any irregular network shape, where each cell has an arbitrary number of neighbors in arbitrary directions.

4.4.5

Convergence issues: a Gaussian modeling approach Unlike in the one-dimensional cellular models, where the graphs are trees, we cannot provide definitive convergence results for our two-dimensional cellular models, in general. It is well known that the sum–product algorithm is not guaranteed to converge when there are loops in the graph. This is the Achilles’ heel of our approach to BS cooperation, and it is an area that requires much further study. However, some insights into the convergence properties can be obtained from the Gaussian model, which we consider next.


x1,1

x1,2

p(y1,1 |·) x2,1

p(y1,2 |·)

x4,1

x2,3

p(y2,2 |·)

x3,3

p(y3,2 |·)

x2,4 p(y2,4 |·) x3,4

p(y3,3 |·)

x4,2

p(y4,1 |·)

p(y1,4 |·)

p(y2,3 |·)

x3,2

p(y3,1 |·)

x1,4

p(y1,3 |·)

x2,2

p(y2,1 |·) x3,1

x1,3

x4,3

p(y4,2 |·)

103

p(y3,4 |·) x4,4

p(y4,3 |·)

p(y4,4 |·)

Figure 4.10. Factor graph for the decomposed probabilistic model for the rectangular cellular array model. Dashed lines show boundaries between cells. The computations of the nodes within a cell are done by the BS of that cell. Any message passing through a cell boundary corresponds to actual message passing between corresponding base stations.

In Example 2 in Section 4.2.2, modeling the source symbols xj as circularly symmetric complex Gaussian in (4.16) also leads to a tractable solution. In that case, all yi s and xj s are jointly Gaussian, and also every local function in the factorization in (4.18) is a Gaussian distribution. As a result, the messages on the graph in Figure 4.10 will also be Gaussian. Let the pair (µx j −y i , σx j −y i ) denote the mean-variance pair of the message from xj to yi , and (µy i −x j , σy i −x j ) denote the mean-variance pair of the message from yi to xj . Note that they are both means and variances of the variable xj . Using the properties of complex Gaussian distributions, the mean and variance of the message from yi to xj can be shown to be yi − µy i −x j =

σ2 + σy i −x j =

hi (xl )µx l −y i

x l ∈n y i \{x j }

, hi (xj ) |hi (xl )|2 σx l −y i

x l ∈n y i \{x j }

|hi (xj )|2

(4.61)

.

(4.62)

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Turbo base stations

The mean and variance of the message from xj to yi can be shown to be µπx j σxπj µx j −y i =

k ∈n x j \{i}

1 + σx j ⎛

σx j −y i = ⎝

+

µy k −x j σy k −x j

k ∈n x j \{i}

1 + σxπj

1

,

(4.63)

σy k −x j

k ∈n x j \{i}

⎞−1 1 ⎠ σy k −x j

,

(4.64)

where (µπx j , σxπj ) denotes the prior mean and variance of the symbol xj . At termination, estimates of the mean and variance of the posterior distribution are µy i −x j µπx j + σxπj σy i −x j i µx j = (4.65) 1 , 1 + σx j σy i −x j i −1 1 1 σx j = + . (4.66) σx j σy i −x j i The goal here is to analyze how the means and variances evolve, as the y-to-x message updates in (4.61)–(4.62) and x-to-y message updates in (4.63)–(4.64) are computed iteratively. Next, we provide results from [40] which say that the convergence of the variances is always guaranteed, whereas the convergence of the means is closely related to the spectral radius of an iteration matrix Ω. First, consider the convergence of the variances. Equations (4.62) and (4.64) show that the evolution of the variances is independent of the means or the observations themselves. To simplify notation define: σi,j = σy i −x j . Let the graph be for a system with n input variables {x1 , . . . , xn } and also n output variables {y1 , . . . , yn }. For iteration t define the vector of variances of messages from y to x nodes -T , v(t) = σ1,1 . . . σ1,n σ2,1 . . . σ2,n . . . σn ,1 . . . σn ,n . The following result is proven in [40], and is described in detail (but without proof) in [41]. This result, and the next one, make the simplifying assumption that the variances of all the observation variables (the yi s) are unity. Theorem 4.1 The sequence of vectors v(t) always converges to a unique fixed point for any v(0) , i.e., lim v(t) = v∗ .

t→∞


105

Moreover, the sequence is monotonically decreasing under the initialization (0) σx j −y i = 1. Next, consider the convergence of the means in the updates in (4.61) and (4.63) assuming that the variance messages are fixed to the converged values: v(t) = v∗ . Define µi,j = µy i −x j

(4.67)

and for iteration t , m(t) = µ1,1

...

µ1,n

. . . µn ,1

...

µn ,n

-T

the channel matrix ˜ 1,n , . . . , h ˜ n ,1 . . . , h ˜ n ,n }, ˜ 1,1 , . . . , h ˜ = diag{h H ˜ i,j is the channel coefficient from source xj to observation yi . Let Ω be where h ˜ −1 (Σx − I)H(I ˜ + D(Σf V∗ −1 Σf ) − V∗ −1 )−1 (Σf − I)V∗ −1 , Ω=H

(4.68)

where Σx = diag{1n ×n , . . . , 1n ×n }, V∗ = diag{v∗ }, ⎡ In I n . . . ⎢ .. .. Σf = ⎣ . . In

In

...

⎤ In .. ⎥ , . ⎦ In .

1n ×n is an n × n block of ones, In is the n × n identity matrix, and D(·) is the operator defined as D(A) = diag{A11 , A22 , . . . , An n } for a n × n matrix A. The following theorem provides a necessary and sufficient condition for the convergence of the means. It was proven in [40] where it was shown to follow from Theorem 5.3 in [7]. Theorem 4.2 The sequence of vectors m(t) converges to the fixed point ˜ −1 y m∗ = (I + Ω)−1 H for any m(0) if and only if the spectral radius ρ(Ω) < 1. This theorem confirms that in some scenarios, where the spectral radius condition is not met, the sum–product algorithm will not converge. When the condition is violated it is necessary to switch to another form of preprocessing, perhaps at a lower data rate using SCP – or one can declare an outage. Note that the

106

Turbo base stations

same issue arises for power control algorithms, where instability can also occur if the system loading is too high. Preliminary investigation of practical methods to deal with this issue have been examined in [40], but much further work, both practical and theoretical, is required to characterize properly the conditions of convergence in more general settings, and to determine what to do about lack of convergence when it arises. We have undertaken extensive numerical experiments using different channel parameter values. For a deterministic channel model, where the channel coefficient for a mobile user is 1 to its own BS and α (cross-coupling factor) to an adjacent cell’s BS (symmetric deterministic channel model), we have observed the following for the case of Gaussian symbols: at realistic SNRs less than 30 dB, and cross-coupling factors less than 1/2 (the typical cross-coupling between two adjacent cells is quite low, usually less than 1/2), we have never observed lack of convergence of the sum–product algorithm. However, convergence is not guaranteed at higher levels of the cross-coupling factor, when the SNR is high. Similar convergence problems were also observed for the discrete symbol model, when the deterministic channel described above was utilized. On the other hand, the convergence problems are greatly mitigated when we replace the deterministic channel gains with independent, Rayleigh fading gains with the same means as above. Thus, even if the network is symmetric with respect to average gains, convergence problems almost completely disappear if the instantaneous gains are random (e.g., Rayleigh distributed). From our numerical experiments, we found that when the sum–product algorithm failed to converge, it was typically due to a symmetric network realization of channel coefficients. However, symmetry can be perturbed by noise. If the SNR is sufficiently low, the realizations of noise amplitudes are large enough to perturb the symmetry of the network. On the other hand, when the channel coefficients are modeled as independent random variables (e.g., complex Gaussian), the system lacks symmetry with high probability. In other words, the probability of a realization of h that is symmetric enough to cause failure of convergence is extremely small. In a practical system, the channels of different mobile users are indeed independent, due to the fact that they are located in different cells. The simulations in Figures 4.11–4.13 are for such a scenario: in each simulation realization, independent samples of channel coefficients hi,j (m, n) are generated. In those figures, no error floors are observed, even for very low uncoded bit error rates. There may still be an error floor, but it is too low to be detected. Note that if there were a set of channel realizations that always cause convergence failure, irrespective of SNR, then the probability of such a set must be very small, as it would provide an error floor at this probability. We emphasize that here convergence means the convergence to the true posterior probabilities of the symbols, not to the true values of the symbols. The true APP can still result in an incorrect estimate of the symbol, however if the true APP can be attained, the lowest possible error rate is obtained.


107

0

10

SP: state−based SP: decomposed Ind. optimum SU lower bound −1

10

−2

Pb

10

α=0.5, SNR = 7 dB −3

10

α=1, SNR = 5 dB −4

10

α=0.5, SNR = 11 dB

−5

10

0

4

8

12 16 20 Number of serial real number passings

24

28

Figure 4.11. Probability of error of the algorithms and the single-user lower bound as a function of the number of serial real number transmissions between c 2008 IEEE). BSs for node (2, 2) of a 4 × 4 network (

In the next section, we present some numerical results that indicate the relative performance of the different schemes we have proposed so far.

4.4.6

Numerical results We now present some numerical results [5] comparing the aforementioned approaches for rectangular cellular arrays given in Figures 4.11, 4.12, and 4.13. In these simulations, a fading channel model is considered where each hi,j (m, n) is complex Gaussian distributed with zero mean and variance 1 if (m, n) = (0, 0) and variance α2 otherwise. Thus α2 represents the average power of the intercell interference (ICI) from each neighbor. The additive noise zi,j is complex Gaussian with zero mean and variance σ 2 . The signal to noise ratio (SNR) is defined as 1/σ 2 . The transmitted symbols are binary and from the set {−1, 1}. For comparison, the performance of individually optimum multiuser detection and the single-user lower bound is also given. The single-user lower bound is the performance of a system with a single user (with no interference) and multiple receiving base stations. Each message passing requires an amount of serial real number transmissions among base stations, and in Figure 4.11 the performance is shown as a function of those transmissions. Figure 4.11 illustrates that performance very close to the interference-free case can be achieved after 3–4 message passing steps, with the decomposed model outperforming the clustered approach. In Figure 4.12, the performance of the optimum receiver for a base station that cannot communicate with other base stations is also shown. For the cooperative

Turbo base stations

0

10

α =1 α =0.5

−1

10

α =0.25 α=0 −2

10

Pb

α=0.25 −3

10

α=0.5 α=1

Single−cell processing BCJR BP−clustered BP−decomposed Ind. optimum SU lower bound

−4

10

−5

3

0

5

10

15

20

SNR (dB)

Figure 4.12. Probability of error of the algorithms and the single-user lower c 2008 IEEE). bound as a function of the SNR for cell (2, 2) of a 4 × 4 network (

0

0

10

10 BCJR SP: state−based SP: decomposed SU lower bound

SP: state−based SP: decomposed SU lower bound

−1

−1

10

10

−2

Pb

Pb

108

10

−3

10

−2

10

−3

α = 0.5

10

α =0.5, SNR = 9 dB

−4

10

−5

−4

0

5 SNR (dB)

10

10

0

4 8 12 16 20 24 28 Number of serial real number passings

Figure 4.13. Probability of error of the algorithms and the single-user lower bound as a function of the SNR and as a function of number of real number c 2008 IEEE). transmissions in series for cell (10, 10) of a 20 × 20 network ( cases, the values plotted are the error probabilities after enough iterations have occurred to satisfy the convergence criterion. As the ICI power increases, it is observed that the distributed decoding algorithms not only can handle the ICI, but they can also exploit the extra energy and diversity provided by it.


109

The error rate performance of the sum–product algorithms on the clustered and decomposed graphs is very close to the single-user lower bound at low error probabilities. Thus, we observe a very large gain is possible from local message passing to reduce the ICI. The BCJR algorithm, implemented iteratively on the columns and rows of the rectangular array, does not perform as well as the sum–product algorithms; a 0.5 dB gap is observed. In Figure 4.13 performance is shown for a larger network. We observe that the performance on this 20 × 20 network is essentially the same as in the smaller network of size 4 × 4. The observation that the speed of convergence remains roughly the same is explained by the fact the ICI is a local effect even though the overall network size is growing.

Simplification of messages sent by factor nodes In the decomposed graph approach, there are two types of computations: computation of variable-to-factor node messages in (4.19), and the computation of factor-to-variable node messages in (4.20). Upon examining these two types of messages, one sees that the main cause of computation complexity of this approach is the computation of the latter: factor-to-variable node messages. In [9], a simplification of the messages sent by the factor nodes was proposed. The key idea here is to recognize that the message µy i −x j (xj ) is the individually optimal soft MUD of xj given the observation yi and the prior distributions of ny i \{xj }. If this is computationally unacceptable, suboptimal MUD methods can be substituted for this purpose. An arbitrary choice of MUD may, however, not be suitable. The MUD should be able to incorporate the prior distributions of ny i \{xj } to produce a posterior distribution of xj . If the MUD uses prior distributions of all ny i , then the prior information xj should be canceled in the message to xj . This is because the information received from a node is not fed back to that node in factor graph methods. In [9], an iterative groupwise MUD was considered.

4.4.7

Ad-hoc methods utilizing turbo principle One approach to BS cooperation is to have the BSs share their soft (or hard) bit estimates and reconstruct the interference components at the output. After subtracting the interference components from the observation, the BSs repeat the decoding. This approach was suggested in [37] for a two-cell model. In this model, the received signal at a BS comprises a desired signal component and an interference component from other-cell mobiles. For a convolutionally coded system, the BSs perform single-user decoding, ignoring the interference component completely. Then the soft bit estimates are shared between the BSs, which use this information to reconstruct and subtract the interference components from their received signals. Repeating this procedure, an iterative “turbo” BS

110

Turbo base stations

cooperation method is obtained. The performance of this method was investigated for various quantization strategies and constellation sizes in [37]. Note, however, that this iterative approach is ad hoc, and is not based on graph algorithms. The turbo principle and sharing soft information with the adjacent BSs was also considered in [28]. Again, coding is included in the interference reconstruction and cancellation in [28]. The turbo principle is utilized for a general cellular network. The BS cooperation methods in [28, 37] are not explicitly based on algorithms on graphs. They are ad-hoc implementations of the turbo principle among BSs which exchange soft decisions in order to improve their decisions.

4.4.8

Hexagonal model All of the methods described for the rectangular cellular array model can be extended to the more realistic hexagonal array model. The positioning of the cells is shown in Figure 4.14: for example, the decomposed factor graph for this model is as in Figure 4.15.

4.5

Distributed transmission in the downlink So far our focus has been on BS cooperation for the uplink of a wireless communication network. In this section, we will shift our attention to the downlink of a wireless network. The scenario where a BS simultaneously transmits independent information to multiple uncoordinated users over the wireless channel can be classified as a broadcast channel (BC) . We will first summarize the main information-theoretic results for a MIMO (vector) BC and present some practical transmission techniques proposed in the literature. Since wireless communication networks for commercial applications are multicellular, we will then briefly discuss the impact of ICI and some possible solutions. Finally, we will present turbo BS cooperation in the downlink as a practical approach for providing high spectral efficiency in the presence of ICI.

4.5.1

Main results for the downlink of a single-cell network Consider the downlink of a single-cell MIMO network where a BS with n antennas is transmitting information to m users each with a single antenna. Assuming the channel is flat fading with no mobility, the vector of received signals at the users is modeled as y = Hx + z,

(4.69)

, -T where y = y1 y2 · · · ym denotes the vector of received signals at the -T , users, x = x1 x2 · · · xn denotes the transmitted signal vector, and H is the m × n channel matrix with the (i, j) entry representing the channel gain

111

4.5 Distributed transmission in the downlink

BS 11

BS 12

MS S 11 BS 21

MS 12 BS 22

MS 21 BS 31

MS 51

MS 52

MS 35 BS 44

MS 43 BS 52

BS 35

MS 34 BS 43

MS 42 BS 51

MS 24 BS 34

MS 33 BS 42

MS 41

BS 24

MS 23 BS 33

MS 32 BS 41

MS 13 BS 23

MS 22 BS 32

MS 31

BS 13

MS 44 BS 53

MS 53

Figure 4.14. Hexagonal cellular array model. The cells are positioned on a hexagonal grid. Each cell has one active MS. The signal transmitted in one cell is received at that cell, and also six neighboring cells (except for edge cells). Dashed lines show boundaries between cells. from the jth antenna of the BS to the ith user. Let hi denote the 1 × n channel vector for user i. Then the (i, j) entry of H can be written hi (j). The elements of the noise vector, z, are assumed to be independent zero-mean Gaussian distributed random variables. Unless stated otherwise, we assume that both the base stations and the users have perfect CSI. This system model is classified as a BC in network information theory [14]. Even though the capacity region of a general BC is still an open problem, for the special case of a degraded BC superposition coding [10] is shown to achieve the capacity region. However, when the transmitter has more than one antenna, i.e., n > 1, the system can in general no longer be modeled as a degraded BC. Rather, the capacity region of this vector Gaussian BC is shown to be equal to the dirty paper coding (DPC) [12] rate region [56]. DPC is a nonlinear coding technique based on the observation that if the Gaussian interference is known noncausally at the transmitter but not the receiver, under a transmit power constraint, the effect of the interference can be precanceled. In the case of a vector Gaussian BC

112

Turbo base stations

x11

x12

x13

p(y1,1 |·)

p(y1,2 |·)

p(y1,3 |·)

x21

x22

x23

x24

p(y2,1 |·)

p(y2,2 |·)

p(y2,3 |·)

p(y2,4 |·)

x31

x32

x33

x34

x35

p(y3,1 |·)

p(y3,2 |·)

p(y3,3 |·)

p(y3,4 |·)

p(y3,5 |·)

x41

x42

x43

x44

p(y4,1 |·)

p(y4,2 |·)

p(y4,3 |·)

p(y4,4 |·)

x51

x52

x53

p(y5,1 |·)

p(y5,2 |·)

p(y5,3 |·)

Figure 4.15. Factor graph for the decomposed probabilistic model for the hexagonal cellular array model. Dashed lines show boundaries between cells. The computations of the nodes within a cell are done by the BS of that cell. Any message passing through a cell boundary corresponds to actual message passing between corresponding BSs.

under perfect CSI the BS can precalculate noncausally the interference created by one user to the other. In this case for an arbitrary ordering of the users, using the DPC technique it is possible to encode the information of a user such that it is not affected by the interference caused by previously encoded users. The capacity region of a vector Gaussian BC described in (4.69) under transmit covariance constraint Q = E[xxH ] S for positive semidefinite S (where A B implies that B − A is a positive semidefinite matrix) is given as [56] C = qhull

3

4 R(π, S, σ , H) , 2

(4.70)

π ∈Π

where qhull denotes the convex closure of the sets, π is an arbitrary permutation of user indices, Π corresponds to the set of all possible user permutations, σ 2

113


denotes the variance of the elements of the noise vector z, and " i " 2 hi ( l=1 Bπ (l) )hH " i +σ 2 R(π, S, σ , H) = (R1 , . . . , Rm )"Ri = log H 2 " hi ( i−1 l=1 Bπ (l) )hi + σ for some {B1 , . . . , Bm } such that Bi 0 ∀i and S

m

4 Bi ,

i=1

(4.71) where hi is the 1 × n channel vector for user i and π(l) denotes the index of the user encoded in the lth position. Correspondingly, the sum capacity of the vector Gaussian BC under total transmit power constraint P is computed as Csum =

max

Q :Q 0, tr(Q )≤P

log(|σ 2 Im + HQHH |),

(4.72)

where Im denotes an identity matrix of size m, | · | denotes a matrix determinant and tr(·) denotes the trace operator. In [24] it was shown that CSI at the transmitter is essential in achieving the capacity gains of a vector Gaussian BC and at high SNR, with perfect CSI at the BS, the sum capacity scales linearly with n provided that m > n. The capacity achieving transmission strategy is a combination of nonlinear DPC and linear precoding (beamforming). The difficulties in implementing a practical DPC encoder have led to most attention being focused on suboptimal linear precoding schemes. In linear precoding the user data symbols are mapped to the transmitted signal vector via x = Td,

(4.73)

where d is the m × 1 vector of data symbols with dj , the data symbol intended for user j, taken from a finite constellation with E[|dj |2 ] = 1 and where the ith column of the n × m beamforming matrix, ti , is the beamforming vector for user i. It should be noted that the power allocated to the ith user is given by P i = tH i ti . One approach for dealing with multiuser interference is to use zero-forcing (ZF) beamforming, where T satisfies HT = D with D being a diagonal matrix. One solution is T = HH (HHH )−1 D,

(4.74)

where D is determined according to the power constraint. The drawback of ZF beamforming is that transmit power might not be used as efficiently when attempting to cancel multiuser interference completely. An alternative linear precoding scheme is regularized channel inversion (RCI) where the beamforming matrix is of the form T = HH (HHH + βI)−1 D,

(4.75)

114

Turbo base stations

where D is determined according to the power constraint and β is a regularization parameter. For small β the RCI beamformer approaches the ZF beamformer while for large β the RCI beamformer tends towards the maximal ratio combining beamformer, the beamformer that maximizes the received signal strength while ignoring the resultant interference. The power allocation to users is done based on an optimization criterion under a power constraint. Optimization problems considered in the literature typically include maximization of the sum rate under a total power constraint and minimization of the total transmit power under individual minimum rate requirements for each user. However, a total transmit power constraint might result in an unbalanced power output over the transmit antennas, which is undesirable in practical systems since each antenna is limited by the linear region of the power amplifiers in its own RF chain. Power allocation based on more practical per antenna power constraints has been considered [60]. Optimization problems involving RCI and related beamformers are challenging since the beamformer vectors of the users are coupled. An alternative design criterion is to maximize the signal-to-leakage-and-noise ratio (SLNR), where leakage refers to the interference caused by the user considered to other users [46]. Leakage-based precoding is attractive since the optimization problem becomes decoupled. There are several works proposing practical nonlinear precoding techniques based on the DPC idea [16, 25, 31]. These works mainly use vector quantization or trellis/lattice precoding approaches to achieve a performance close to DPC.

4.5.2

Main results for downlink of a multicellular network In a multicellular network where several BSs simultaneously serve the users in their respective cells, cochannel interference is the major performance limiting factor. This is especially true for users near cell boundaries. This communication scenario is referred to as the interference channel [2]. The capacity region of a general interference channel is still an open problem. There are some results for the extreme cases of strong interference [13] and weak interference [6]. There are also several inner and outer bounds, the best-known inner bound for discrete memoryless interference channels being the Han–Kobayashi bound [22]. As discussed in Section 4.1, the traditional method for mitigating cochannel interference in multicellular networks has been to use frequency planning such that neighboring cells use different frequency bands for transmission. If a sufficiently low frequency-reuse factor is used, one can ignore the effect of cochannel interference and the communication scenario is reduced to a number of independent single-cell downlink problems. However, as the data rate requirements for next generation wireless networks increase, it has become evident that new paradigms to mitigate cochannel interference are required. In order to increase the spectral efficiency of the system a frequency-reuse factor of 1 can be used, i.e., the whole frequency band is utilized simultaneously


115

in every cell. However, this results in a reduction in the achievable data rates due to interference, especially for users near cell edges. At this point BS cooperation in the downlink is an attractive solution which actually takes advantage of the interference to increase the spectral efficiency of the system. Assuming that the BSs are connected to each other with high capacity links over the backhaul, the cooperative system can be viewed as a virtual MIMO BC with macrodiversity, i.e., transmit antennas are distributed geographically. In that case the problem is reduced to downlink transmission in a single-cell network as discussed in Section 4.5.1, the only difference being that the transmission schemes have to be implemented in a distributed manner. Several works have considered simple and suboptimal linear precoding schemes for the cooperative downlink. In [18], performance gains of cooperative zeroforcing beamforming were analyzed. In [26] several linear precoding techniques for downlink BS cooperation were compared in terms of sum rate per cell in the asymptotic regime. Most of the literature on downlink BS cooperation assumes that the backhaul is very high capacity. In [36], however, a finite capacity backhaul was considered and the performances of several transmission schemes involving DPC compared. Another assumption made in most of the literature is that the BSs can perfectly synchronize their transmissions. In practice, network-wide synchronization is very difficult to achieve. In [62] it was demonstrated that even though BSs can perform timing advancement perfectly such that the transmissions from different BSs arrive at the user at the same time, the interference is inevitably asynchronous. This asynchronicity causes significant performance degradation for linear precoding techniques. The techniques considered are then modified to better handle asynchronous interference.

4.5.3

BS cooperation schemes with message passing As we have highlighted previously, cooperative schemes that can be implemented in a distributed manner offer several advantages over schemes requiring a central processing unit. Firstly, distributed schemes are more robust since they do not have a central processing unit as a single point of failure. Secondly, they are more scalable since schemes requiring a central processing unit require new BSs to be connected to the central processing unit as the network expands. Therefore it is of great interest to develop cooperative transmission and resource allocation schemes that only require local information exchange between BSs. In this section, we discuss several iterative BS cooperation algorithms that require information exchange between BSs. We first focus on distributed beamforming and power allocation schemes in the literature. We then present a graphbased approach that requires only local information exchange between BSs.

Distributed beamforming and power allocation schemes In [15] an iterative algorithm for computing the optimal beamforming vectors and power allocation was presented for a cooperative multicellular system. The

116

Turbo base stations

algorithm iteratively finds the solution of the following optimization problem: minimize

b

αj tr(TH j Tj ),

(4.76)

j =1

subject to: Γi ≥ γj ,

i = 1, 2, . . . , m,

(4.77)

where Tj is the n × mj beamforming matrix used at the BS in the jth cell with mj users, b is the number of BSs (cells) in the network each with n transmit antennas, αj is the weighting factor of the transmit power of the jth BS, γj denotes the target SINR constraint for user i, and Γi is the SINR of user i expressed as Γi = m k =1 k = i

2 |hi,j (i) tH j (i),i |

.

(4.78)

2 2 |hi,j (k ) tH j (k ),k | + σ

In (4.78) hi,j denotes the 1 × n channel vector between user i and BS j, j(i) denotes the index of the cell at which user i is located, tH j (i),i is the beamforming 2 vector used for user i by the BS in its cell, and σ is the variance of the Gaussian noise at the user i. Note that in this scheme BSs do not jointly transmit data to all the users in the network, rather each BS transmits data to the users in its cell. However, the beamforming vectors used by BSs are jointly chosen to achieve the target SINRs of the users, taking the ICI into account while minimizing the weighted transmit power. The iterative algorithm utilizes uplink–downlink duality by solving the Lagrangian dual of the optimization problem. Alternatively, in [11] an iterative joint transmission and power allocation scheme was proposed. In the joint transmission scheme considered, a multicell precoding approach is employed where the data of each user are available at all BSs and all BSs simultaneously serve each user using a beamforming vector. In this case the transmitted signal vector at BS j is expressed as xj = Tj d, where d is the data vector of all the users in the network and the ith column of beamforming matrix Tj is the beamforming vector used by BS j for user i. The optimization problem of maximizing the sum rate of the users under individual transmit power constraints at each BS is difficult to implement in a distributed manner and requires channel knowledge to be shared by all BSs. As a result, the authors proposed a heuristic beamforming and power allocation scheme that is fully distributed and requires only statistical channel knowledge. The scheme utilizes the leakage-based beamforming approach described in Section 4.5.1 to simplify the optimization of the beamforming vectors. Furthermore, the beamforming vectors were selected to maximize the average SLNR averaged over channel realizations. The power allocation proposed is also heuristic, allocating more of the transmit power to the user with the best channel gain.


117

In [61], an iterative beamforming scheme for multicellular networks is proposed. The system model assumed is similar to the one in [15], where BSs do not employ multicell precoding, each BS serves a single user in its cell using a beamforming vector and the beamforming vectors are chosen such that observed ICI is taken into account. The proposed scheme can be implemented in a distributed manner as it only requires local channel knowledge. The idea is to select the beamforming vector for each BS as a linear combination of the zero-forcing beamformer and maximum ratio combining beamformer (which maximizes the received signal power ignoring the interference generated at other users). The combining weights are iteratively updated based on feedback from the users, until a Pareto optimum point is reached.

Cooperative beamforming based on factor graphs We now present a cooperative downlink beamforming approach that can be implemented in a truly distributed manner based on message passing on graphs. We will first demonstrate how the downlink beamforming problem can be formulated as a virtual LMMSE estimation problem [42]. Once this is done we will be able to make use of the message passing algorithms developed for the uplink in the earlier parts of this chapter. We focus on a cooperative downlink beamforming scenario where a cellular network with n cells employs an orthogonal multiple access scheme within each cell so that users do not experience intracell interference. However, since a frequency reuse factor of 1 is used, users will experience interference from neighboring cells. For simplicity, it is assumed that each BS and user has only one antenna. The vector of received signals at the users is as given in (4.69) where the data vector of the users is mapped to the transmitted signal vector using joint linear precoding as in (4.73). We wish to implement regularized channel inversion beamforming as discussed in Section 4.5.1. Define ˆ = HH (HHH + βI)−1 , T

(4.79)

where β is a regularization parameter [45], and the beamforming matrix is written as ˆ T = TD.

(4.80)

The diagonal matrix D denotes the power allocation matrix whose diagonals correspond to power allocated to the corresponding user under a given power (total or per BS) constraint. ˆ = Dd, the transmitted signal x = T ˆ ˆd The key observation is that defining d can be seen as the LMMSE estimate of some vector u under the signal model ˆ = Hu + w, d

(4.81)

where u and w are n × 1 vectors of i.i.d. random variables with zero mean and variance 1 and β, respectively. Note that u and w have no physical relationship

118

Turbo base stations

with the original beamforming problem and also that the problem in (4.81) is quite different to the uplink–downlink duality concept used to simplify the downlink problem [55]. With the observation that the downlink beamforming problem can be seen as a virtual LMMSE estimation problem, one can employ distributed LMMSE estimation techniques such as the distributed Kalman smoothing algorithm described in Section 4.3.2 for one-dimensional cellular networks and techniques based on the sum–product algorithms for two-dimensional cellular networks presented in Section 4.4.5. We first consider the one-dimensional linear cellular array depicted in Figure 4.1 which models the communication scenario with BSs placed evenly on the side of a highway or subway tunnel or access points along a corridor. The channel matrix entries hi,j are of the form hi,j =

hi (k),

j = i + k,

0,

|i − j| > 1,

(4.82)

where i, j ∈ {1, 2, . . . , n} and k ∈ {−1, 0, +1}. One can take advantage of the local connectivity of the network to implement a distributed beamforming algorithm. Assuming that appropriate power allocation is already performed, the ˆ is treated as the observation vector from which the transdata symbol vector d mitted signal vector x is obtained as the LMMSE estimate of u. Due to the Markov structure of the problem, one can apply the message passing algorithm described in Section 4.3.2 for the uplink problem with Gaussian input -T , symbols. Defining the state vector for cell i as si = ui−1 ui ui+1 , the statespace model is si+1 = Af si + bf ui+2 , b

b

si−1 = A si + b ui−2 , ˆ i si + wi , î = h d

(4.83) (4.84) (4.85)

f b f b î = are defined in Section 4.3.2, h ,where A , A , b - , and b with u0 = un +1 = h1 (−1) = hn (+1) = 0. Running hi (−1) hi (0) hi (1) a forward and backward Kalman estimator based on this state-space model and combining the two estimates, we obtain a forward–backward beamforming algorithm for the cooperative downlink. Assuming the virtual data vector u is Gaussian distributed (an assumption we are free to make since u does not have a physical meaning), the LMMSE ˆ i.e., the conditional mean vector of the jointly Gaussian ˆ = E[u|d], estimate is u ˆ As a result, BS i can find the signal that it should conditional density f (u|d). ˆ using the transmit by computing the mean of the marginal distribution, f (ui |d), sum–product algorithm described in Section 4.3.2 running on the factor graph depicted in Figure 4.6. The steps of the algorithm are summarized below [43].


119

Forward-backward cooperative downlink beamforming algorithm

r Initialization: The BSs at the two edges of the cellular array compute the mean vector and the covariance matrix of the distribution information, (ˆsi|i , Mi|i ) for i = 1 and n, as ˆ H (h î h ˆ H + β)−1 dî ˆsi|i = h i i ˆ H (h î h ˆ H + β)−1 h î , Mi|i = Îi − h i

where

⎡

0 Î1 = ⎣0 0

0 1 0

(4.86) (4.87)

i

⎡

⎤ 0 0⎦ , 1

1 În = ⎣0 0

⎤ 0 0⎦ . 0

0 1 0

(4.88)

r Pass the estimates: BS i, i ∈ {1, . . . , n} computes the forward and the backward estimates as the required information becomes available as ˆsfi+1|i = Af ˆsfi|i ,

(4.89)

Mfi+1|i = Af Mfi|i Af

T

T

+ [i = n]bf bf ,

ˆsbi−1|i = Ab ˆsbi|i ,

(4.90) (4.91)

Mbi−1|i = Ab Mbi|i A

bT

bT

+ [i = 1]bb b

,

(4.92)

where ˆsf1|1 = ˆs1|1 and ˆsbn |n = ˆsn |n are described in (4.86). Then message (ˆsfi+1|i , Mfi+1|i ) is passed to the neighboring BS on the right and (ˆsbi−1|i , Mbi−1|i ) is passed to the neighboring BS on the left. r Correct the estimates: BS i, i ∈ {1, . . . , n} corrects the received forward and backward estimates using the observation dî as ˆ i ˆsf ), ˆsfi|i = ˆsfi+1|i + kfi (dî − h i+1|i Mfi|i

= (I3 −

f ˆ kfi h)M i+1|i

(4.93) (4.94)

with kfi

ˆH Mfi+1|i h = ˆ f h ˆH β + hM

(4.95)

i+1|i

and ˆ i ˆsb ), ˆsbi|i = ˆsbi−1|i + kbi (dî − h i−1|i

(4.96)

b ˆ Mbi|i = (I3 − kbi h)M i−1|i

(4.97)

ˆH Mbi−1|i h . ˆ b h ˆH β + hM

(4.98)

with kbi =

i−1|i

120

Turbo base stations

r Combine the estimates: Having computed both ˆsf and ˆsb , they are comi−1|i i|i bined using

ˆsi = Mi (Mfi|i )−1 ˆsfi|i + (Mbi−1|i )−1 ˆsbi−1|i , −1 Mi = (Mfi|i )−1 + (Mbi−1|i )−1 − Îi ,

(4.99) (4.100)

where Îi = I3 for n = 2, . . . , n − 1 and Î1 and În are defined in (4.88). The transmitted signal from the ith BS, xi , is set to be the middle element of the vector ˆsi . It should be pointed out that the algorithm described above has a fully distributed nature requiring only local information exchange between the BSs. Prior to running the algorithm, however, the power allocation to users is assumed to have been done (D is known), and this might well require network-wide knowledge of quantities such as the channel gains. Fortunately, since the channel gains typically change much more slowly than the data symbols, global sharing of the network knowledge might still be feasible at this slower time scale. Another point we would like to emphasize is that, as stated in Section 4.3.2, since the factor graph depicted in Figure 4.1 is free of loops, the message passing algorithm described above is guaranteed to converge to the optimal solution. It should further be noted that the delay experienced by the BSs at the edges of the cellular array grows linearly with the size of the array. In fact, the precoding delay experienced by BSs is location-dependent with the minimum delay experienced by the BS in the middle of the array. In [43] a suboptimal limited extent distributed beamforming algorithm was proposed based on the observation that due to the local connectivity structure of the channel, the information sent by BS i is expected to be less important for BS j if |i − j| is sufficiently large. Therefore, one can achieve a fixed delay, if the extent of the information exchange between BSs is limited. In the proposed limited extent beamforming algorithm, each BS starts by computing a ‘self-estimate’ based on dî using (4.86) and (4.87). Then this information is shared with both neighbors and received estimates are corrected using forward and backward correction equations (4.93)–(4.98). After τ phases of information exchange between the BSs, forward, backward and selfestimates are combined and the middle element of the state vector ˆsi is then an approximation to xi . With this algorithm, the precoding delay experienced by all BSs is τ . Numerical results in [43] demonstrate the clear tradeoff between the performance and the precoding delay. Finally, we will discuss the extension of the proposed distributed beamforming algorithm to two-dimensional networks. As an example, we will consider a hexagonal network with n = 7 cells, a special case of the hexagonal network depicted in Figure 4.14. As in the one-dimensional linear array case, the downlink beamforming problem can be posed as the virtual LMMSE problem of estimating a virtual ˆ Assuming the virtual data vector data vector u from the observation vector d. is Gaussian distributed, the LMMSE estimate corresponds to the mean vector


121

ˆ As of the MAP estimate, i.e., u maximizing the conditional distribution f (u|d). a result, one can use the sum–product algorithm on the factor graph in Figure 4.15. For the downlink, the same factor graph, in which variable nodes now represent ui and the factor nodes represent the local function fdî = f (dî |u). In addition, assume that for each variable node there is a pendant factor node that is connected only to that variable node, fu i = p(ui ) = N (ui ; σf u i −u i , µf u i −u i ), denoting the prior distribution of the virtual data symbols. Since all the distributions are Gaussian, the messages passed between variable and factor nodes are actually the mean vector and covariance matrix of the underlying distribution. Assuming a flooding schedule [30] where at each iteration the messages on the graph are updated simultaneously, the sum–product update equations for kth iteration are summarized as follows [43]: dî − (k ) µf ˆ −u j d

u l ∈n f

=

i

u l ∈n f

(k )

σf ˆ

di

−u j

(k ) µu j −f ˆ d

=

dî

= i

=⎝ i

hi,l µu k −f ˆ

di

,

hi,j

\{u j }

i

(k )

⎝

(4.101)

(k −1) d −u j

(hi,l )2 σf ˆ

(hi,j )2

⎛ (k ) σu j −f ˆ d

µf −u j (k )

f ∈n u j \{f dˆ } σf −u j i ⎞−1 1 ⎠

⎛ (k ) σu j −f ˆ d

dî

β+

(k −1)

\{u j }

i

(k ) f ∈n u j \{f dˆ } σf −u j

,

(4.102)

⎠,

(4.103)

⎞

(4.104)

i

with initialization as (0)

(0)

µu j −f ˆ = 0,

σu j −f ˆ = 1

di

(4.105)

di

for all i, j for which uj is connected to fdî , nk denoting the set of nodes connected to node k on the factor graph and hi,j denoting the channel gain between the jth BS and the user in cell i. After the termination conditions are met at step m, the transmitted signal from BS j is obtained as ⎛ ⎞ (m ) µ f −u j (m ) (m ) ⎠ xj = σu j −f ˆ ⎝ (4.106) (m ) d f ∈n u σf −u j j

with ⎛

1

f ∈n u j

(m ) σf −u j

σu j −f ˆ = ⎝ (m )

d

⎞−1

⎠

.

(4.107)

122

Turbo base stations

Since the factor graph in Figure 4.15 contains loops, the convergence of the sum–product algorithm is not guaranteed. However, since the underlying distributions are all Gaussian, following the discussion in Section 4.4.5 it can be shown that the variance updates always converge [40, 41]. The necessary and sufficient condition for the convergence of the mean updates is that the spectral radius of the iteration matrix in (4.68) is strictly less than 1. As observed for the uplink problem, the convergence conditions are violated when the SNR is high and the interference created by the channel is strong. In [40], two approaches to improve the convergence of the algorithm for the downlink were proposed. In the first approach, a tunable parameter is introduced that multiplies the regularization parameter β. The value of is chosen so that the sum–product algorithm converges or converges at the desired rate. The disadvantage of this approach is that the sum–product algorithm no longer computes the desired LMMSE estimates resulting in some loss in performance. In the second approach, a switched beam system is used where a cell is divided into angular sectors and each sector is covered by a narrow beam generated by a directional antenna. Comparing the signal strength from all sectors, the BS selects the best beam to transmit data to a user. In this way interference is reduced, and the loops in the factor graph can be reduced or eliminated.

4.6

Current trends and practical considerations Much work has demonstrated the huge performance gains that are possible when BSs cooperate to receive signals from mobile users on the uplink, and to send data to mobile users on the downlink. In this chapter we have examined methods for implementing BS cooperation in a distributed manner via message passing. These message passing techniques require communication between neighboring BSs only and have processing and communication requirements that remain constant with increasing network size. They are, in some sense, the natural algorithms to use in large cellular networks. However, in terms of both theoretical analysis and practical implementation of these turbo-style approaches, we have only scratched the surface. We list below some exciting areas where much work is still to be done. (1) Convergence issues. Many questions are still unanswered regarding the convergence of the sum–product algorithm on graphs with loops, as mentioned in Section 4.4.5. A more thorough treatment of convergence is required in order to understand the limitations of the distributed BS processing techniques presented in the chapter and to find methods to improve the convergence properties. (2) Limited backhaul traffic. Backhaul traffic is the traffic between BSs required to implement cooperative schemes. For a practical system, the backhaul traffic is not unlimited. Given a certain limit on the backhaul traffic, can we still

References

(3)

(4)

(5)

(6)

123

get the performance gains we see in this chapter? How should the message passing techniques be modified to reduce the backhaul traffic load? Synchronization. Perfect synchronization of BSs in the downlink has been assumed in this chapter. We have also assumed it for the uplink, although the assumption may be less critical there. What is the impact of synchronization errors on the performance? It may be possible that a synchronization imperfection that is tolerable in conventional single-cell processing may have more degrading effects in the case of BS cooperation. Imperfect channel information. We have assumed that perfect CSI is available at the BS transceiver. What will be the impact of imperfections in channel estimates on the attainable gains due to base station cooperation? What will be the impact on the convergence of the proposed methods? Coded systems. We have not considered error control coding in this chapter. In practice, common decoders are often based on graphical methods and it would be possible to combine the factor graphs we use for joint detection of mobile users and the graphs which model the code constraints, to form one large graphical model on which message passing algorithms could be applied. What will happen to the convergence properties of the sum–product algorithm on this space-time factor graph? What are the other issues to consider for distributed decoding in a cellular system? Distributed resource allocation. If we are allocating channels to mobile users in order to maximize the throughput, how can this be done in a BScooperating network in a distributed manner?

Some excellent work has already begun to answer some of these questions: channel estimation and coding [63], limited backhaul traffic and coding [28, 37], and resource allocation [1]. However, many questions remain unanswered and numerous challenges must be overcome if we are to realize the full potential of turbo-based methods for BS cooperation.

References [1] A. Abrardo, P. Detti, and M. Moretti, “Message passing resource allocation for the uplink of multicarrier systems,” in Proc. of IEEE International Conference on Communications, 2009, pp. 1–6. IEEE, 2009. [2] R. Ahlswede, “The capacity region of a channel with two senders and two receivers,” Annals of Probability, 2, 1974, 805–814. [3] E. Aktas, J. Evans, and S. Hanly, “Distributed decoding in a cellular multiple-access channel,” in Proc. of IEEE International Symposium on Information Theory, 2004, p. 484. IEEE, 2004. [4] E. Aktas, J. Evans, and S. Hanly, “Distributed base station processing in the uplink of cellular networks,” in Proc. of IEEE International Conference on Communications, 2006, pp. 1641–1646. IEEE, 2006.

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5

Antenna architectures for network MIMO Li-Chun Wang and Chu-Jung Yeh

5.1

Introduction In conventional cellular systems, cochannel interference is a serious issue that degrades system performance. The spectral efficiency of cellular networks is fundamentally limited by the interference between cells and users sharing the same channel for both downlink and uplink. Generally, there are two kinds of cochannel interference: intracell interference and intercell interference. The intracell interference can be resolved by allocating orthogonal frequency resources. To mitigate intercell interference, there are several general approaches such as frequency reuse, cell sectoring, and spread spectrum transmission. The most commonly used technique is to avoid using the same set of frequencies in neighboring cells. This approach leads to the decrease of the number of available channels within each cell. Universal frequency reuse, i.e., reuse factor of 1, is preferred for future broadband wireless communications systems, such as the Third Generation Partnership Project (3GPP) long-term evolution (LTE) and worldwide interoperability for microwave access (WiMAX). In the orthogonal frequency-division multiple access (OFDMA) systems, which do not have processing gain as the code-division multiple access (CDMA) system, how to achieve the goal of both universal frequency reuse and reducing intercell interference is a key challenge. The concept of fractional frequency reuse (FFR) has been suggested to improve spectrum efficiency by applying reuse partition techniques, in which the inner region of the cell is assigned the whole frequency spectrum and the outer region is only assigned a small fraction of the frequency spectrum [1]. The capacity and outage rate of an FFR-based OFDMA cellular system with proportional fair scheduling was studied in [2]. To analyze the joint effect of the FFR factor, the cell inner region, and the bandwidth assignment on cell throughput, an optimization problem was formulated in [3]. The resource allocation problem in an FFR-based multicell OFDMA system was translated to a graph coloring problem in [4]. In [5] FFR was applied to a tri-sector cellular OFDMA system. It was shown that the intercell interference is reduced and cell throughput was improved by the Cooperative Cellular Wireless Networks, eds. Ekram Hossain, Dong In Kim, and Vijay K. Bhargava. Published by Cambridge University Press. C Cambridge University Press, 2011.

5.1 Introduction

129

proposed subcarrier scheduling according to location or signal-to-interferenceplus-noise ratio (SINR) of users. Under a similar FFR-based tri-sector cellular OFDMA system, an interference mitigation scheme using combining partial reuse and soft handover was proposed in [6]. The network multiple-input multiple-output (MIMO) technique has become a hot topic which aims to mitigate the intercell interference by coordinating the multicell transmission for downlink or reception for uplink among a few geographically separated antennas (base stations, BSs). To effectively reduce the intercell interference, the network MIMO requires a reliable and high-speed backhaul connection between BSs to pass the channel state information (CSI) and mobile messages between those cooperating cells. With full BS cooperation, the downlink transmission can be modelled as a multiuser MIMO broadcast system [7–9]. The interstream interference-free transmission of a MIMO broadcast system is now translated to intercell interference cancelation in a multicell network MIMO system. For downlink transmission in a cellular network, the concept of coprocessing at the transmitting end was proposed in [10]. In [11] a distributed network beamforming in a cellular system was proposed and its performance was analyzed based on Wyner’s circular array model [12]. Coordinated strategies with grouped interior and edge users based on Wyner’s circular array model were studied in [13]. Downlink network MIMO transmission with multiple transmit and receive antennas under a general channel model was analyzed in [14–17]. In [18] downlink network MIMO coordination was compared with a denser BS deployment. For uplink network MIMO, coordinated BSs perform the reception of user signals within their coverage area and suppress interference between users by means of coherent linear (received) beamforming across BSs. The spectral efficiency gain with different numbers of neighboring rings with which a BS is coordinated was investigated in [19]. In [20], the data rates of users assigned to each coordinated cluster were further chosen to be proportionally fair. A fundamental question for network MIMO is: how many cells should be coordinated to provide adequate SINR performance. Most of the studies on network MIMO assumed a global coordination which can eliminate the intercell interference completely. However, it is impractical to have cooperation (or coordination) among too many cells. The huge computational complexity and synchronization needed with a large number of cells are quite challenging. In practice, only a limited number of BSs can coordinate and jointly process the received or transmit signals. For uplink network MIMO, an isolation-based user grouping algorithm to optimize the capacity under a strongly constrained backhaul between seven coordinated sites was proposed in [21]. An uplink BS coordination with a dynamic BS clustering approach was investigated in [22]. This approach leads to significant sum rate gain compared with the static BS clustering schemes proposed in [19, 20]. For the downlink network MIMO, the isolation-based user grouping algorithm used in [21] was modified to the downlink scenario for capacity improvement under a limited backhaul [23]. In [24], downlink coordination with limited distributed antenna arrays was compared with centralized antenna

130


arrays. Under a fixed number of antennas per cell, the impact of different numbers of sectoring per cell was evaluated in [25]. Also the impact of the number of coordinated cells was investigated. The objective of this chapter is to discuss a FFR-based network MIMO interference cancelation scheme for a downlink multicell system. Although both FFR and inter-BS coordination are being considered as possible intercell interference cancelation techniques in both WiMAX and LTE, combining network MIMO with FFR to mitigate the intercell interference is still an interesting problem. Due to the geographical distribution of cells and mobiles, the potential advantages of network MIMO can be further explored by utilizing different frequency partition and cell sectorization instead of complex joint multicell transmission techniques. In addition, a group of coordinated cells still cause interference in the neighboring coordinated groups. This intergroup interference (IGI) should be taken into account for network MIMO under arbitrary coordinated sizes. In this chapter, we will also explore the potential gain of network MIMO by using a near minimum number of coordinated cells, i.e., only three cells. In a cellular system with an omni-directional antenna, the received signal quality is severely affected by IGI under three- and seven-cell coordinated network MIMO. However, the proposed FFR-based three-cell network MIMO architecture can approach the traditional seven-cell network MIMO with omni-directional antenna. The rest of this chapter is organized as follows. In Section 5.2 we define the system model. In Section 5.3, we briefly review the concept of network MIMO. In Section 5.4 we examine the IGI issue for network MIMO systems. In Section 5.5, we present the proposed three-cell network MIMO architecture with FFR. In Section 5.6, we show numerical results and give concluding remarks in Section 5.7.

5.2

System model We consider a cellular system with Ncell = 19 cells, where the center cell has twotier neighboring cells, as shown in Figure 5.1. For simplicity, we assume that each BS of a cell has a single transmit antenna and each mobile user has a single receive antenna. For a cellular system with three-sectored cells, the number of transmit antennas per sector is also 1. The sectors are created using directional antenna at the BS. The antenna gain pattern used for each BS sector is specified as 6 5 2 θ A(θ)dB = − min 12 (5.1) , Am , θ3dB where A(θ)dB is the antenna gain measured in decibels in the direction θ and θ ∈ [−180◦ , 180◦ ] is the direction of the mobile user with respect to the broadside direction of the considered BS. The 3 dB beamwidth θ3dB is the angle at which the antenna gain is 3 dB lower than the peak (the broadside direction). The parameter Am = 20 dB is the maximum attenuation for the sidelobe.

5.2 System model

131

B1 B1 8

B1 9

B2

2

10

B3

18

B3

B3

B3

B3

B3

B2 B1

B2

B2

B3

B3

B2

15

14

Regular frequency partition for cell B1

B1

B2 B1

B2 B1

B3

B3

B3

B2

16

5

13

B1

B B3 2 B1

B2 B1

B2

B3

17

6

4

12

B1

B2 B1

B2 B1

B2

1

B B3 2 B1

0

3

11

B3

B B3 2 B1

B2 B1

B3

B B3 2 B1

B B3 2 B1

B1

7

B3 Considered frequency band Coordinated cells Interferers by directional antenna

B2

Interferers by side lobe

Figure 5.1. Interference example for FFR-based three-cell network MIMO systems with regular partition (consider cell 0). The general transmission model for mobile user k served by BS j is hk ,i xi + nk , yk = hk ,j xj +

(5.2)

i = j, i∈I

where hk ,j is the channel response between mobile k and BS j, xj is the transmitted signal from BS j, nk is the additive noise at the kth mobile, and I is the interference set for mobile k. The detailed channel response is 7 −µ dk ,j , (5.3) hk ,j = αk ,j βk ,j A(θk ,j ) dref where αk ,j is the fast (Rayleigh) fading between BS j and mobile k, βk ,j is the log-normal shadowing from BS j to mobile k, A(θk ,j ) is the antenna gain for mobile k with respect to BS j, dk ,j is the distance between BS j and mobile k, dref is a reference distance, and µ is the path-loss coefficient. The value of A(θk ,j ) is a function of θk ,j based on (5.1) for the sectorized cell and A(θk ,j ) = 1 for an omni-directional transmission cell. Note that the reference distance dref is the distance between the cell center and the cell vertex. The received SNR of mobile k from BS j is −µ dk ,j 2 SNR k ,j = |αk ,j | βk ,j A(θk ,j ) Γ, (5.4) dref where the reference SNR Γ represents the interference-free SNR defined as the SNR measured at the cell boundary (i.e., at the reference distance dref ) for only considering path-loss and ignoring shadowing and fast fading. The parameter Γ captures the effect of various channel and antenna parameters including transmit power, cable loss, transmit and receive antenna heights, thermal noise power, and other link budget parameters. Noise power is normalized to unity. The reference

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SNR Γ = 18 dB for a BS-to-BS distance RB2B = 2 km macrocellular system with 30 watts transmit power in 1 MHz bandwidth [26]. In this case, the reference distance dref ∼ = 1.1547 km. For mobile k served by BS j, the corresponding SINR of mobile k can be expressed as γk ,j =

1+

SNR k ,j i = j, i∈I SNR k ,i

(5.5)

and the corresponding Shannon capacity is given by log2 (1 + γk ,j ) bps/Hz.

5.3

Network MIMO Network coordination is a means to eliminate the intercell interference and improve spectral efficiency in a downlink multicell system [14, 15]. With a highspeed backhaul, the BSs can be connected and synchronized. Assume that all BSs can cooperate and report CSI at each BS via the central coordinator. With full BS cooperation, the downlink transmission can be modeled as a multiuser MIMO broadcast system. Consider a network MIMO system with M coordinated BSs (each site with a single transmit antenna), each of which transmits a data stream to its own target mobile station. The received signal is given by Y = Hx + n,

(5.6)

where H = [hk ,j ]M ×M denotes the channel matrix with element hk ,j being the channel response between mobile k and BS j as defined in (5.3), and n denotes the noise vector. The transmitted signals vector is denoted by x = Ws = [w1 . . . wM ][s1 . . . sM ]T , where sk is the kth mobile user’s data symbol, wk = [w1,k . . . wM ,k ] is the corresponding precoding weight column vector, and (·)T is the transpose operation. For a network MIMO system, the antenna output of the jth transmission site is a linear combination of M data symbols, i.e., xj = M k =1 wj,k sk . The received signal of mobile k can be written as yk = sk ||hk wk || +

M

si ||hk wi || + nk ,

(5.7)

i=1, i = k

where hk = [hk ,1 . . . hk ,M ] is the channel vector of the kth user. Let pk = E[|sk |2 ] denote the average power of symbol sk . According to the network MIMO principle, the following constraint should be satisfied: E[|xj |2 ] ≤ PBS for each BS j = 1, . . . , M . ⎡ ⎤⎡ ⎤ |w1,1 |2 · · · |w1,M |2 p1 ⎢ ⎥ ⎢ .. ⎥ .. .. .. (5.8) ⎣ ⎦ ⎣ . ⎦ ≤ PBS 1M , . . . |wM ,1 |2

···

|wM ,M |2

pM

where PBS is the maximum transmit power at each BS and IM is an M × 1 vector will all one elements.

5.3 Network MIMO

133

It is well known that dirty paper coding (DPC) can achieve the capacity of a multiuser MIMO broadcast system. Due to the high complexity of DPC, some suboptimal but practical schemes were proposed. In this chapter, we consider two suboptimal network MIMO schemes, including zero-forcing (ZF) and zeroforcing dirty paper coding (ZF-DPC).

5.3.1

ZF network MIMO transmission The goal of ZF transmission is to invert the channel to obtain HW = I. This function can be achieved by using the pseudo-inverse of the channel matrix as the weight matrix W. The received signal vector is hence given by Y = Hx + n = HWs + n = s + n.

(5.9)

For the network MIMO system with per-base power constraint (5.8), the objective is to maximize the minimum rate among the coordinated cells subject to the power constraint. The corresponding solution is the maximum equal rate assignment [15] pk =

PBS P BS = , for all k. maxj [WW∗ ](j,j ) maxj k |wj,k |2

(5.10)

Therefore, the corresponding mobile’s rate is given by log2 (1 + pk /σ 2 ) bps/Hz among all coordinated cells, where σ 2 represents the noise power. Note that there is an excessive transmission power penalty for ZF transmission due to the required interference cancelation power for constructing weight matrix W.

5.3.2

ZF-DPC network MIMO transmission ZF-DPC transmission constructs the linear weight matrix W = Q∗ through the QR decomposition of the channel matrix H = LQ, where L is a lower triangular matrix, Q is a unitary matrix with QQ∗ = Q∗ Q = IM , and (·)∗ is the conjugate transpose operation. The received signal is written as Y = Hx + n = LQQ∗ s + n = Ls + n

(5.11)

and the corresponding kth mobile’s received signal is yk = Lk ,k sk + ∗ i< k Lk ,i si + nk . Note that the weight matrix W = Q ensures that no interference is from symbols with indices i > k. The remaining interference from symbols i < k is taken care of by DPC successive interference cancelation. Based on the result of ZF transmission, if we set pk = p for all k, the per site power constraint (5.8) becomes E[|xj |2 ] = [WW∗ ](j,j ) p = k |wj,k |2 p ≤ PBS for all transmitted signal xj . Recall that the weight matrix W = Q∗ . We have [WW∗ ](j,j ) = [Q∗ Q](j,j ) = [I](j,j ) = 1. Thus, we can set pk = PBS for each coordinated BS. Given the received signal in (5.11), mobile k can achieve the rate log2 (1 + |Lk ,k |2 pk /σ 2 ) bps/Hz.

134


5.4

Effects of intergroup interference

5.4.1

SINR analysis When applying network MIMO to group coordinated cells in a multicellular system, the effects of IGI need to be taken into account. That is, a group of coordinated cells still cause interference in the neighboring coordinated groups of cells even if the intragroup interference has been canceled via network MIMO transmission. Consider a cell with a two-tier surrounding cells layout under M cell network MIMO coordination. There are some interfering neighboring cells which belong to its corresponding M -cell network MIMO group Gi for i ∈ IG , where IG is the index set of the interference group. For a M -cell network MIMO group Gi , the transmit antenna output of BS a ∈ Gi is i xG a =

M

Gi Gi wa,b sb ,

(5.12)

b=1 Gi where [wa,b ]M ×M is the precoding weight designed for M -cell network MIMO i group Gi and sG is the data symbol of mobile b ∈ Gi . The SINR of mobile k b considered in (5.7) becomes

γkIGI =

1+

i∈IG

pk ||hk wk ||2 M G i G i G i 2 , a∈G i b=1 pb |hk ,a wa,b |

(5.13)

i i where pG is the data symbol power for mobile b ∈ Gi and hG b k ,a is the channel response between the considered mobile k and the interfering BS a ∈ Gi . As in (5.5), the noise power has been normalized to unity. The kth mobile’s rate is now log2 (1 + γkIGI ) when considering the effect of IGI in a multicellular system. By applying the ZF-based network MIMO coordination, the SINR of (5.13) becomes pk GI , (5.14) γkI ,Z F = Gi 2 Gi Gi 1 + i∈IG a∈G i M b=1 p |hk ,a wa,b |

Gi i where pG for all b can be found via (5.10). For network MIMO with b =p ZF-DPC transmission, the corresponding SINR is

γkIGI ,ZFDPC =

5.4.2

1+

i∈IG

PBS |Lk ,k |2 . M Gi Gi 2 a∈G i b=1 PBS |hk ,a wa,b |

(5.15)

Example of IGI: network MIMO with omni-directional cell planning In this subsection, we show examples of IGI in the network MIMO system. We consider a conventional cellular network with omni-directional cell planning. Figure 5.2 shows IGI for the three-cell and seven-cell network MIMO systems. Take cell 0 as an example, it forms a three-cell network MIMO group G0 with cells 4 and 5. The intragroup interference coming from cells 4 and 5 is canceled via network MIMO transmission. However, the remaining two-tier cells still

5.4 Effects of intergroup interference

135

G7 G1

7 18

8 G8

G1

9

G6

1

9

16 G0

3

5 15

G3

13

G4

(a)

17

G0

3

16 G5

5 4

11 G3

14

12

0

10

G6

6

2

G5

4

11

18 1

G2

0

10 G2

17

6

2

7

8

15 14

12 13

G4

(b)

Figure 5.2. An example of IGI for: (a) the three-cell and (b) seven-cell network MIMO systems. cause interference to cell 0. In this case, IG = {G1 , G2 , . . . , G8 }, where the corresponding cells in each group are G1 = {1, 2, 8}, G2 = {3, 10, 11}, G3 = {12, 13}, G4 = {14}, G5 = {15, 16}, G6 = {6, 17, 18}, G7 = {7}, and G8 = {9}. There are still four first-tier interfering cells and all the second-tier interfering cells. Note that all interferers transmit coordinated signaling via M -cell network MIMO. With seven-cell network MIMO, the coordinated partners of cell 0 are cells {1, 2, 3, 4, 5, 6}. The IGI from the second-tier cells is still unavoidable even if the interferences from surrounding cells {1, 2, 3, 4, 5, 6} are canceled. Figure 5.3 shows the effects of IGI for network MIMO with ZF-DPC transmission. We first consider the advantage of using network MIMO. The dotted line represents the SINR for cells with omni-directional antenna. The SINR is evaluated according to (5.5) with I = 18 neighboring cells. We consider 19-cell, 7-cell, and 3-cell network MIMO without IGI (denoted by solid lines). In this case, the received signal quality is averaged over M coordinated cells. Clearly, the received signal quality is largely improved via network MIMO. More importantly, we find that the SINR performance of seven-cell network MIMO is close to that of 19-cell network MIMO. This result implies that the coordination size M = 7 is sufficient when designing network MIMO systems. However, this result is obtained by ignoring the effects of IGI. The received signal quality will be greatly affected when interference from the other groups is considered. The dashed lines denote the SINRs for 3-cell and 7-cell network MIMO with IGI as shown in Figure 5.2. The SINR degradation for 7-cell network MIMO is about 14 dB and that for 3-cell network MIMO is about 23 dB. The received signal quality for M = 3 is almost equivalent to the case in which there is no multicell coordination.

5.4.3

Unbalanced signal quality caused by IGI Based on the observations for the seven-cell network MIMO system, the IGI results in an unbalanced signal quality when using larger coordination size. That

136


1 0.9 0.8

19-cell with reuse one 3-cell coord. (with IGI)

0.7 7-cell coord. (with IGI) CDF

0.6 0.5 0.4 3-cell coord. (no IGI) 0.3 0.2

7-cell coord. (no IGI)

0.1 19-cell coord. (no IGI) 0 −30

−20

−10

0

10 20 30 Received SINR (dB)

40

50

60

Figure 5.3. Effect of IGI for the three-cell and seven-cell network MIMO systems. (CDF: cumulative density function.)

is, the central cells in a coordinated group have better signal quality than the cells at the edge. Take the seven-cell network MIMO as the example: the IGI of cell 0 is from the second-tier interferers as mentioned before. However, for the edge cells {1, 2, 3, 4, 5, 6}, each of them has three first-tier IGIs and 15 second-tier IGIs. As a result, in a cooperating group of M cells, the edge cells suffer more serious IGI than the central cells. The signal quality among M coordinated cells is unbalanced in conventional network MIMO coordination. This unfair performance metric in a group becomes more obvious as coordination size M increases. To sum up, the IGI causes not only severe performance degradation but also results in unfairness in multicell network MIMO systems. Note that three-cell-based network coordination does not suffer from this unbalanced service since each member of a coordinated group has the same geographic condition. In other words, each cell can be considered to be an “edge cell” within the three-cell group with the same interference distribution. However, the performance improvement induced by a small group of coordinating cells is poor. In the following section, we propose novel network MIMO architectures to improve the signal quality and simultaneously achieve fairness among a group.

5.5

Frequency-partition-based three-cell network MIMO

5.5.1

Fractional frequency reuse (FFR) FFR, also called reuse partition, allows different frequency reuse factors to be applied over different frequency partitions during the period of transmission. Figure 5.4 shows the considered FFR partition for a tri-sector cellular system.

5.5 Frequency-partition-based three-cell network MIMO

Power level

fB1

fB2

137

fB3

N resource units (RU)

fA

Frequency

fB

B1 B1

CellGai B3

2

B3

1

6

Cell

B1

B1

B2

Regular

B3

B2

2

B1

B3

CellGci

B2

B1

B1

5

B2

B3

B2

4

3

B3

6 B3

B2

B1

Network MIMO group for fB1 Network MIMO group for f B2 Network MIMO group for fB

B2

B1

0 3

B2

B1

B3 B3

5 4

B3

B2

B2

B2 Gi b

B3

1

B2

B1

0 B3

B1

B2

B2 B1

3

B3

B1

B3

Rearranged

Figure 5.4. Frequency partition and cell planning for proposed three-cell network MIMO coordination. The FFR partitions the frequency into inner frequency bands fA and outer frequency bands fB , where fB is further partitioned into three subbands fB 1 , fB 2 , and fB 3 (the gray, slash, and cross-hatched areas, respectively). In general, the inner frequency band fA adopts a reuse factor of 1 and is used by interior cell users; the outer frequency band fB adopts a reuse factor of 1/3 for each sector for cell edge users. By means of the tri-sector FFR, the intracell interference can be avoided due to four orthogonal subbands, and the intercell interference can be significantly reduced. For use in a wireless broadband system (like the OFDM system), the frequency partitions can be assumed to be such that fB 1 , fB 2 , and fB 3 have the same bandwidth and there are N frequency resource units (RU) in each outer subband, i.e., fB p = {fB p , 1 , . . . , fB p , N } for p = 1, 2, 3. Note that FFR is usually integrated with other functions such as power control or antenna technologies for adaptive control. In this chapter, we consider two kinds of frequency planning: regular and rearranged frequency partitions. In regular frequency partition, each cell has the same frequency planning in the outer region (e.g., the left hand cellular system in Figure 5.4). Similar designs can be found in [5, 6]. In rearranged frequency partition, each cell has different frequency planning compared with its surrounding cells as shown in the right hand cellular system in Figure 5.4. Later we will design network MIMO systems based on the two frequency partitions. We know intuitively that the rearranged frequency partition will suffer from more severe cochannel intercell interference than the regular frequency partition. With the network MIMO technique, we find that the three-cell network MIMO under the rearranged frequency partition has the better performance.

138


5.5.2

FFR-based network MIMO with regular frequency partition In this section, we consider a novel multicell architecture combining FFR with network MIMO. As mentioned before, the entire frequency band is partitioned into different zones by FFR frequency planning. Compared with the conventional 19-cell layout, the tri-sector cellular system combined with FFR can significantly reduce the interference sources, while fully utilizing the frequency band in each cell. As an example, in Figure 5.1 when a mobile user at cell 0 uses an RU fB 1 , n (n = 1, . . . , N ) in frequency band fB 1 , the interference comes from cells 4, 5, 12, 13, 14, 15, and 16 under the assumption of perfect 120◦ sectoring by directional antenna. In conventional systems, the mobile receives interference from all the other 18 cells. Here, the question is: how can we further improve the SINR on top of FFR? The solution proposed in this chapter is to integrate FFR with the network MIMO technique. From Figure 5.1, we find that among the seven interfering sources, two critical interferers are first-tier neighbors (i.e., neighboring cells 4 and 5) and five weaker interferers (due to larger path-loss) are second-tier neighbors. Therefore, we use the network MIMO technique to cancel out the two most severe interferences. Instead of a huge number of coordinated cells, we propose a coordination scheme with only three coordinated cells. We define those coordinated cells as a group i shown in Figure 5.4. For arbitrary group Gi , we label the three cells as CellG a , Gi Gi Cellb , and Cellc . For the three-cell coordination structure, we can apply network MIMO transmission to each subband fB p , n for p = 1, 2, 3 and n = 1, . . . , N . For the example on cell 0, under the assumption of perfect sectoring by directional antenna, the channel matrix of fB 1 , n in the group {0, 4, 5} is ⎡

h(0),0 H(fB 1 , n ) = ⎣ 0 0

h(0),4 h(4),4 0

⎤ h(0),5 0 ⎦, h(5),5

(5.16)

where (x) denotes the corresponding served user in cell x. We eliminate the interference caused by h(0),4 and h(0),5 (coming from cells 4 and 5) by network MIMO. As a result, the two most severely interfering sources are canceled through a small (3 × 3) matrix computation. Importantly, for system design, this cooperation can be applied to all cells. For example, at a certain time slot we have many cooperating groups among the 19 cell in the layout: cells {0, 4, 5}, {8, 2, 1}, {10, 11, 3}, and {18, 6, 17}. Not only is the middle cell (cell 0) coordinated with its neighboring cells, but the cells in the outer layer are also coordinated simultaneously.

Cell regrouping and partner selection We now discuss a cell regrouping and partner selection scheme that addresses the service fairness issue for the regular partition-based network MIMO system. We

139


B1

B1

7

B1

8

B1 B

B3

B2 B1

B 10 B3 B2 1

B2 B1

11

B3

B3

B2

B3 B2

B2 Slot one: group with cells 4 and 5 Primary band

B3

B1

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B1

18 B3 B 1

B3 B2 B1

17 B3 6

B3 B2 B1

5

B3 B2 B1

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B

B3 B2 B1

0 B3 B2 1 3

B3 B2 B1

B2 11 B3 B 1

4

B2

9

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13 B3 B2 B2

Slot two: group with cells 1 and 6 Primary band

B3 B2 B1

3

B3 B2 B1

B3

1

B3 B2 B1

B1

18 B3B

1

0

B2 11 B3 B 1

15 B3 14 B3 B2

2 B3 B2 B1

B2 B1

7 B3 B2 B1

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B2 B1

16

B3 B2 B1

B2 12 B3 B 1

B2

8

B1

1

2 2 B3 B B

B2 B1

15 B3 14 B3 B2

13

B3

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9 B2 B1

16 5

4

B3 B2 B1

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17 B3 6

0 3

B3 B2 B1

8

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1

B1

7

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18 B3B 1

2

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B3 B2 B1

9 B3 B2 1 B2 B1

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5

B3 B2 B1

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16 B3

B3 B2 B1

B2 12 B3 B 1

B2

17 B3 6

15 B3 14 B3 B2

13 B3 B2 B2

Slot three: group with cells 2 and 3 Primary band

Figure 5.5. Example of cell regrouping and partner selection for cell 0.

consider the service fairness issue in the following. Among an arbitrary group i Gi , the cell labeled “CellG a ” can be free from intragroup interference within the whole subband fB 1 = {fB 1 , 1 , . . . , fB 1 , N } under network MIMO. That is, the two most severely interfering sources are canceled via network MIMO. However, subbands fB 2 and fB 3 still suffer interference from seven interferers, i.e., two firsttier cells and five second-tier cells. We therefore define fB 1 as the primary bands i of CellG a for group Gi . Similarly, we define fB 2 and fB 3 as the primary bands Gi i of Cellb and CellG c , respectively. Therefore, the cell users served by different subbands from a group will have different signal quality. Note that this service fairness issue is different from the unbalanced signal quality issue mentioned in Section 5.4.3. The service fairness issue can be resolved by the proposed regrouping and partner selection scheme. Assume that cell 0 is grouped with cells 4 and 5 with primary band fB 1 at time slot 1 as shown in Figure 5.5. Cell 0 regroups with cells 1 and 6 at the next time slot, slot 2 by rotating counter-clockwise to reselect coordinating partner. After this regrouping, the primary band of cell 0 becomes fB 2 . Similarly, cell 0 regroups with cells 2 and 3 at time slot 3 by another counter-clockwise selection of the coordinated partner and the corresponding primary band becomes fB 3 . In this way, all cells simultaneously “rotate” and regroup with two new neighboring cells at each new time slot, where “rotate” means selecting with the coordinated partner reselection procedure. Take the cells {0, 4, 5} as an example: those cells form a group at time slot 1. At time slot 2, cell 0’s regroup set is now {1, 0, 6}, cell 4’s regroup set is {3, 12, 4}, and cell 5’s regroup set is {5, 14, 15}. Similarly, at time slot 3 cell 0’s regroup set becomes {2, 3, 0}, cell 4’s regroup set is {4, 13, 14}, and cell 5’s regroup set is {6, 5, 16}. Each cell has the chance to cooperate with its neighboring six cells in order and each sector has the opportunity to become the primary band under this kind of time-division multiple access (TDMA) based regrouping and partner selection scheme.

140


Three kinds of frequency partition for cell

B2 7

B1 8

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11

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B3

B3

B1

B1

Considered frequency band Coordinated cells

B2

Interferers by directional antenna

B1

Interferers by sidelobe

Figure 5.6. Interference example for the FFR-based three-cell network MIMO systems with rearranged frequency partition (consider cell 0).

5.5.3

FFR-based network MIMO with rearranged frequency partition We now propose another multicell architecture with rearranged frequency partitions among cells. As shown in Figure 5.4, there are in total three kinds of frequency partitions for cell planning, for example, the different frequency partitions for cell 0, cell 1, and cell 2. After this rearranged frequency partition among a multicell system, a cell coordinates with six neighboring cells to form three individual network MIMO groups for each subband. Take cell 0 as an example: it coordinates with cells 1 and 2 for subband fB 1 , with cells 3 and 4 for subband fB 2 , and with cells 5 and 6 for subband fB 3 . In other words, we perform three-cell network MIMO transmission in each subband (or frequency partition). As the example in Figure 5.6 shows when a mobile user of cell 0 uses an RU fB 1 , n (n = 1, . . . , N ) in frequency band fB 1 , the interference sources are cells 1, 2, 11, 12, 14, 16, and 17 under the assumption of perfect 120◦ sectoring by a directional antenna. Similarly we use the network MIMO technique to cancel the two severest interferences, i.e., the only two first-tier interferences from cells 1 and 2 (the dotted area in Figure 5.6). The channel matrix for the group {0, 1, 2} in fB 1 , n is ⎡

h(0),0 H(fB 1 , n ) = ⎣ h(1),0 h(2),0

h(0),1 h(1),1 h(2),1

⎤ h(0),2 h(1),2 ⎦ . h(2),2

(5.17)

For the user in cell 0, we eliminate the interference caused by h(0),1 and h(0),2 (coming from cells 1 and 2) by network MIMO. As a result, the two severest sources of interference are canceled through a small (3 × 3) matrix computation. Ideally, there are only five second-tier interferers for each subband. As with


141

1 0.9 Omni-cell with reuse 1

0.8 0.7

Diamond-shaped (120°) sector FFR

CDF

0.6

FFR-based 3-cell network MIMO (ZFB)

0.5 0.4

FFR-based 3-cell network MIMO (ZF–DPC)

0.3 0.2 0.1

Regular frequency partition 0 −30

−20

−10


30

40

50

Figure 5.7. The CDFs of received SINR for the omni-directional cellular systems with universal frequency reuse 1, tri-sector FFR cellular systems and the proposed regular partition-based three-cell network MIMO systems (120◦ cell sectoring).

1 0.9 0.8 0.7

CDF

0.6

Omni-cell with reuse 1

Diamond-shaped (120o) sector FFR FFR-based 3-cell networ k MIMO (ZFB)

0.5 0.4

FFR-based 3-cell network MIMO (ZF−DPC)

0.3 0.2 0.1

Rearranged frequency partition 0 −30

−20

−10


30

40

50

Figure 5.8. The CDFs of received SINR for the omni-directional cellular systems with universal frequency reuse 1, tri-sector FFR cellular systems and the proposed rearranged partition-based three-cell network MIMO systems (120◦ cell sectoring).

the regular partition-based network MIMO systems, this cooperation can also be applied to all cells not only to a particular cooperating group. Compared with the regular partition-based network MIMO, there is no service fairness issue for network MIMO systems with a rearranged partition. As a result, we avoid the necessity for cell regrouping which reduces the complexity of system design.

142


Table 5.1. Spectral efficiency for three-cell network MIMO with regular frequency partition

(bps/Hz)/base Improvement

5.5.4

Reuse 1

Tri-sector FFR

ZFB

ZF-DPC

2.5437

3.7844 48.78%

2.4977 -1.81%

4.4275 74.06%

Effect of frequency planning among coordinated cells We next present the received SINR performance for the proposed three-cell coordination architectures. The regular and rearranged partition frequency partition scenarios are shown in Figures 5.7 and 5.8, respectively. The cell planning is 120◦ sectoring. The results for the conventional 19-cell layout with universal frequency reuse 1 (denoted by the dotted line) and the tri-sector FFR layout with directional antenna (denoted by the bold black line) are also presented for comparison. From Figure 5.7, by comparing the dotted line with the bold line we see that the gain in interference sources reduction (from 18 reduce to 7) of the tri-sector FFR layout is quite significant: about 10 dB improvement at 90th percentile (i.e., CDF = 0.1) of the received SINR. However, the gain is not so obvious (2 dB improvement) for the rearranged partition-based cellular layout. This is because there are two neighboring interferers for each RU in the rearranged partition-based cellular layout. In this case the advantage of using just frequency partition and directional antenna is limited. With the three-cell network MIMO techniques, both ZF and ZF-DPC transmissions, can indeed improve the received SINR, especially for ZF-DPC scheme as shown in Figure 5.8. At the 90th percentile of the received SINR, the improvement (compared to the tri-sector FFR layout) is about 9 dB for ZF and 15 dB for ZF-DPC. Although rearranged frequency partition causes interference from neighboring cells, network MIMO can enhance signal quality effectively by interferences cancelation. As for cells with regular partition, the gain of executing network MIMO shown in Figure 5.7 is not as significant as that in Figure 5.8. The gain of ZF-based network MIMO is actually lower than that of the tri-sector FFR layout using the regular partition-based cellular system. Recall the TDMA-based regrouping and partner selection scheme for regular partitionbased network MIMO. Equivalently, the signal quality of only one third of the resources can be enhanced in each time slot. Additionally, because of the transmission power penalty of ZF transmission, the actual data symbol power (5.10) becomes weaker even if there is no first-tier interference (due to coordination). Note that there is no power penalty for ZF-DPC transmission. From the perspective of capacity improvement, Tables 5.1 and 5.2 show the spectral efficiencies of regular and rearranged partition-based cellular systems under 120◦ cell sectoring, respectively.


143

Table 5.2. Spectrum efficiency for three-cell network MIMO with rearranged frequency partition (120◦ sectoring)


Reuse 1

Tri-sector FFR

ZFB

ZF-DPC

2.5437 –

3.2890 29.30%

3.2553 27.97%

5.7534 126.18%

Figure 5.9. Interference example for FFR-based three-cell network MIMO systems with 60◦ cell sectoring (consider cell 0).

5.5.5

Effect of cell planning with different sectorization Cell planning for 60◦ cell sectorization To address the effect of cell planning with different sectorization, we design threecell network MIMO systems with 60◦ cell sectoring. Here we consider rearranged partition-based frequency planning to avoid the cell regrouping procedure. Figure 5.9 shows an example of the proposed rearranged partition-based 60◦ sectoring network MIMO systems. In this design, each cell has three hexagon-shaped sectors with different frequency partitions. Cells with 60◦ and 120◦ sectoring are also called clover-leaf-shaped cells and diamond-shaped cells, respectively [27, 28]. Due to the antenna pattern, the clover-leaf-shaped cells can match the sector contour better than cells with diamond-shaped sectors [27]. Additionally,


1 0.9 0.8 0.7 0.6 CDF

144

Omni- cell with reuse 1

Clover-leaf- shaped (60°) sector FFR FFR-based 3-cell network MIMO (ZFB)

0.5 0.4

FFR-based 3-cell network MIMO (ZF–DPC)

0.3 0.2 0.1

Rearranged frequency partition 0 −30

−20

−10


30

40

50

Figure 5.10. The CDFs of received SINR for omni-directional cellular systems with universal frequency reuse 1, tri-sector FFR cellular systems and the proposed rearranged partition-based three-cell network MIMO systems (60◦ cell sectoring). cells with 60◦ sectoring can use spectrum more efficiently [28]. Similarly to 120◦ sectorized cell planning, each cell forms three individually three-cell network MIMO coordinations with its six neighboring cells for each frequency partition. The two first-tier interferers (the dotted areas in Figure 5.9) are canceled via network MIMO transmissions. The three-cell coordination structure can be implemented for all cells, not only for a particular cell. Note that actual cell sectorization is not perfect when using a directional antenna pattern (5.1). The other cells also affect the received signal quality of cell 0. However, the harm caused by sidelobe and backlobe transmissions (the cross-hatched areas in Figures 5.1, 5.6, and 5.9) is not significant compared to the cell planning with omni-directional transmission. Finally, the features of the proposed FFR-based three-cell network MIMO systems can be summarized as: (i) they use a small coordination size M = 3 to obtain low complexity network MIMO systems, (ii) they reduce the effect of IGI via the combination of FFR and directional antennas, (iii) they avoid the unbalanced signal quality issue caused by a larger coordination size M .

Performance comparison under 60◦ cell sectorization Next, we consider the effect of cell planning with different directional antennas. Figure 5.10 shows the corresponding received SINR performance using 60◦

5.6 Simulation setup numerical results

145

Table 5.3. Spectrum efficiency for three-cell network MIMO with a rearranged frequency partition (60◦ sectoring)


Reuse 1

Tri-sector FFR

ZFB

ZF-DPC

2.4933 –

4.0360 61..88%

2.9478 18.23%

5.6337 125.96%

sectorized cell planning. We find that the advantage of using pure sectorization is obvious under 60◦ cell sectoring. Traditionally, a cell with 60◦ sectoring has better performance than one with 120◦ sectoring. The poor signal quality of 120◦ tri-sector FFR with rearranged partition in Figure 5.8 can be improved using 60◦ cell sectoring (see Figure 5.10). When applying three-cell network MIMO, the SNR performance of 60◦ sectorized cells is similar to that of 120◦ sectorized cells by the ZF-DPC transmission. However, the gain of the ZF scheme is not very significant at the 90th percentile of the received SINR, and is actually lower than that obtained by using the tri-sector FFR scheme. In other words, under rearranged partition-based cellular systems, the proposed three-cell network MIMO enhances signal quality more efficiently on cell planning with 120◦ sectoring. Note that the performance of the 19-cell layout with universal frequency reuse 1 will be different to that in Figure 5.8 due to the different cell planning. However, the difference is not very significant. Table 5.3 shows the average spectrum efficiency improvements of three-cell network MIMO with a rearranged frequency partition under 60◦ cell sectoring.

5.6

Simulation setup numerical results We have shown the SINR performance of the proposed FFR-based three-cell network MIMO schemes. In our simulation environment, we consider a multicell system with BS-to-BS distance RB2B = 2 km. The interference-free SNR at the cell edge is Γ = 18 dB for 120◦ sectorized cells. The same values of BS-to-BS distance and Γ (for same transmission power comparison) are used for cloverleaf-shaped cells. The standard deviation of shadowing is 8 dB, the path-loss exponent µ = 4. Mobile users are uniformly distributed within each sector/cell. The channel response between any user-and-cell pair is represented by (5.3), where the angle-dependent antenna pattern is taken into consideration. In this chapter, we do not consider the effect of the inner cell. In fact, how to design the inner region is an important issue for a FFR multicell broadband system. We do not discuss this issue here and leave it as a future work.


Table 5.4. Spectrum efficiency improvement for network MIMO with FFR and directional antenna Proposed three-cell network MIMO

Conventional setup

Three-cell 7-cell network 60◦ network MIMO MIMO sectorization (bps/Hz)/base Improvement

3.0946

5.1579 66.67%

5.6337 82.05%

120◦ sectorization 5.7534 85.92%

1 0.9 0.8 0.7 0.6 CDF

146

3-cell omni-coordination (with IGI) 7-cell omni-coordination (with IGI)

0.5 0.4 0.3 Diamond: FFR-based 3-cell network MIMO under 120o−shaped cell

0.2

Square: FFR-based 3-cell network o MIMO under 60 −shaped cell

0.1 0

−20

−10

0

10 20 Received SINR (dB)

30

40

50

Figure 5.11. Performance comparison of proposed three-cell FFR-based network MIMO with general omni-directional three-cell and seven-cell network MIMO systems. Finally, we show the potential gains of combining frequency partition and network MIMO in Figure 5.11. Take ZF-DPC as an example. As studied in Section 5.4.2, the performance degradation caused by IGI for three-cell and seven-cell network MIMO systems is significant. However, taking advantage of joint frequency partition and network MIMO, the proposed FFR-based three-cell network MIMO architecture (for both cell sectorizations) can even outperform conventional seven-cell network MIMO system using omni-directional cell planning. The improvement is about 2 dB for 60◦ sectorized cell planning and 3 dB for 120◦ sectorized cell planning at the 90th percentile of the received SINR. This result indicates that network MIMO systems with a small number of coordinated cells are also comparable to network MIMO systems with a large number of coordinated cells as long as directional antennas and sector frequency arrangement techniques can be adopted appropriately. Table 5.4 shows the spectrum efficiency

5.7 Conclusion

147

improvement of the three-cell network MIMO with the proposed frequency rearranged method for different sector antennas.

5.7

Conclusion We have discussed joint FFR and network MIMO architecture for multicellular systems. Taking advantage of FFR to reduce cochannel interference by partitioning the frequency band into different zones, we have exploited the performance gain of the coordinated network MIMO techniques. We have provided a three-cell coordinated scheme for network MIMO based on a sector frequency rearrangement method, rather than a huge number of coordinated cells. We have shown that using a small number of coordinated cells can outperform the seven-cellbased coordination with omni-directional transmission. Future research topics for small network MIMO could include the design of the inner region of the FFR system and the low-complexity joint multicell transmission techniques. We hope that this study will focus the attention of future researchers on BS architecture and system deployment for network MIMO systems.

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Part III Relay-based cooperative cellular wireless networks

6

Distributed space-time block codes Matthew C. Valenti and Daryl Reynolds

6.1

Introduction In this chapter, we consider space-time coding strategies for multiple-relay cooperative systems that effectively harness available spatial diversity. More specifically, the goal is to examine ways to forward signals efficiently from multiple relays to the destination while addressing the important practical issue of synchronization among the relays. We assume a general two-phase transmission protocol as illustrated in Figure 6.1. In the first phase of the protocol, the source broadcasts a message which is received by the relays and (possibly) the destination. During the second transmission phase, a subset of the relays, possibly in conjunction with the source, transmits additional information to the destination. This protocol is useful in practical scenarios where signals received at the destination due to transmissions directly from the source (Phase 1) will not carry enough useful information because of noise, fading, and/or interference.

Phase 1

Phase 2

Figure 6.1. Illustration of the two-phase transmission protocol using a distributed space-time code. In the first phase (left) the source transmits to several relays, while in the second phase (right), the relays simultaneously transmit to the destination. Cooperative Cellular Wireless Networks, eds. Ekram Hossain, Dong In Kim, and Vijay K. Bhargava. Published by Cambridge University Press. C Cambridge University Press, 2011.

154

Distributed space-time block codes

It is expected that Phase 2 will dramatically increase the reliability of the system, but if the symbols cannot be decoded correctly after the second phase, the protocol can restart by returning to Phase 1 or Phase 2. The primary problem associated with forwarding information from multiple relays to the destination is determining how the information should be spread out among the relays over space and time. This is analogous to the classic spacetime coding problem in point-to-point multiple-transmit-antenna systems, and so it is often called the distributed space-time coding problem. Similar to the point-to-point scenario, performance can vary dramatically based on the coding scheme, so care must be taken to achieve high performance in terms of diversity and coding gain while accounting for the practical limitations of cooperative systems. In fact, poorly designed distributed space-time coding schemes may perform worse than point-to-point systems, especially considering that the twostage protocol consumes additional degrees of freedom (time resources) relative to direct transmission. A conservative solution to the distributed space-time coding problem is for each terminal that participates in the second phase to transmit using orthogonal subchannels, which could be implemented using disjoint time slots, different frequency subbands, or orthogonal spreading codes (assuming that they can be synchronized). When disjoint time slots are used, this strategy is a distributed form of delay diversity [22]. However, there are two problems associated with this approach: (1) it is known that orthogonalizing system resources is suboptimal [18], and (2) enforcing orthogonalization in time, frequency, or code space would require significant additional signaling overhead, e.g., feedback and/or synchronization, and, in many cases, may not even be possible. A more efficient, albeit more aggressive, approach is for the terminals transmitting in the second phase to use a distributed space-time block code1 [10, 15]. There are two main varieties of forwarding mechanisms that can be used with distributed space-time coded systems: decode-and-forward (DF) [10] and amplifyand-forward (AF) [8]. In DF protocols, the source’s signal is encoded with a forward error correcting code that must be successfully decoded by a relay before that relay may participate in the transmission of the distributed space-time code. After decoding, the information is reencoded and remodulated. A linear combination of the remodulated symbols and their conjugates is transmitted by each participating relay. While the DF protocol avoids error propagation or the amplification of noise received over the source–relay channel, its implementation is complicated by fact that the set of relays that are able to decode and so participate in the space-time code in the second phase is random and unknown to the system. Therefore, unlike with point-to-point multiple-antenna systems, extra

1

Distributed space-time trellis codes can be used as well, but we focus here on block codes and refer the interested reader to, for example, [13].

6.2 System model

155

care must be taken to ensure that the relays coordinate in the transmission of the space-time codeword. With AF protocols, a fixed number of relays participate in the second phase by transmitting a linear combination of the time samples of the noisy received signal (not decoded symbols) they receive from the source. Because the number of relays is fixed, AF does not have to manage which relays transmit which part of the space-time codeword, unlike DF. However, with AF the noise received over the source–relay channels is amplified, which has the potential to degrade performance. There are a number of challenges associated with practical distributed spacetime code implementation, some of which are shared with conventional spacetime coding used in point-to-point multiple-antenna systems, but some are unique to the distributed scenario. As with conventional space-time codes, distributed codes typically (but not always) require the destination receiver to have knowledge of the channels between the relays and the destination. Unlike conventional space-time codes, however, distributed space-time codes are subject to some challenging synchronization issues. Because the transmitters are widely separated and have different time references, and due to differences in the propagation delay between the relays and the destination, the different signals received by the destination will generally be offset in time. Although this problem can perhaps be overcome with appropriate synchronization protocols, it can be handled more effectively with delay diversity, delay-tolerant distributed space-time codes, or space-time spreading. The remainder of this chapter is as follows. In Section 6.2, we give a system model that will be used throughout the chapter. In Section 6.3, we review concepts related to fixed space-time block codes (STBCs). In Section 6.4, we describe the DF protocol, and in Section 6.5 we describe the AF protocol. We discuss synchronization issues in Section 6.6, and conclude in Section 6.7.

6.2

System model Consider a wireless network consisting of a source node, a destination node, and a set of R relay nodes N = {Ni : 1 ≤ i ≤ R}. Each node has a half-duplex radio and a single antenna. Messages are transmitted according to a two-phase protocol. During the first phase, a signal of duration T1 symbol periods is broadcast by the source and received by the relays. During the second phase, a subset of the relays simultaneously, but perhaps not synchronously, transmits signals of duration T2 symbol periods, and the destination receives a noisy sum of the relay signals. After approximately T = T1 + T2 consecutive symbol periods (depending upon transmission and channel delays), the source moves on to the next message (or a retransmission of a failed message). For ease of exposition, we assume that there

156


is no direct link between the source and destination, although the protocols and performance analyses can easily be generalized to allow for such a link. We adopt a discrete-time model, whereby the signal transmitted by the source during the first phase is represented by the vector s = [s1 , ..., sT 1 ]t . The individual symbols s , 1 ≤ ≤ T1 are each drawn from a complex constellation X of M symbols. The signal constellation is normalized so that its average energy is unity, i.e., (1/M ) s∈X |s|2 = 1. The normalized signal is amplified and transmitted by the source with power P1 during the first phase. Let fi represent the complex gain of the channel between the source and node Ni . Then the signal received by node Ni during the first phase is ri = fi P1 s + vi , (6.1) where vi = [vi,1 , ..., vi,T 1 ]t is a noise vector containing independent circularly symmetric complex Gaussian random variables with zero mean and unit variance. In the second phase, a subset K ⊆ N of the relays simultaneously, but perhaps without symbol-level synchronization, transmits to the destination. During this phase, node Ni ∈ K transmits a signal represented by the discrete-time vector ti = [ti,1 , ..., ti,T 2 ]t with power P2 . When the signals are perfectly synchronized, the signal received at the destination is x = gi P2 ti + w, (6.2) i:N i ∈K

where gi is the complex gain of the channel between node Ni and the destination, and the noise vector w = [w1 , ..., wT 2 ]t contains independent circularlysymmetric complex Gaussian random variables with zero mean and unit variance. When the signals are not synchronized, the model must be generalized to account for time offsets. In general, the powers E[|fi |2 ] and E[|gi |2 ] of the channel gains fi and gi will depend on the topology of the network and the propagation characteristics of the wireless channel, and will usually be unequal. However, for ease of exposition, we make the simplifying assumption that the fi s and gi s are independent and identically distributed (i.i.d.). In particular, each fi and gi is assumed to be a circularly symmetric complex Gaussian with zero mean and unit variance, so that their envelopes |fi | and |gi | are Rayleigh distributed. The coefficients fi are held fixed for the transmission of the signal s, and the coefficients gi are held constant for the transmission of the ti , i.e., we assume a Rayleigh block fading model. Just as the channel gains might have unequal powers, the powers P2 transmitted by the relays can, in general, be selected such that they are unequal, in which case our notation needs to be modified to indicate the different powers. However, in the following discussion we impose the simplifying limitation that all relays transmit with the same power P2 , which is optimal when the average

6.3 Space-time block codes (STBCs)

157

channel powers are all equal and the transmitters operate without channel state information. Note that this is a fairly general model which leaves unaddressed several critical design and implementation issues. For example, the composition of the set K depends on the protocol being used. In DF protocols, K contain only relays that successfully decoded the source’s transmission, while in AF protocols, K may contain any (or all) of the relays. Another key issue is the selection of the signals ti that are to be transmitted by the nodes in K during the second phase of the protocol. These signals can be jointly coded, but in a distributed way, using a space-time code, or they can use simpler strategies, e.g., delay diversity or spacetime spreading. We will discuss all of these options in this chapter. Finally, the allocation of power between P1 and P2 for the two transmission phases and the allocation of time over the two time phases are protocol-dependent optimization problems that must be solved to maximize performance.

6.3

Space-time block codes (STBCs) As described in the introduction, one of the primary problems associated with forwarding information from relays to a destination in a cooperative wireless network is how information is transmitted from the relays over time, i.e., the space-time transmission scheme. One natural strategy is to extend the concept of STBCs, typically used for point-to-point multiple transmit antenna systems, to relay networks, where they are called distributed space-time block codes. We begin with a description of conventional STBCs under the quite general linear dispersion paradigm [6]. Suppose for the moment that the first-phase transmission is perfectly received by all R relays. Under the linear dispersion paradigm, the ith relay transmits a linear combination of the T1 symbols in s and their complex conjugates, ti

= Ai s + Bi ¯s,

(6.3)

where ¯s is the column vector containing the complex conjugates of s and the complex T2 × T1 matrices Ai and Bi are called dispersion matrices. These matrices define the space-time code. Each nonzero matrix Ai or Bi is constrained to be unitary, and since the signal set X is normalized to unit energy, the symbols transmitted by the relays will also have unit energy. The family of space-time block codes that can be represented by (6.3) are called linear dispersion (LD) codes [6]. This family of codes includes many wellknown space-time codes as special cases. For example, one linear dispersion code that has been proposed for cooperative communications with R = 2 relays is

158


described by the dispersion matrices [9]

A1 =

+1 0 0 +1

, A2 = 02×2 ,

B1 = 02×2 , B2 =

0 −1 +1 0

,

(6.4)

where 0m ×n is an m × n matrix of all-zeros. This code is simply a transpose of the well-known Alamouti space-time block code [1]. For many codes of interest, including the one specified by (6.4), either Ai or Bi is a matrix of zeros for every i. This means that a particular relay will transmit a linear combination of the symbols in s or ¯s, but not both. If we define Ci

=

Ai ,

if Bi = 0,

(6.5)

Bi , if Ai = 0

and s

(i)

=

s, if Bi = 0,

(6.6)

¯s, if Ai = 0

then we can write (6.3) more compactly as = Ci s(i) .

ti

(6.7)

Assume that nodes N1 , ..., NR participate in the second-phase transmission with the same power P2 . The signal received at the destination is x

=

P2 Sh + w,

(6.8)

where S

=

,

C1 s(1)

...

CR s(R )

...

gR

-

(6.9)

is the T2 × R space-time codeword, and h

=

,

g1

-t

(6.10)

is the channel vector. The maximum-likelihood (ML) detector at the destination estimates the source signal as 8 8 8 8 ˆs = arg min 8x − P2 Sh8 , T s∈X

1

where · indicates the Frobenius norm.

(6.11)

159


Unless the distributed space-time code, described by the set of all possible codewords S, has some special structure, ML detection will have exponential complexity in the number of source symbols T1 . Fortunately, several classes of codes admit reduced complexity ML decoding, including the wellknown orthogonal design family [15], whose orthogonal structure allows decoupling of the symbols in the codeword, permitting symbol-by-symbol ML detection with linear complexity in T1 . The (Alamouti) code given by (6.4) is one example of an orthogonal design. Another orthogonal design which has been applied to cooperative diversity with R = 4 relays is described by the dispersion matrices [9] ⎡

1 ⎢ 0 A1 = ⎢ ⎣ 0 0 ⎡ 0 ⎢ 0 A4 = ⎢ ⎣ 0 −1

0 0 0 0 0 0 1 0

⎤ 0 0 ⎥ ⎥, 0 ⎦ 0 ⎤ 0 1 ⎥ ⎥, 0 ⎦ 0

⎡

0 ⎢ 0 A2 = ⎢ ⎣ 0 0 ⎡ 0 ⎢ 0 B1 = ⎢ ⎣ 0 0 ⎡ 0 ⎢ 0 B3 = ⎢ ⎣ −1 0

⎤ 1 0 0 0 ⎥ ⎥, 0 0 ⎦ 0 0 ⎤ 0 0 −1 0 ⎥ ⎥, 0 1 ⎦ 0 0 ⎤ 0 0 0 0 ⎥ ⎥, 0 0 ⎦ −1 0

⎡ ⎢ A3 = ⎢ ⎣ ⎡ ⎢ B2 = ⎢ ⎣

0 0 0 0 0 1 0 0

0 0 0 0 0 0 0 0

1 0 0 0 0 0 0 1

⎤ ⎥ ⎥, ⎦ ⎤ ⎥ ⎥ , (6.12) ⎦

B4 = 04×3 .

Note that for this code, only B4 is all-zero and thus the model given by (6.5)– (6.10) must be generalized slightly. See [8, 9] for details. The rate of a STBC is T1 /T2 , and a code is said to be full rate if it has a rate of unity. While the rate of the code specified by (6.4) is unity, the rate of the R = 4 code specified by (6.12) is only 3/4. No full-rate orthogonal STBC exists for R > 2 when complex symbols are used [11], although reduced-rate orthogonal codes can be designed for any number of transmit antennas. Thus, for R > 2, the convenience (linear ML decoding complexity) of using an orthogonal design comes at the cost of reduced spectral efficiency. An alternative to using orthogonal designs is to use quasi-orthogonal designs [7], which can achieve full rate with four antennas with higher complexity than orthogonal designs, but much lower than worst-case ML complexity. The additional complexity over orthogonal designs is because quasi-orthogonal codes reduce the ML detection problem to the joint detection of pairs of complex symbols, whereas orthogonal designs reduce it to the detection of individual complex symbols. The ML detector for a quasi-orthogonal code thus requires that each of the T1 /2 pairs of symbols be compared against M 2 hypothesis. An example quasi-orthogonal STBC

160


considered for cooperative-diversity with R = 4 relays is given by [9] ⎡

1 0 ⎢ 0 1 A1 = ⎢ ⎣ 0 0 0 0 ⎡ 0 0 ⎢ 0 0 A4 = ⎢ ⎣ 0 −1 1 0

⎤ 0 0 0 0 ⎥ ⎥, A2 = 04×4 , 1 0 ⎦ 0 1 ⎤ 0 1 −1 0 ⎥ ⎥ , B1 = 04×4 , 0 0 ⎦ 0 0 ⎡ 0 ⎢ 0 B3 = ⎢ ⎣ 1 0

A3 = 04×4 , ⎡

0 ⎢ 1 B2 = ⎢ ⎣ 0 0 0 −1 0 0 0 −1 0 0 0 1 0 0

−1 0 0 0 ⎤ ⎥ ⎥, ⎦

⎤ 0 0 0 0 ⎥ ⎥ , (6.13) 0 −1 ⎦ 1 0 B4 = 04×4 .

In Figure 6.2, four systems are compared by plotting the bit error rate (BER) of each system as a function of the signal-to-noise ratio (SNR). Three values of R are considered, R = {1, 2, 4}, and all systems transmit with a spectral efficiency of 3 (bits per second) per Hertz (bps/Hz). The signals are transmitted over Rayleigh fading channels, and the power is split evenly across the R transmit antennas. Since the noise power is unity, the transmitted power is P2 = SNR/R. The R = 1 system represents conventional point-to-point communications between a pair of terminals, each with a single antenna and no space-time coding. The R = 2 system uses the transposed Alamouti code given by (6.4). Two systems are compared for use with R = 4 transmitting antennas, the orthogonal code of (6.12) and the quasi-orthogonal code (6.13). The rate of the orthogonal spacetime code used with R = 4 antennas is 3/4, while the rates of the other STBC are all unity. In order for the spectral efficiency to be maintained at 3 bps/Hz, gray-labeled 8-PSK modulation is used for the full-rate systems (including the system with no space-time coding), while gray-labeled 16-QAM modulation is used for the rate 3/4 system. The worst-performing system is the one that uses just one transmit antenna (R = 1), while the next worst-performing system is the one with two transmit antennas (R = 2). The two systems’ four transmit antennas (R = 4) exhibit the best performance. The most significant feature to notice in Figure 6.2 is the steepness of the curves. At high SNR, these curves become straight lines, implying that asymptotically there is a linear relationship between the logarithm of the error probability and the SNR expressed in decibels. The negative slope is called the diversity of the system, also known as the diversity order or diversity gain. Inspection of the diagram reveals that the diversity of the R = 1 system is equal to 1 (i.e., the BER drops by an order of magnitude with every decade of SNR), while the diversity of the R = 2 system is equal to 2. Although the SNR is not sufficiently high in the figure to show it, the diversity of both two R = 4 systems is equal to 4. A system with R antennas is said to have full diversity if its diversity order is

161


R R

Figure 6.2. BER performance of four systems: An uncoded system with R = 1 transmit antenna, an Alamouti-coded system with R = 2 transmit antennas, an orthogonal STBC with R = 4 transmit antennas, and a quasi-orthogonal STBC with R = 4 transmit antennas. In each case, the spectral efficiency is 3 bps/Hz and the signals are transmitted over independent Rayleigh fading channels.

R. Thus, all four systems shown in Figure 6.2 exhibit full diversity, as seen by the fact that their error probabilities decay proportional to 1/SNRR . The performance of a space-time coded system can be determined by analyzing the pairwise error probability (PEP) between all pairs of distinct space-time codewords Sk and S . The PEP can be bounded by, for example, a Chernoff bound. By taking the limit with respect to the SNR, the diversity order is then determined. Full diversity is achieved by ensuring that Sk − S is full rank for all k = [15]. Linear dispersion codes need not be orthogonal or quasi-orthogonal. For instance, the linear dispersion codes presented in [6] were designed to maximize the mutual information between the transmitter and receiver under a power constraint. However, such codes do not lend themselves to the very simple decoder structures that are possible with orthogonal or quasi-orthogonal codes. While a brute-force ML decoder requires comparison against all M T 1 hypotheses, the complexity can be greatly reduced by using a sphere decoder [2]. Another option is to use the designs in [17], which permit decoupled symbol-by-symbol decoding and full-rate at the cost of reduced diversity.

162


6.4

DF distributed STBC Returning to the two-phase relay network configuration, consider the case that the first-phase transmission must take place over a channel that is corrupted by noise and fading. Now, there is no guarantee that any particular node will receive the transmission correctly. With a DF protocol, the source encodes its transmissions with a channel code. Each relay attempts to decode using the signal it receives, and can only participate in the second-phase transmission if it successfully decodes the message sent by the source. The condition that a node can only transmit in the second phase if it successfully decodes the message requires that the code be used not only as an error correcting code, but also as an error detecting code (i.e., the relay needs to detect the existence of uncorrectable errors). The set of nodes K that successfully decode the source’s message and may transmit during the second phase is called the decoding set [10], and the number of nodes in the decoding set is K = |K|. During the second phase, nodes in K transmit using a distributed space-time code. A major complicating factor is that the size of the decoding set is random, yet the space-time code must be designed with a certain number of transmitting antennas in mind. Because of this, the number of relays that actually transmit should be limited to the maximum number of antennas supported by the spacetime code, which we denote Km ax . It is possible that K < Km ax , which means that there are not enough relays participating in the second phase to use the entire space-time code. This implies that the space-time code should be “scale free”, meaning that it still offers the maximum possible diversity even if some of the transmitting antennas are not used. When K < Km ax , the maximum possible diversity order is reduced from Km ax to K. It is known that orthogonal space-time codes have this scale-free property [9]. If relay Ni ∈ K transmits during the second phase, then it does so by transmitting a signal vector ti of the form given by (6.3), where s is the signal obtained by decoding, reencoding, and remodulating, and the Ai and Bi are the dispersion matrices currently assigned to that relay. Note that since the composition of the set of transmitting nodes changes after each source transmission, the set of dispersion matrices assigned to a particular relay may also change. The protocol must be careful to make sure that each transmitting relay is allocated a distinct set of dispersion matrices. When either Ai or Bi is all zeros for all i, the received signal at the destination is as given by (6.8), where the columns of the space-time codeword S will be the signals transmitted by the relays. When K < Km ax , fewer relays transmit than there are columns in S and Km ax − K columns in S will be all zeros.

6.4.1

Performance analysis The performance of a DF system depends on the error control code or codes used. If the system uses a capacity-approaching code, such as a turbo code or a

6.4 DF distributed STBC

163

low-density parity-check (LDPC) code, then the codeword error rate over a particular link may be approximated by the information-outage probability of that link. The information-outage probability is the probability that the conditional mutual information between the channel input and output is below some threshold. For the first phase, the channel between the source and each relay is an additive white Gaussian noise (AWGN) channel when it is conditioned on the fading gain fi . The conditional mutual information between the signal transmitted by the source and the signal received by the ith relay is given by I(s, ri |fi ) = log2 (1 + P1 |fi |2 ),

(6.14)

where P1 |fi |2 is the “instantaneous” SNR of the link between the source and the ith relay. Note that (6.14) represents the mutual information when the source– relay channel is used all the time. However, in the DF protocol, the relay source– relay link is only used for T1 out of every T symbol periods. Thus, the mutual information needs to be scaled by the ratio T1 /T when computing the probability that a relay is in an outage. The information-outage probability of the link from the source to node Ni is

T1 I(s, ri |fi ) < r , (6.15) pi = Pr T where r is the rate of the error control code. Substituting (6.14) into (6.15) gives

T1 log2 (1 + P1 |fi |2 ) < r pi = Pr T , 2 (6.16) = Pr |fi | < Γ1 , where Γ1

=

2r T /T 1 − 1 . P1

(6.17)

Equation (6.16) is the cumulative distribution function (CDF) of the random variable |fi |2 evaluated at Γ1 . If we assume that fi is circularly symmetric complex Gaussian with zero mean and unit variance, then |fi |2 will be exponential with unit mean. By recalling the CDF of an exponential random variable, the information-outage probability is pi

=

1 − e−Γ 1 .

(6.18)

Because the fi s are i.i.d. and the threshold Γ1 is common to all relays, pi is the same at all R relays and may be denoted as p. Let Zi = {0, 1} be an indicator variable that equals unity when the ith relay is in an outage. Zi is a Bernoulli random variable with P [Zi = 1] = p. The number of relays K = |K| that successfully decode the first-phase transmission is K = R i=1 Zi . Because the channels are independent, so are the Zi s, and it follows that K is a binomial random variable. The probability that the random variable

164


K is equal to k is given by the probability mass function of K, pK [k]

= P r[K = k] R (1 − p)k pR −k . = k

(6.19)

The second-phase transmission may also be characterized in terms of an outage probability. However, the outage probability at the destination depends on the number of nodes K in the decoding set as well as the maximum number of nodes Km ax that may transmit during the second phase of the protocol. Define the conditional end-to-end information-outage probability for the second phase of the DF protocol as " , Pr[Outage|k] = Pr I(S, x|h) < r"K = k , (6.20) where S is the space-time codeword and h is a length min(k, Km ax ) vector containing the coefficients gi corresponding to those relays that transmit during the second phases. Equation (6.20) represents the probability that the destination is in an outage during the second phase given that the decoding set has k relays in it. When using a rate T1 /T2 orthogonal STBC over a point-to-point link, the mutual information is [11] I(S, x|h)

T1 log2 1 + P2 ||h||2 . T2

=

(6.21)

This mutual information expression assumes full use of the channel. However, in the DF protocol, the relay–destination link is only active for T2 out of every T channel uses, and thus (6.21) must be scaled by T2 /T . Substituting the scaled version of (6.21) into (6.20) results in

" T1 2 " log2 1 + P2 ||h|| < r K = k Pr[Outage|k] = Pr T " , = Pr ||h||2 < Γ2 "K = k , (6.22) where Γ2

=

2r T /T 1 − 1 . P2

(6.23)

This is the CDF of ||h||2 evaluated at Γ2 . When there are min(k, Km ax ) relays transmitting in the second phase, then ||h||2 is Erlang-m with min(k, Km ax ) degrees of freedom. Using the CDF of an Erlang-m distribution, the outage probability becomes

m in(k ,K m a x )−1

Pr[Outage|k]

=

1−

n =0

Γn2 −Γ 2 e . n!

(6.24)


165

Of course, when k = 0, Pr[Outage|k] = 1 since the system is always in an end-toend outage when no relays receive the source transmission (recall that we assume no direct link from source to destination). From the theorem on total probability, the overall end-to-end outage probability may be found from the conditional outage probabilities as Pr[Outage]

=

R

pK [k]P r[Outage|k].

(6.25)

k =0

By substituting (6.19) and (6.24) into (6.25), we get the following expression for end-to-end outage probability ⎛ ⎞ m in{k ,K m a x }−1 n R R Γ2 −Γ 2 ⎠ R k R −k ⎝ (1 − p) p e 1− . pD = p + k n! n =0 k =1

(6.26)

6.4.2

Numerical results By using (6.26), we can determine the outage probability for a network comprising R relays that uses a particular space-time code. Consider two examples, one that uses the transposed Alamouti code with dispersion matrices given by (6.4), and another that uses the orthogonal STBC with dispersion matrices given by (6.12). Both systems use a rate r = 1/2 error control code. With the Alamouticoded system, no more than Km ax = 2 relays may transmit during the second phase, while with the other orthogonal system, no more than Km ax = 4 relays may transmit. Let K = min(K, Km ax ) be the number of relays that actually transmit during the second phase, where K is the number of relays that successfully decode the source’s transmission. The total transmitted power of all relays is P = P1 + K P2 . As explained later in this section, the powers P1 and P2 are selected to minimize the outage probability subject to the total power constraint. Figure 6.3 shows the information-outage probability as a function of SNR for both space-time codes and a variable number of relays. Since the noise power is unity, the SNR is equal to the total power P . For the Alamouti-coded system, the number of relays is between 2 and 8, while for the other orthogonal system, the number of relays is between 4 and 10. For both systems, performance improves with increasing R. Even though no more than Km ax relays can be used during the second transmission phase, it is still advantageous to have more than Km ax relays present in the network. This is due to the diversity present in the first phase transmission. Having more than Km ax relays makes it more likely that at least Km ax relays will be able to decode the source’s transmission, and thus it is very likely that Km ax relays will transmit the entire space-time codeword during the second phase. From the curves, it is seen that the Alamouti code provides a diversity order of Km ax = 2 while the other orthogonal system provides a

166


Kmax Kmax

Figure 6.3. Comparison of the information-outage probability of several systems: direct, DF using the Alamouti code and up to Km ax = 2 transmitting relays, DF using orthogonal STBC and up to Km ax = 4 transmitting relays. For each value of Km ax , a set of seven curves is shown corresponding to a different number of relays R. For the Km ax = 2 system, the total number of relays R is between 2 and 8, while for the Km ax = 4 system there were between 4 and 10 relays. For each value of Km ax performance improves with increasing R.

diversity order of Km ax = 4. Using additional relays does not improve the overall system’s diversity order, but it does provide an additional coding gain. Also shown in Figure 6.3 is the performance of a direct point-to-point link transmitting with transmission power P = SNR and using a single antenna at each end of the communication link. Because this is just a single-input singleoutput (SISO) system, the diversity order is only equal to 1, and thus asymptotically the performance of the direct transmission is worse than the considered DF protocols. However, at very low SNR, the performance of the direct link is actually better than the systems that use a distributed STBC. This is because the system using a direct link may concentrate all of its power into the single transmission rather than diluting the energy across the transmissions of the two hops. Thus, at very low SNR, a direct link might be more effective than using the distributed STBC. However, keep in mind that these results assume that all channels have unity power gain. When relays are placed between the source and destination, then it is possible that channels used by the system with the

1

1

0.9

0.9

0.8

0.8

0.7

0.7

0.6

0.5

0.4

0.5

0.4

0.3

0.2

0.2

0.1

0.1

0

10 20 SNR (in dB)

0

30 (b)

167

0.6

0.3

0 (a)

Optimal power ratio

Optimal power ratio


0

5

10 SNR (in dB)

15

20

Figure 6.4. The optimal power ratio for: (a) the Km ax = 2 system and between 2 and 8 relays and (b) the Km ax = 4 system with between 4 and 10 relays. The optimal power ratio decreases with increasing R.

distributed STBC (i.e., the gains from source to relays and the gains from relays to destination) will have a higher gain than the channel used by the system that uses direct transmission. Let P1 /(K P2 ) be the ratio of the power used during the first phase to the power used during the second phase. The results shown in Figure 6.3 assume that the power is selected to minimize the information-outage probability subject to the total power constraint P = P1 + K P2 . To find the optimal power ratio for each SNR point, we compute the information-outage probability for all ratios between 10−4 and 1 in increments of 10−4 , and pick the ratio that minimizes the information-outage probability. The result of this optimization is shown in Figure 6.4. Figure 6.4(a) shows the optimal power ratios for the Km ax = 2 system (Alamouti coded) and Figure 6.4(b) shows the optimal power ratios for the Km ax = 4 system. For each system, a family of curves is shown corresponding to the different values of R considered in Figure 6.3. The power ratio decreases with increasing R and with increasing SNR. This is because as R grows, the likelihood that Km ax relays can decode the source’s signal improves as a function of P1 , and thus the system can afford to decrease P1 and devote more power to the second-phase transmission.

168


6.5

AF distributed STBC In contrast to DF protocols, AF protocols do not require that each relay fully demodulates and decodes the signal it receives from the source. Instead, relay Ni obtains the vector ri given in (6.1) by down-converting the received signal to baseband and passing it through a pair of filters matched to the in-phase and quadrature basis functions. The matched filters are sampled at the symbol rate, resulting in a set of T1 complex samples that are placed into the vector ri . Rather than demodulating and decoding ri , the relay transmits a linear combination of the samples in ri and its conjugates at power P2 [8]. We can write the normalized signal transmitted by node Ni in vector form as 1 (Ai ri + Bi ¯ri ) , ti = (6.27) P1 + 1 where Ai and Bi are the dispersion matrices assigned to node Ni . The two major differences between (6.27) and the DF transmitted signal in (6.3) are: (1) in AF, the transmitted signal is a linear combination of the samples in the received vector ri (and its conjugates) rather than a linear combination of the remodulated symbols in the vector s (and its conjugates), and (2) because the noise power is unity, the average received signal power is P1 + 1, and the scaling 1/(P1 + 1) is required to normalize the signal. For the important special case where either Ai or Bi is zero, we can simplify the transmitted signal similar to (6.7) as 1 Ci r(i) , ti = (6.28) P1 + 1 where

* r(i) =

r, ¯r,

if Bi = 0, if Ai = 0

(6.29)

and Ci is as given by (6.5). Using (6.2) and assuming perfect symbol-level synchronization, the resulting received signal vector at the destination can be written as x =

R gi P2 ti + w.

(6.30)

i=1

Substituting (6.1) into (6.29) and (6.30) results in R R P1 P2 P2 (i) x = Ci s + gi fi gi Ci vi + w. P1 + 1 P1 + 1 i=1 i=1 n This may be represented compactly as P1 P2 x = Sh + n, P1 + 1

(6.31)

(6.32)

6.5 AF distributed STBC

where the T2 × R space-time codeword S is as is ⎡ f1 g1 ⎢ f2 g2 ⎢ h = ⎢ . ⎣ ..

169

given in (6.9), the channel vector ⎤ ⎥ ⎥ ⎥, ⎦

(6.33)

fR gR and the complex noise vector n is Gaussian when conditioned on the {gi } and will generally be colored because the signal transmitted by the relay will contain a linear combination of the elements of the white noise vector vi . Compared with the DF case (6.8), the AF received signal in (6.32) differs in three ways: (1) all R relays transmit a signal during the second phase, not just those that can decode the source’s transmission, (2) the channel vector consists of the product of the source–relay and relay–destination channel gains instead of just the relay–destination channel gains, and (3) the additive noise will have a higher power and will generally be colored. As was the case for DF, the T2 × R matrix S in (6.32) plays the same role as a space-time code matrix in a conventional point-to-point multiple-input multipleoutput (MIMO) system, except that, in the distributed space-time code scenario, the matrix is generated without access to s. For this reason, we say that S defines a distributed space-time code operating in AF mode. We can think of h as the equivalent channel matrix and n as additive noise, although n is clearly a function of the space-time code. Because of the similarities to conventional STBCs, we can analyze the diversity gain and coding gain performance of this family of distributed AF space-time codes using the same technique we use for conventional codes, i.e., bounding the pairwise error probability.

6.5.1

Performance analysis The achievable diversity of LD codes operating in an AF system can be determined using the same technique that is often used for point-to-point space-time coded systems, i.e., by bounding the pairwise error probability. The exact results are complex and we refer the reader to [8] for details. The main result, however, is that the achievable diversity is log log P , (6.34) d=R 1− P which is achieved whenever the Sk − Sl is full rank for all l = k. This result converges to R for very large power P , so LD coding operating in AF systems achieves approximately the same diversity as a point-to-point system with R antennas.2 2

Note that here we assume that no information is passed directly between the source and destination. If such a link exists, the diversity result simply increases by 1.

170


Interestingly, when the number of relays is large and the power is also large, the coding gain for distributed LD codes is the same as for LD codes operating in point-to-point systems. On the other hand, when the power P is moderate, the code matrices should be designed such that the code is “scale-free,” i.e., it should perform well when some relays are not working. Mathematically, this requires the codeword difference matrices to remain full rank when some columns are deleted.

6.5.2

Practical distributed STBC for AF systems Although arbitrary LD codes can achieve almost full diversity with mild conditions on the Ai matrices, they are generally difficult to decode because ML decoding, i.e., 8 8 8 8 P1 P2 8 8 Sh8 , (6.35) arg min 8x − s 8 P1 + 1 8 has high computational complexity for the general case. This problem can be alleviated by using extending well-known orthogonal [15] or quasi-orthogonal [7] code designs for point-to-point systems to the distributed scenario, as discussed in [9]. The results are distributed codes that are fully diverse, allow low-complexity decoding, and are scale-free, yielding good coding gain for moderate transmit powers. Because the noise vector n is not generally white, true-ML detection cannot be achieved through linear processing methods such as the decoupleddecoding approach commonly used for orthogonal codes operating over point-topoint links. However, as reported in [9], the performance when using decoupled decoding is only slightly inferior to that of using true ML detection (i.e., around 0.5 dB).

6.6

The synchronization problem One of the key challenges when designing high-performance distributed spacetime coded systems is symbol-level synchronization among the relay nodes. In conventional point-to-point space-time coded MIMO systems, colocated antennas obviate this issue. In cooperative systems, sometimes described as virtual MIMO, the antennas are separated by wireless links. One approach is simply to use appropriate hardware and higher-layer protocols to ensure that transmissions from every participating relay are synchronized. Unfortunately, this may not be possible in practice and, in any case, it would require significant signaling overhead that may dramatically increase bandwidth requirements. Other approaches that effectively circumvent the synchronization problem include delay diversity, delay-tolerant distributed space-time codes, and space-time spreading (STS). We will next consider each of these approaches briefly.

6.6 The synchronization problem

6.6.1

171

Delay diversity It is well known that point-to-point communication over multipath fading channels provides diversity that can be exploited by appropriate receiver design [18]. In cases where intersymbol interference (ISI) is negligible, as is common in spread-spectrum systems, RAKE reception is sufficient. When ISI cannot be ignored, ML sequence detection can be performed using the Viterbi algorithm to extract full diversity in the number of resolvable paths. Mathematically, this involves transforming the frequency selective SISO system into an equivalent flat-fading multiple-input single-output (MISO) system that uses a particular space-time code induced by the frequency selective channel. Interestingly, the reverse is also possible. That is, we can transform a flat-fading MISO system into a virtual frequency selective SISO system by using a space-time code described by the following scheme: in the first time slot, the symbol x[1] is transmitted on antenna 1 and all other antennas are silent. In the second time slot, x[1] is transmitted from antenna 2 and x[2] is transmitted by antenna 1 and all other antennas remain silent. At time slot m, x[m − l] is transmitted on antenna l + 1 for l = 0, 1, . . . , L − 1. This transmission scheme yields a received signal that is identical to that received in a SISO frequency selective channel with L paths. This special point-to-point space-time coding scheme is called delay diversity [22]. Delay diversity cannot be implemented in cooperative communication systems in exactly this way without requiring what we are trying to avoid, i.e., synchronization to determine which relay transmits which symbol in which order. Fortunately, it is straightforward to implement delay diversity in a distributed manner. The simplest way to do this is simply for the relays to wait a random amount of time before they retransmit the symbol or signal they have most recently received. The destination will receive a signal that is equivalent to that received in a SISO multipath channel, so full diversity will be achievable (with probability 1), assuming ML detection at the destination. Linear detectors/equalizers can also be used at the destination, e.g., minimum mean-squared error (MMSE), or decorrelating equalization, with some diversity loss. Interestingly, MMSE detection in conjunction with serial interference cancellation (decision feedback implementation) achieves full diversity [21] with much lower complexity than ML detection when the number of relays is large.

6.6.2

Delay-tolerant space-time codes Another approach to distributed space-time coding without synchronization involves the use of so-called delay-tolerant distributed space-time codes whose performance is insensitive to delays among the received signals from each relay. It is well known that the diversity order of a STBC is equal to the minimum rank of the difference matrix over all pairs of distinct code matrices [15]. A spacetime code is said to be τ -delay tolerant if for all distinct code matrices Sk and

172


S , the difference matrix Sk − S retains full rank even though the columns of the code matrices are transmitted or received with arbitrary delays of duration at most τ symbols. Let S be a codeword matrix from a synchronized STBC, as in (6.9), and let ∆S be the code matrix received at the destination due to transmission or propagation delays. Then ∆S can be written as ⎤ ⎡ 0∆ 2 ··· 0∆ R 0∆ 1 (6.36) ∆S = ⎣ C1 s(1) C2 s(2) · · · CR s(R ) ⎦ . 0τ −∆ 1 0τ −∆ 2 · · · 0τ −∆ R The collection of all such codewords ∆S constitutes a τ -delay-tolerant space-time code if for all delay profiles {∆k }R k =1 such that ∆k ≤ τ for all k, it achieves the same diversity as the synchronized code. Work on delay-tolerant codes under this framework includes [3, 5, 13, 16]. Although delay diversity extracts full diversity in the number of relays, delay-tolerant space-time codes promise better coding gain and, in some circumstances, lower decoding complexity.

6.6.3

Space-time spreading (STS) Delay diversity is successful in achieving full diversity in part because the distinct delays for the received signals from each relay provide a unique signature enabling the receiver to separate each resolvable path before cophasing and combining. A similar unique signature can be implemented with coding, i.e., STS. One of the simplest STS strategies is to assign the source and each relay a unique spreading code, as in code-division multiple access (CDMA) communications. When the relays are not synchronized, the signal received at the destination is similar to that obtained in a conventional (noncooperative) asynchronous CDMA uplink, so that the transmissions from the source and each relay can be separated using well-known multiuser detection (MUD) signal processing strategies, cophased, and recombined to extract full diversity without symbol-level synchronization. Note that, although CDMA is a spread-spectrum signaling format, it does not need to operate in a spectrally inefficient mode. In fact, it was shown in [19] that the information outage probability of an asynchronous cooperative CDMA uplink under decorrelating MUD is minimized when the system is slightly overloaded, i.e., when the number of relays is slightly larger than the processing gain. This is not surprising because an overloaded CDMA system is operating at high spectral efficiency. A more sophisticated STS strategy was designed in [14]: it does not require synchronization among the relays, channel estimation, or complex multiuser signal processing at the destination or relays. The necessity for channel information is obviated by the use of differentially encoded symbols from each source, as in [4], during the first transmission phase. During the second transmission phase, dedicated relays use an STS AF strategy described in [4] that allows low complexity decoding and large diversity gain without channel estimation. Because high-complexity MUD strategies are not used here, the residual multiple access

References

173

interference (MAI) and ISI must be mitigated by the use of specially designed spreading codes that provide an “interference-free window” (IFW), where the offpeak aperiodic autocorrelation and crosscorrelation values become zero, resulting in zero MAI and ISI, provided the maximum asynchronous delay is within the IFW [20]. The resulting system extracts full diversity without channel knowledge or complex MUD at the destination or relays.

6.7

Conclusion Distributed STBCs are able to effectively exploit the spatial diversity present in a multirelay network. With a distributed space-time code, each relay transmits a particular column of a space-time codeword. The DF strategy is appropriate when there are more relays than there are columns in the space-time codeword, since only a subset of relays may participate in the transmission of the distributed space-time codeword, namely those that receive the source’s transmission. However, DF protocols require coordination among the relays to ensure that each relay transmits a specific column of the space-time codeword. AF protocols are well suited to the case that the number of relays is equal to the number of columns in the space-time code, since with AF protocols every relay participates in the transmission of the space-time codeword regardless of the quality of the source–relay transmission. In addition to the implementation challenges that are common to conventional MIMO systems, the lack of synchronization at the destination receiver imposes additional challenges to systems that use distributed space-time codes. The synchronization problem can be alleviated by using delay diversity, STS, or delay-tolerant space-time codes.

References [1] S. M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE Journal on Selected Areas in Communications, 16, 1998, 1451–1458. [2] M. O. Damen, A. Chkeif, and J. Belfiore, “Lattice code decoder for spacetime codes,” IEEE Communications Letters, 4, 2000, 161–163. [3] M. O. Damen and A. R. Hammons, “Delay-tolerant distributed TAST codes for cooperative diversity,” IEEE Transactions on Information Theory, 53, 2007, 3755–3773. [4] M. El-Hajjar, O. Alamri, S. X. Ng, and L. Hanzo, “Turbo detection of precoded sphere packing modulation using four transmit antennas for differential space-time spreading,” IEEE Transactions on Wireless Communications, 7, 2006, 943–952.

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[5] A. R. Hammons and M. O. Damen, “On delay-tolerant distributed spacetime codes,” in Proc. of IEEE Military Communications Conference (MILCOM), 2007. IEEE, 2007. [6] B. Hassibi and B. M. Hochwald, “High-rate codes that are linear in space and time,” IEEE Transactions on Information Theory, 48, 2002, 1804–1824. [7] H. Jafarkhani, “A quasi-orthogonal space-time block code,” IEEE Transactions on Communications, 49, 2001, 1–4. [8] Y. Jing and B. Hassibi, “Distributed space-time coding in wireless relay networks,” IEEE Transactions on Wireless Communications, 5, 2006, 3524– 3536. [9] Y. Jing and H. Jafarkhani, “Orthogonal and quasi-orthogonal designs in wireless relay networks,” IEEE Transactions on Information Theory, 53, 2007, 4106–4118. [10] J. N. Laneman and G. W. Woernell, “Distributed space-time-coded protocols for exploiting cooperative diversity in wireless networks,” IEEE Transactions on Information Theory, 49, 2003, 2415–2425. [11] E. G. Larsson and P. Stoica, Space-time Block Coding for Wireless Communications. Cambridge University Press, 2008. [12] R. Nabar, H. Bolcskei, and F. Kneubuhler, “Fading relay channels: Performance limits and space-time signal design,” IEEE Journal on Selected Areas in Communications, 22, 2004, 1099–1109. [13] Y. Shang and X. G. Xia, “Shift-full-rank matrices and applications in spacetime trellis codes for relay networks with asynchronous cooperative diversity,” IEEE Transactions on Information Theory, 52, 2006, 3153–3167. [14] S. Sugiura, S. Chen, and L. Hanzo, “Cooperative differential space-time spreading for the asynchronous relay aided CDMA uplink using interference rejection spreading code,” IEEE Signal Processing Letters, 17, 2010, 117– 120. [15] V. Tarokh, H. Jafarkhani, and A. Calderbank, “Space-time block codes from orthogonal designs,” IEEE Transactions on Information Theory, 45, 1999, 1456–1467. [16] M. Torbatian and M. O. Damen, “On the design of delay-tolerant distributed space-time codes with minimum length,” IEEE Transactions on Wireless Communications, 8, 2009, 931–939. [17] D. Torrieri and M. C. Valenti, “Efficiently decoded full-rate space-time block codes,” IEEE Transactions on Communications, 58, 2010, 480–488. [18] D. Tse and P. Viswanath, Fundamentals of Wireless Communication. Cambridge University Press, 2005. [19] K. Vardhe, D. Reynolds, and M. C. Valenti, “The performance of multiuser cooperative diversity in an asynchronous CDMA uplink,” IEEE Transactions on Wireless Communications, 7, 2008, 1930–1940. [20] H. Wei, L. Yang, and L. Hanzo, “Interference-free broadband single and multicarrier DS-CDMA,” IEEE Communications Magazine., 43, 2005, 68– 73.

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[21] S. Wei, D. L. Goeckel, and M. C. Valenti, “Asynchronous cooperative diversity,” IEEE Transactions on Wireless Communications, 5, 2006, 1547– 1557. [22] A. Wittneben, “A new bandwidth efficient transmit antenna modulation diversity scheme for linear digital modulation,” in Proc. of IEEE International Conference on Communications (ICC), 1993. IEEE, 1993.

7

Collaborative relaying in downlink cellular systems Chandrasekharan Raman, Gerard J. Foschini, Reinaldo A. Valenzuela, Roy D. Yates, and Narayan B. Mandayam

7.1

Introduction The deployment of relays in cellular system has been standardized in the WiMAX, IEEE 802.16j [1] standard and is a topic of discussion in the advanced specifications of Third Generation Partnership Project (3GPP) long-term evolution (LTE) [3]. Although commercial relay deployments in cellular systems are not prominent at present, future wireless cellular systems will involve operation with dedicated relays to improve coverage, increase cell-edge throughput, deliver high data rates, and assist group mobility. The proposed architecture is such that relays would be placed at certain locations (planned or unplanned) in the cell to help in forwarding the message from the base station to the user in the downlink, and from the user to the base station in the uplink. Relays will be more sophisticated than simple repeaters and could perform some digital base band processing to help the destination terminal get better reception. These relays will rely on air interfaces, and hence avoid the considerable backhaul costs involving data aggregation and infrastructure costs associated with backbone connectivity. However, there are a lot of open issues that require research to answer.

7.1.1

Research challenges Some of the major research issues in relay-based cellular systems are as follows: (1) Throughput gains due to relay deployments In cellular networks that are coverage limited, deploying relays can help in multihop transmission and provide power gains due to a reduction of distance attenuation [4]. These power gains, in turn, translate to throughput improvements for the edge users. However, in interference limited settings, as is common in cellular systems, uncoordinated transmission by relays leads to an increase in the overall interference levels in the cell and could be counter-productive by reducing the signal-to-interference-plus-noise (SINR) levels of users in the system. Coordination of transmissions in the system would require centralized control and incur high costs and overheads, especially in the uplink. Cooperative Cellular Wireless Networks, eds. Ekram Hossain, Dong In Kim, and Vijay K. Bhargava. Published by Cambridge University Press. C Cambridge University Press, 2011.

7.1 Introduction

177

Thus, there is a need for a thorough evaluation of throughput improvements in a cellular system. In the cellular systems literature, there have been simulation studies to evaluate throughput gains in cellular systems, e.g., [5, 6, 8]. Even though the studies were conducted under different sets of (idealized) assumptions, throughput improvements in interference-limited cellular systems were shown to be around 30–40% for the edge users. In this chapter, we evaluate the gains due to relay deployment by two different relaying strategies and the results indicate that throughput gains are of the same order. However, there may exist better practical schemes – which remain open – or specific scenarios where relays provide larger throughput improvements. A simple case where relays provide throughput improvements is the downlink scenario where the edge user is in a deep canyon and the relay is placed in the line of sight of both the base station and the shadowed user. (2) Relay placement The benefits from relay deployment depend on where the relays are placed in the cell. Throughput improvements depend on the transmit power, relay antenna pattern, and location of the relays in the system. Placing relays closer to an edge user helps the edge user. However, when relay transmissions are uncoordinated, the relays may cause near line-of-sight interference to an edge user of the neighboring cell. The optimal relay placement depends on the transmission and scheduling strategies, transmit power of the relays, etc. An issue closely related to the relay placement problem is the choice of height of the deployed relays. In macrocellular environments, propagation characteristics of the base–relay link and the relay–user link could be completely different, depending on whether the relays are mounted on tall poles or on roof tops. These factors may very well affect the system performance due to relay deployments. There are not many measurementbased models to cover all the scenarios of relay placement; some empirical models were described in [2]. These issues apart, service providers often do not have much choice in placing the relays in a given geographical area. (3) Lack of good models for relaying in cellular systems Multihopping in wireless networks has been studied in the context of ad-hoc networks and peerto-peer networks [7]. The main issue addressed in such networks is the routing problem. Interference constraints are abstracted as combinatorial constraints and many insightful results and good algorithms have been proposed to improve the throughput of such networks. Cellular networks, however, are unique in that the traffic is one-to-many in the downlink and many-to-one in the uplink. Direct application of the solutions obtained in the context of ad-hoc networks is not optimal for cellular systems. Hence, performance evaluation of relays in cellular system requires fresh thought to be given to the problem. On the other hand, the information theoretic relay channel [9] has been an active area of research since the 1980s. However, for some coding strategies proposed by Cover and El Gamal in [10] for special cases of the

178


single-relay channel, the capacity of the general relay channel is still unknown [11]. Though most of the earlier work assumes that the relay can transmit and listen over the same band, the half-duplex constraint (the relay cannot simultaneously transmit and receive in the same band) is taken into account in later work, for example [12, 13]. Information theoretic studies reveal that when there are one or two relays, the best strategy is to make use of both the source and relay transmissions at the user location, rather than multihopping from the source to the destination through the relay(s). The user can make use of signals from both the source and the relay to get a better signal strength and hence a better rate. Multihopping, on the other hand, ignores the signal from the source, however strong it is. The information theoretic relaying protocols mentioned above often involve complicated multiuser coding and decoding techniques, which are far from practical implementation. There has been some work trying to bridge the gap between the information theoretic and practical multihopping schemes, e.g., [14, 15]. Most of the results in these works correspond to the case of a linear network of nodes, where there is a single commodity flow of message from the source node to the sink node through a set of relay nodes. Any interference is due only to simultaneous transmissions from different relay nodes. This can be completely eliminated by multiuser coding/decoding techniques. Such an analysis does not carry over directly to the cellular systems since there are multiple simultaneous flows and multiuser techniques may incur significant overheads. (4) Fairness Service level agreements between cellular service providers entail certain fairness requirements. For example, in the cellular system, the edge users and the users near the cell require the same level of service. Many other fairness schemes, including proportional fairness [16] and max–min fairness [17, Chapter 6] have been proposed for cellular systems serving voice and data. Present-day cellular systems implement schedulers in the MAC layer to provide various degrees of fairness to users. In this work, we assume that 90% of users are required to be served at a common rate. When relays are present in the system, designing distributed scheduling schemes to provide fairness is an active area of research. In this chapter, we evaluate the performance of low-cost half-duplex relays in the downlink of a cellular system. The deployment scenario we consider is to mount a low-cost (preferably low-powered) device per sector over roof-tops of buildings. Such devices can relay the information from the base station to users in the cell.

7.1.2

Related work Relay deployment in a cellular system has been proposed to solve the issue of a lack of coverage over a large area [1]. The use of relays in cellular systems has also

7.1 Introduction

179

been proposed to bring capacity improvements [18]. Viswanathan and Mukherjee [5] studied the performance of a centralized throughput-optimal scheduler on a cellular network with relays. They presented a centralized downlink scheduling scheme that guarantees the stability of user queues for the largest set of arrival rates into the system. Each user has a queue at the base station and a queue at its serving relay and the objective of the scheduler is to stabilize both queues while maximizing the throughput. The throughput results obtained by simulations in [5] suggest that simultaneous transmissions (due to multihopping) exploiting spatial reuse could lead to cell-wide throughput gains in a cellular network.

7.1.3

Overview of contribution In addition to a multihopping model, wherein the message travels to the destination in two hops, in this chapter we evaluate the performance of a collaborative power addition (CPA) scheme with a single relay available per user. We bring an additional dimension to the benefits of relays in a cellular system, by quantifying the power savings due to the deployment of relays. Peak power savings in cellular networks are very important elements of amplifier costs in base stations. Significant peak power savings can reduce the cost of amplifiers and hence the capital expenses for deploying cellular networks. Also, average power savings while operating cellular networks can save operational expenses such as electricity bills for the cellular operators. In the peak CPA (P-CPA) scheme, we first consider a hypothetical model where 90% of the users are required to be served a file (henceforth, we use the terms message and file interchangeably) of a fixed size before a certain deadline. Depending on the interference seen by each user, the mutual information (MI) or the instantaneous “rate” of the users varies over time. Users leave the system as they get the complete file before the deadline. We use an offline computation to find the 10% of users who are least able to get the whole file before the deadline and discard them at the beginning. We run the real system without the users in outage. When relays are present in the system, we evaluate the peak power savings at the base station to deliver a file of the same size to the same number of users in the system as when the base stations and relays are transmitting at their peak power limits. We also find the improvements in common rate for the users in the presence of the relays when the peak power of the base stations is fixed for both the baseline and the system with relays. We then consider the power control capability to the base stations and relays. We evaluate the power savings and throughput improvement in the power control CPA scheme (PC-CPA). For a desired common rate requirement for 90% of users in the system, we find the common peak power constraint in the baseline case and in the system with relays to guarantee the common rate. When the relays get the complete message, they collaborate with the base station to transmit the message to the users. Each time a relay becomes eligible to transmit, the optimal set of powers are found to satisfy the desired rate requirement. The

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set of users that violate the peak power constraint are discarded at the beginning. The improvements in common rate are also evaluated through a similar procedure. The second relaying scheme we evaluate is simple multihopping, wherein the base stations and relays transmit in orthogonal time slots. The baseline system is similar to the baseline in the P-CPA scheme described above. When relays are present in the system, we simulate a time-slotted system. For a common rate requirement for 90% of users in the system, the base stations transmit at peak power in odd time slots. The relays and users are in the receive mode. In the even time slots, the base stations are turned off and relays transmit to the respective users. The relays employ power control to target the remainder of the user population to provide the residual rate to the users. We describe the system in detail in Section 7.2. We do not consider multiuser scheduling gains, MIMO gains, or any other complex interference mitigation techniques. Thus the gains shown in the network arise purely from the power gains at the user location due to the relay transmissions.

7.2

System model Our work evaluates the power savings and improvement in common rate among users due to relay deployments in a cellular system. However, to model and simulate all dynamics of a cellular system may be too complicated. In order to overcome such difficulties, we make some reasonable simplifying assumptions and take an idealized look at the model and operation of a cellular system. In order to make a fair comparison, the assumptions are kept consistent across systems with and without relays. We consider a cellular system with idealized hexagonal cells with a base station at the center of each cell. The topology is shown in Figure 7.1. The first two tiers of interferers are considered and the activities of the farther tiers of cells are mirrored by the central ring of 19 cells. The site-tosite distance (distance between any two base stations) is taken to be 1 mile. The cells are divided into 120 degree sectors, with each sector illuminated by a base station antenna pattern given by 2 θ (7.1) , Amax A(θ) = − min 12 θ3dB where A(θ) is the antenna gain in dBi in the direction θ, −180 ≤ θ ≤ 180, min(.) denotes the minimum function, θ3dB = 70 degrees is the 3 dB beamwidth and Amax = 20 dB is the maximum attenuation. The antenna gain pattern is shown in Figure 7.2. At the receiving terminal (relay or user), the transmitted power undergoes attenuation due to the distance traveled and shadowing effects around the

7.2 System model

181

Figure 7.1. Wrap-around simulation model. The central ring of 19 cells is used for the simulation. The surrounding cell activity is mirrored in the center ring. The directions of the arrows represent the directions of the main lobe of the sectorized antenna.

receiver. The propagation attenuation between a transmitting terminal (base station or relay) and a receiving terminal (relay or user) consists of the pathloss and the shadowing component. At any receiving terminal, the transmitted power is attenuated in dB as PL(d) = −31.5 − 38 log10 d, where d is in meters. The shadowing is modeled as lognormal with mean 0 dB and a standard deviation of 8 dB. The shadowing is assumed to be spatially uncorrelated and fixed for a given set of user locations. The base station and the relay antenna gains are taken to be 15 dB (at zero degree horizontal angle) and user antenna gain as −1 dB. Other losses account for 10 dB. Together with the above losses, we include the antenna pattern loss to calculate the received power. The receiver noise figure is set at 5 dB, and the thermal noise power at each receiving terminal

182


Figure 7.2. Antenna gain pattern (from [2]) as a function of the horizontal angle in degrees. The mathematical expression for the gain is given in (7.1). (relay or user) is assumed to be −102 dBm. The effect of multipath small-scale fading is ignored in our simulations. All users share the same band of frequencies and hence simultaneous transmissions can interfere with each other. The total interference at each receiving terminal from all transmitters in the system is modeled as Gaussian noise and assumes that other users use Gaussian codebooks. The achievable rate to a user i at time t is calculated as the Shannon rate Ri (t) = log2 (1 + ρi (t)),

(7.2)

where ρi (t) denotes the SINR for user i at time t The parameters used in the above-mentioned simulation set-up are summarized in Table 7.1. We use this simulation set-up to evaluate all relaying methodologies proposed in this chapter. We simulate a downlink OFDM-like system wherein users in orthogonal time or frequency slots do not interfere with each other. However, users in the same resource unit interfere with the other transmissions in the band. We simulate the worst-case scenario where the system is fully loaded, i.e., users are present in all available resource units (or time–frequency slots) in all the sectors. The time– frequency slots are reused in each sector. We assume that the time–frequency slots are orthogonal, and focus only on a particular time–frequency slot within which we simulate the complete cellular system such that there is one active user per sector at a given time. Hence, in a 19-cell network with three sectors

7.2 System model

183

Table 7.1. Simulation parameters Network topology Site-to-site distance Bandwidth Path-loss model Path-loss exponent Shadowing Multipath fading Antenna pattern Antenna gains Other losses Thermal noise power at the receiver Outage

19 cells, three sectors per cell with wraparound 1 mile 5 MHz COST-231 Hata model α = 3.8 Lognormal, with zero mean, 8 dB standard deviation for access and backhaul None Sectorized for base stations; omnidirectional for relays 15 dB (for base station and relays); −1 dB for users 10 dB −102 dBm 10% for baseline and relays

per base antenna, at most 57 users are served in a given time–frequency slot. In our simulations, we use the following heuristic to create a random user population along with an association rule. Users are placed one-by-one in a uniformly random fashion across the network until all 57 base station sectors are occupied. For each random realization of a user location, the base station sector with the highest received signal strength is chosen to associate with the user. If the base station sector is already occupied by another user, the user is not allowed into the system and a new user location is generated. Along with a random realization of a user location, independent lognormal random variables are also instantiated to account for the shadow fading gains between each base station and the user in the baseline system. If relays are present in the system, the fading gains are also generated for base station–relay links and relay–relay links. In this way, random placement is carried out until all 57 sectors are occupied by exactly one user per sector. Each user is equipped with an omni-directional antenna. A relay with an omni-directional antenna is placed in the direction of the main lobe of each base station sector antenna as shown in Figure 7.3. The relays always associate with the corresponding base station sector. The relay placement is an important parameter to be considered since the power gains and throughput improvements depend on the interference generated by the relays, which in turn depends on the transmit power, geographic location of the relays, and the propagation environment. In our simulations, we experiment with various relay placements and the simulation results are presented for the relay locations for which the gains are found to be maximum. The relay powers are also varied so that we get the maximum peak power savings.

184


Figure 7.3. Position of relay location in a cell. The relays (represented by small circles) are placed at half the cell radius in the direction (given by the arrows) of the main lobe of the sector antenna. The base station at the center of the cell is represented by a square.

7.3

Collaborative relaying in cellular networks In the CPA scheme devised in [19], the relay collaborates with the base station to help the message reach the destination. In our simulation model, each base station sector has a single user to be served and a relay that may help the source to deliver the message to the user associated with the source. In what follows, we focus our attention on an isolated triplet of base station (source), relay, and user in a single sector. Gaussian encoding is used across all other sectors, the interference from other sectors is considered as if it were additive Gaussian noise. Suppose the source wants to transmit one of the M messages to the destination, under a power constraint P . The source transmits a Gaussian codeword of length N = (log M )/R, where R is the rate of the code. By Shannon’s channel coding theorem [20, Chapter 9], if N is large enough, the message can be decoded reliably at the destination provided R < log(1 + ρ), where ρ is the received SINR. In our simulations, we are interested in achievable rates and assume that the instantaneous mutual information at the receiver is exactly R = log(1 + ρ). Assume that the source picks a rate R code C1 and sends one of M equally probable messages to the destination, using a codeword of length N . Let the received SINR ρS R between the source and relay be greater than the received SINR ρS D at the destination. Then, there exists some β > 1 such that log(1 + ρS R ) = β log(1 + ρS D ),

(7.3)

i.e., the capacity of the channel from source to relay is β times greater than that of the channel from source to destination. We can now construct codebook C2 derived from C1 by observing only the first N/β symbols of every codeword. The relay can then reliably decode the received message since the rate of C2 is R =

log M < log(1 + ρS D ). N/β

(7.4)

7.3 Collaborative relaying in cellular networks

Source

Relay

185

Destination

Figure 7.4. Collaborative relaying: before the relay decodes the message.

Source

Relay

Destination

Figure 7.5. Collaborative relaying: after the relay decodes the message.

In [21, Appendix F], the authors discuss the coding interpretation of a similar collaborative strategy. They also discuss the connection of such a coding setting with coding for an arbitrary varying channel (AVC), which was first dealt with in [22] and subsequently studied in [23]. We simulate a similar collaborative coding strategy wherein before the relay decodes the message as shown in Figure 7.4, the received power at the destination node is only due to the base station transmission. After it decodes the message, the relay joins the base station to help the base station in delivering the message to the destination as shown in Figure 7.5. At this point, if we assume that transmit symbol time slots at the relay and base station are synchronized and the code books are shared, the system can be viewed as a 2 × 1 multiple-input single-output (MISO) system without channel information at the transmitter. There is an effective power addition of the base station and relay transmissions at the destination [24, Chapter 3]. A similar scheme has been proposed in the literature as the dynamic decode-and-forward (DDF) scheme [25]. We simulate this collaborative relaying strategy in two ways:

r Base station and relay transmit at their respective peak powers. In this case, the transmit power is fixed and the users get variable rates depending on SINR at the user locations. When a target rate is obtained by a user, the user leaves the system and the corresponding base station sector is turned off, thus reducing the amount of interference in the system. We term this

186


the peak collaborative power addition (P-CPA) scheme. This is described in Section 7.4. r Base station and relay operate with power control so that the users obtain a target desired rate. In the baseline case, for a given desired rate requirement r0 bps/Hz, a feasible set of powers are found to better satisfy the rate requirement, allowing certain users to be in outage. When the relays decode the message in the collaborative scheme, the optimal powers are recalculated to find another feasible set of powers to satisfy the rate requirement at the same outage level. This is the PC-CPA scheme. It is described in Section 7.5.

7.4

CPA with peak power transmissions (P-CPA)

7.4.1

Principle of operation P-CPA baseline In the baseline of the P-CPA scheme, each base station sector transmits at its peak power to its own intended user. Since all users share the same band of frequencies, they receive interference from all the base station sectors in the system. If at time t, pi (t) is the peak power of the transmitting base station sector corresponding to the ith user, hij is the channel gain, including path-loss and shadowing, from the jth base to the ith user, and σ 2 is the variance of the noise power at the receiver, the instantaneous received SINR for user i is given by hii pi (t) . 2 j = i hij pj (t) + σ

ρi (t) =

(7.5)

Since we assume Gaussian signaling, the mutual information (MI) or the instantaneous “rate” to each user is Ri (t) = log2 (1 + ρi (t)) bits/symbol.

(7.6)

At time t = 0, all base stations simultaneously transmit to their associated user. As time progresses, for any small time interval [t, t + ∆t], user i accumulates MI Ii (∆t) = Ri (t)∆t. The MI for user i at time t is given by . Ii (t) =

t

log2 (1 + ρi (ξ)) dξ.

(7.7)

0

If user i accumulates MI corresponding to the required amount L of data before the deadline T , i.e., τi = min {t : Ii (t) = L}, 0≤t≤T

(7.8)

7.4 CPA with peak power transmissions (P-CPA)

187

then the user leaves the system and the associated base station sector is turned off at time τi , reducing the overall interference levels in the system. Hence, * pi (t) =

P, t < min(τi , T ), 0, t ≥ min(τi , T ),

(7.9)

where P is the peak power of the base station transmission. Note that the ρi (t) of user i and the rate Ri (t) are time-varying quantities. At time t = T , the users that remain in the system are those users that did not get the complete file. It is these remaining users that are in outage.

P-CPA system with relays The operation of the P-CPA system with relays is as follows. The requirement is the same as for the baseline case: to deliver a file of size L to as many users within the time T . At time t = 0, the base stations transmit at peak power to users associated with them. The relay node placed in the sector also receives the data sent to the user by the base station. If the relay receives the complete file before the user does, the relay can potentially be useful to the user by helping it receive the message faster. On the other hand, the relay transmission can create additional interference for the other users in the system. In our simulations, we follow a myopic1 policy on whether to turn on the relay or not: the relay transmits at peak power to help its user only if the instantaneous sum-rate of the whole system increases by turning the relay on. The sum-rate of the system is calculated as the sum total of the instantaneous rates of the existing users in the system and is a natural system-wide metric to use in order to decide whether the relays should transmit or not. At every epoch, one relay among the set of all relays that are eligible to be turned on, receives the message, the myopic sumrate metric is applied, and those relays that increase the sum-rate are turned on to help the users in the system. If the relay increases the sum-rate of the system, the relay is turned on and helps the user with a transmission reinforcing the same message as the base station using the code described in Section 7.3. If qi (t) is the power transmitted from relay i at time t and gij is the channel gain from user i to relay j, the effective SINR at ith user location when the relay is active is given by

ρri elay (t) =

1

hii pi (t) + gii qi (t) . 2 j = i hij pj (t) + gij qj (t) + σ

(7.10)

The policy is myopic since, at the time when the relay receives the message, the global optimal decision whether the relay should transmit or not is unknown.

188


The instantaneous rate and the mutual information for user i at time t are given by Rir elay (t)

= log2 (1 + ρri elay (t)), . t = Rir elay (ξ)) dξ.

Iir elay (t)

(7.11) (7.12)

0

If Hij denotes the channel gain from the jth base station to the ith relay, . t Hii pi (ξ) dξ (7.13) log2 1 + Ji (t) = 2 0 j = i Hij pj (ξ) + σ represents the cumulative MI at the relay at time t. Suppose relay i becomes eligible to transmit at time t, i.e., Ji (t) > L, then denote the sum-rate of the system at time t as a function of qi (t) as hii pi (t) + gii qi (t) . (7.14) log2 1 + SR(t, qi (t)) = 2 j = i hij pj (t) + gij qj (t) + σ i The relay power at time t is given by * Q, if Ji (t) > L, SR(t, Q) > SR(t, 0) and t < T, qi (t) = 0, otherwise,

(7.15)

where Q is the peak power constraint of the relays. Each user sees a time-varying SINR and the time-varying rate given by Ri (t) = log2 (1 + ρri elay (t)). As with the baseline case, for any interval of time [t, t + ∆t], user i accumulates MI amounting to Ii (∆t) = Ri (t)∆t and the MI for user i at time t is . t Ii (t) = log2 (1 + ρri elay (ξ)) dξ. (7.16) 0

Similarly to the baseline case, if the user accumulates MI amounting to the full file size L within the stipulated time T , the user leaves the system and the associated base station and relay are switched off. Thus the effective interference in the system is reduced. At time t = T , the users that remain in the system are those users that did not receive the complete file.

7.4.2

User discarding methodology The user discarding procedure can be divided in two phases: (i) A learning phase where we learn the power threshold, which is used as a criterion to determine the users in outage. All the users that are not in outage require their corresponding base stations to have peak powers lower than the power threshold. The network will be operated with peak powers of all base stations capped at the power threshold. (ii) After the power threshold is found, we assume the availability of a very fast computing facility and perform an off-line computation to find out the


189

set of users that are in outage. Such users could be discarded before the start of the simulations so that the other users benefit from the absence of interference from these users. Hence, this takes care of the causality of the discarding phase from the operation of the real network. We conduct Monte Carlo simulation runs for the baseline case as well as the case with relays in this chapter. For each simulation run random instantiations of 57 user locations (as per Section 7.2) and associated statistically independent shadow fading values are generated. Once the random values are instantiated, they are stored in our simulation software program. The same set of user locations and shadow fading values serve as inputs to the baseline and the system with relays. We now explain the learning phase. Consider that a single instance of the simulation runs in the baseline case. For the given instantiation, there are 57 users, one in each sector. We fix a peak power threshold P for the base stations and also fix the desired common rate for users as r0 bps/Hz. When the baseline system operation is over, the users that are in outage remain in the system at time T . Let the number of users in outage for the kth instantiation when the power threshold is P and desired common rate r0 be Ok (P, r0 ). For the same power threshold P and common rate r0 , we run a large number K of instantiations. We then find the total number of users in outage as O(P, r0 ) =

K

Ok (P, r0 ).

(7.17)

k =1

The percentage of users in outage for the threshold P and desired rate r0 is then O(P, r0 ) × 100%. 57K

(7.18)

If O(P, r0 ) > 10%, we increase the power threshold to P > P . On the other hand, if O(P, r0 ) < 10%, we decrease the power threshold to P < P . Proceeding in this fashion, the base station peak power thresholds are adjusted such that exactly 90% of the users are guaranteed the desired rate of r0 bps/Hz and the remaining 10% of the users are in outage. We could improve the performance of the system by discarding the users in outage upfront, since the interference due to the presence of these users will be eliminated at time t = 0. In our simulations, for a large user population over K instantiations, we identify 10% users in outage2 by first running K instantiations of the system with all the users present in the system. We store the coordinates of all the users that were in outage at the end of each of the K instantiations. We then eliminate the outage users from the system (by preserving the coordinates of the user locations of only those users not in outage for all the K instantiations) 2

We remark that the eliminated set of 10% of the users in outage is not claimed to be the optimum set as would be obtained by evaluating all possible subsets amounting to 10% of the users. The latter is computationally prohibitive.

190


at time t = 0 in the real network simulations. Thus, the existing users in the system experience less interference due to the absence of those users in outage when the real network is simulated.

7.4.3

Network operation and simulation aspects Our objective is to obtain power savings and throughput improvement due to deployment of relays in a cellular system. To compare systems with and without relays in the CPA-based relaying scheme, we simplify the operation of a cellular downlink system such that 90% of the users in the system are guaranteed to be delivered a file of fixed size L, within a fixed period of time T . The file could be different for all users but the file sizes are fixed. Such an operation brings in the notion of a common rate for the users in the system. In order that the system benefits from the users that receive the message within the fixed time T , the satisfied users leave the system, and thus no longer cause interference to the remaining users. The remaining 10% of the users that are not guaranteed the file of size L are in outage. In our simulations, for the sake of simplicity, all base stations are assumed to have the same peak power threshold values. We run K = 200 (amounting to 11 400 user instantiations) different user instantiations in the system. The common rate requirement is set as 1 bps/Hz. We divide the total time T into 1000 mini-slots and at the end of each mini-slot, we keep track of the cumulative MI Ii (t) of each user i. If at the end of a mini-slot, a particular user’s cumulative MI exceeds the file size L, the base station corresponding to that user is turned off. We run the baseline for different peak power values of the base station (5 W to 30 W in increments of 5 W). For each peak power value, the relay powers are varied as a factor of the base station power. Figure 7.6 shows the variation of outage probability for various base station powers and various relay powers. For the case when there are no relays in the system (ratio of relay power to base station power is zero), increasing the peak powers of the base station decreases the outage. The percentage of outage saturates below a certain threshold as the interference limit sets in. As we increase the relay powers by increasing the ratio of relay power to base station power, the outage reduces but quickly saturates to a certain threshold outage value, because of the interference limit. From Figure 7.6 it is clear that the interference limit is quickly reached and this limits the performance of a system with relays. This is because there is no interference management and peak power transmissions from the base stations and relays lead to a highly interference limited scenario.

7.4.4

Simulation results Power savings The peak power required to guarantee the remaining 90% of the users (after the 10% of users in outage have been removed) a rate of 1 bps/Hz is 21 W in the

191


Table 7.2. P-CPA relaying (base station and relays transmit at peak power) Peak power required to guarantee 1 bps/Hz at 10% outage; baseline (no relays)

Peak power required to guarantee 1 bps/Hz at 10% outage; with relays

Savings in dB

21 W

15 W

1.46

Common rate for 90% users; baseline (no relays)

Common rate for 90% users; with relays

Percentage rate increase

1 bps/Hz

1.21 bps/Hz

21 %

14 Base station power = 15 W Base station power = 20 W Base station power = 25 W

13

Outage percentage at 1 bps/Hz

12 11 10 9 8 7 6 5

0

0.1

0.2

0.3 0.4 0.5 0.6 0.7 Ratio of relay power to base station power

0.8

0.9

1

Figure 7.6. Variation of outage with relay powers and base station powers. As we increase the base station powers with no relays in the system (ratio = 0), the outage decreases and saturates at around 5%, due to the inteference limit. The interference limit sets in very quickly even for smaller values of relay powers. baseline case and it requires 15 W for a system with relays. The relays transmit 1 W of peak power. Hence the peak power saving at the base station locations in this case is 1.46 dB as shown in Table 7.2.

Rate gains In order to evaluate the throughput improvement, we find how much the common rate of 90% of users can be improved with the peak power of the base stations

192


being fixed. For the baseline, we fix the power of the base stations to 21 W, so that 90% of the users are guaranteed to receive 1 bps/Hz (as obtained in the previous section); 10% of the users in outage are eliminated as explained in Section 7.4.2. For the P-CPA system with relays, the peak power threshold of the base stations is fixed to 21 W (the same value as in the baseline case). For the same peak power for the base stations and with relays present in the system, we expect the common rate to be better than 1 bps/Hz. To find the improvement in common rate, we fix a desired common rate r > 1 bps/Hz and run the sytem with relays. If this desired common rate is feasible,3 we double the desired common rate and run the simulations again. Or, if the desired common rate is not feasible, we fix the new desired common rate at half the difference between the highest feasible common rate and the lowest not feasible common rate and rerun the simulations. In this manner, we converge to the achievable common rate in the presence of relays. In our simulations, we find that the common rate can be improved to 1.21 bps/Hz in the CPA-based relaying scheme. Hence the common rate improvement is 21%.

7.5

Power-control-based collaborative relaying (PC-CPA) In Section 7.4.3, we observed that for P-CPA the interference from the other relays and base station sectors limited the peak power savings in the system with relays. The reason for that is that when the relays transmit to help the users, they transmit with peak powers and hence increase the interference levels in the system. If we could find the optimal set of powers to transmit for the base station and the relays, we could reduce the overall interference levels in the system. This may improve the gains in the system. In the following, we describe a framework for power control in the downlink of a cellular system with relays. When the relays are not present, downlink power control in a cellular system has been well studied and understood [26]. When relays are present in the system, power control, if performed jointly at the base stations and relay locations, can provide power savings and throughput improvement. We describe the PC-CPA relaying scheme in the following sections.

7.5.1

Principle of operation PC-CPA baseline For the PC-CPA baseline, the aim is to deliver a desired common rate for 90% of the user population by employing a simple power control scheme. Each base station sector powers down its transmitted power within the peak power limitations so that 90% of users are guaranteed a desired common rate of r0 bps/Hz. 3

The common rate is feasible if all the users present in the system are able to get the desired rate.

7.5 Power-control-based collaborative relaying (PC-CPA)

193

Since all users share the same band of frequencies, they observe interference from all the base station sectors in the system. We use a common subscript for a base station or a user in a particular sector. If at time t, pi is the power of the transmitting base antenna corresponding to the ith user (we drop the argument t), hij is the channel gain, including path-loss and shadowing, from the jth base to the ith user, and σ 2 is the noise power at the receiver, the instantaneous SINR of the ith user in the system is given by ρi (t) =

hii pi . 2 j = i hij pj + σ

(7.19)

Since the transmission uses Gaussian codebooks, the corresponding instantaneous rate for the user i is given by Ri (t) = log2 (1 + ρi (t)) bps/Hz.

(7.20)

The set of feasible powers such that the users not in outage are guaranteed a rate r0 is obtained by solving for the feasibility of instantaneous rates subject to peak power constraints, specified by log2 (1 + ρi (t)) i.e., ρi (t) subject to: pi

≥ r0 , ≥ 2

r0

(7.21) − 1,

≤ pi,max

(7.22) (7.23)

for all users i not in outage. In practice, each base station increases its power autonomously in small increments, until it hits the peak power limit or until the user associated with it attains the desired rate r0 . Users that achieve the power constraint to go active before attaining the desired rate are discarded. We simulate the system without the users in outage such that all users achieve the desired rate. Since the transmit powers of the base stations are such that all users attain a common rate, none of the users leave the system.

PC-CPA system with relays In the PC-CPA system with relays, 10% of users are discarded in a manner similar to that in the baseline system. At time t = 0, the relays do not have the complete message required to relay to the user. Hence, the system starts out as it does for the baseline case. The base stations increase their powers autonomously in small increments targeting the user rates to increase. Users that do not meet the peak power constraints in (7.23) are eliminated one after the other. The remaining users attain the desired rate without violating the peak power constraint at the base stations. While the base station transmissions are targeted to the users, the relay in each sector also listens to the transmission by the base stations. Depending on the channel conditions and coupling of interference from the adjacent sectors, the relays receive their message at different points in time. When the relay in the sector decodes the message from the base station, the relay collaboratively helps the base station such that the user gets a rate corresponding to the total SINR from the relay and the base station. As described

194


in Section 7.3, the code books at the base stations and relays are designed such that the mutual information at the receiver corresponds to the sum of received powers at the user location [19]. In order to maintain the common desired rate for all users, the relay and base station jointly adjust their powers so that the user receives the desired rate. This ensures that the base station and relay transmit just enough power to the user to obtain the desired rate. Let pi denote the power transmitted by the base station sector i at time t and hij be the channel gain, including path-loss and shadowing, from the jth base to the ith user. Let qi be the power transmitted from the relay i at time t and gij be the channel gain to the user i from the relay j. Then, when the relay and base station transmit simultaneously, the effective SINR at the ith user location when the relay is active is given by ρri elay (t) =

hii pi + gii qi . 2 h j = i ij pj + gij qj + σ

(7.24)

As with the baseline case, the set of feasible powers (for both base station antennas and relays) such that the users not in outage are guaranteed a rate r0 is obtained by solving for the feasibility of instantaneous rates subject to peak power constraints log2 (1 + ρri elay (t)) i.e.,

ρri elay (t)

≥ r0 , ≥ 2

r0

(7.25) − 1,

(7.26)

subject to: pi

≤ pi,m ax

(7.27)

and qi

≤ qi,m ax

(7.28)

for all users i not in outage. If we consider the transmit powers of the base stations and relays to be variables of optimization, we have a total of 2N variables, for N base station sectors in the system. Thus, power control in cellular systems in the presence of relays gives us an additional N degrees of freedom over which to optimize. The transmit powers in the system can be optimized to reduce the maximum peak power transmission in the system, to reduce total energy in the system, etc. In what follows, we assume that a central controller has knowledge of all the channel gains between the base stations as well as relays and the users. We explain ways to achieve various aforementioned objectives using linear program (LP) formulations.

7.5.2

Optimization framework Minimizing the total instantaneous transmit power We are interested in evaluating the benefits of relays in minimizing the total instantaneous sum power in the system while delivering the common rate r0 with 10% of the users being omitted from the system. The practical benefit of minimizing the total sum of transmit powers in a cellular system is to save the

195


energy costs in the network. Saving energy costs translates to saving electricity bills at the cell sites for the cellular service provider. The desired common rate for the users is fixed at r0 bits/symbol. We define A(t) as the set of all active relays at time t, i.e., the set of relays that have obtained the message and are ready to help the base station. Ac (t) denotes the complementary set of all inactive relays. For simplicity, we drop the argument and write pi and qi for the base station powers pi (t) and qi (t) at time t, respectively. At a given time t, the central controller solves the following optimization problem: min pi + q i , (7.29a) p ,...,p 1

N

q 1 ,...,q N

subject to:

i

log2

hii pi + gii qi 1+ 2 h j = i ij pj + gij qj + σ

≥ r0 , i = 1, . . . , N,

(7.29b)

0 ≤ pi ≤ pi,m ax , i = 1, . . . , N,

(7.29c)

0 ≤ qi ≤ qi,m ax , i ∈ A(t),

(7.29d)

qi = 0, i ∈ A (t).

(7.29e)

c

The solution to the optimization problem (7.29), p∗i , qi∗ , i = 1, . . . , N defines the powers pi (t) = p∗i and qi (t) = qi∗ that are used at time t. The optimization problem (7.29) is an LP, since we can write the constraint (7.29b) as 1 (hii pi + gii qi ) − (hij pj + gij qj ) ≥ σ 2 (7.30) r 0 2 −1 j = i

for i = 1, . . . , N . Rewriting (7.29) in vector form, we have s∗ (t) = min p,q

subject to:

where

⎛

⎜ ⎜ A=⎜ ⎝ ⎛ ⎜ ⎜ B=⎜ ⎝

1T (p + q),

(7.31a)

Ap + Bq ≤ −σ 2 1,

(7.31b)

0 ≤ p ≤ pmax ,

(7.31c)

0 ≤ q ≤ qmax ,

(7.31d)

−h11 /(2r 0 − 1) h21 .. .

h12 −h22 /(2r 0 − 1) .. .

··· ··· .. .

h1N h2N .. .

hN 1

hN 2

···

−hN N /(2r 0 − 1)

−g11 /(2r 0 − 1) g21 .. .

g12 −g22 /(2r 0 − 1) .. .

··· ··· .. .

g1N g2N .. .

gN 1

gN 2

···

−gN N /(2r 0 − 1)

⎞ ⎟ ⎟ ⎟ , (7.32) ⎠ ⎞ ⎟ ⎟ ⎟, ⎠

(7.33)

196


and p(t)

=

[p1 (t) . . . pN (t)]T ,

q(t)

=

[q1 (t) . . . qN (t)]T ,

pmax

=

[p1,max . . . pN ,max ]T ,

qmax

(7.34)

T

=

[q1,max . . . qN ,max ] ,

with qi,max = 0, i ∈ Ac (t). The solution to the above LP provides the optimal power values that minimize the instantaneous total power in the system. We take a myopic approach of minimizing the total sum power of the system at time t in order to reduce the total average power transmission in the system. Each time a relay becomes eligible for transmission, the LP is solved to find the best set of powers by minimizing the instantaneous powers in the system. Note that in some cases, when a relay is eligible to help the base station, turning off the base station may be the optimal thing to do. This choice comes out as a solution to the optimization program.

Minimizing the peak transmit power Minimizing the peak transmit power leads to peak power savings in the system. A practical benefit of peak power savings is the significant savings in the cost of power amplifiers for the cellular base stations. If by deploying low-power relays in the system, we save on the cost of the power amplifiers of the base stations, cellular operators could save on capital expenses. To this end, we solve the following optimization problem of minimizing the maximum instantaneous transmit powers at the base stations: min

p 1 ,...,p N q 1 ,...,q N

subject to:

max pi , i

(7.35a)

log2

hii pi + gii qi 1+ 2 j = i hij pj + gij qj + σ

≥ r0 , i = 1, . . . , N,

(7.35b)

0 ≤ pi ≤ pi,max , i = 1, . . . , N,

(7.35c)

0 ≤ qi ≤ qi,max , i ∈ A(t),

(7.35d)

qi = 0, i ∈ A (t).

(7.35e)

c

Rewriting the above LP in vector form yields, p∗ (t) = min p,q

subject to:

α,

(7.36a)

Ap + Bq ≤ −σ 2 1,

(7.36b)

0 ≤ p ≤ pmax ,

(7.36c)

0 ≤ q ≤ qmax ,

(7.36d)

α1 ≥ pmax ,

(7.36e)

where A and B are given by (7.32) and (7.33), respectively.


197

Improving the common rate As a corollary to the above approaches, if we keep the peak power constant across both the baseline and the system with relays, we can increase the common targeted rate in the system with relays. The problem of maximizing the common rate can be posed as an optimization program with the transmit powers of the base station and relays as the variables. A central controller then solves the optimization program: max

p 1 ,...,p N

subject to:

r0 ,

(7.37a)

log2

hii pi + gii qi 2 j = i hij pj + gij qj + σ

1+

≥ r0 , i = 1, . . . , N,

(7.37b)

0 ≤ pi ≤ pi,max , i = 1, . . . , N,

(7.37c)

0 ≤ qi ≤ qi,max , i ∈ A(t),

(7.37d)

qi = 0, i ∈ A (t).

(7.37e)

c

The optimization program can be viewed as a sequence of linear feasibility problems because the constraint set is nonconvex. We solve this program by an iterative approach. We start with a low easily achievable target rate r0 so that the constraint set (7.37b)–(7.37e) is feasible. We increase the target rate in small increments until the constraint set becomes infeasible. In each step, we get a set of feasible power assignments. The last set of feasible power assignments is the solution to the optimization program. The method converges, since the iterations generate a bounded sequence of increasing rates.

7.5.3

User discarding methodology In our simulations, we eliminate 10% of users (over a large number of user realizations) in the following way. The procedure is identical for both the baseline and the system with relays. We simply assume the same peak power constraints for all base stations across the network. We fix the peak power threshold pmax for each base station. Consider a single instantiation, where there are 57 users in the system. We increase the transmit power in all base stations in small incremental steps to improve the rate of the users in the system. As we do so, we discard the user associated with the base station whose power constraint goes active first. The base station is also turned off. This reduces the interference coupled with other users. Within the remaining set of users, we can increase the transmit powers further. We then discard the next user causing the power constraint to become active and continue in this fashion until all remaining users in the system are guaranteed the desired rate of r0 bps/Hz, without violating the peak power constraints. This procedure is repeated for a large number K of users instantiations. Let the number of users in outage for the kth instantiation when the power threshold is pmax and desired common rate r0 be Ok (pmax , r0 ).

198


We then find the total number of outage users for K instantiations when the peak power threshold is pmax and the desired rate is r0 is calculated as O(pmax , r0 ) =

K

Ok (pmax , r0 ).

(7.38)

k =1

The percentage of users in outage for the threshold pmax and desired rate r0 is then O(pmax , r0 ) × 100 %. 57K

(7.39)

If O(pmax , r0 ) > 10%, we increase the power threshold to pmax > pmax . On the other hand, if O(pmax , r0 ) < 10%, we decrease the power threshold to pmax < pmax . Proceeding in this fashion, the base station peak power threshold pmax is adjusted such that exactly 90% of the users are guaranteed the desired rate of r0 bps/Hz and the remaining 10% of users are in outage. The coordinates of the discarded users are stored and the same set of users are discarded when relays are present in the system too. We remark here that the order in which the users are discarded results in different power levels from the base stations, due to variations in the interference coupling among the users. Hence, the order in which the users are dismissed must be chosen carefully depending on the peak powers limitations at the base stations.

7.5.4

Network operation and simulation aspects Baseline operation We operate the baseline system as well as the system with relays such that, over a large number of user loading iterations, 90% of users obtain a common average rate of 1 bps/Hz. We follow the approach described in Section 7.5.3 to discard users in the system. For the PC-CPA baseline, we solve a series of linear feasibility problems to obtain the base station powers that guarantee the desired common rate. One after another, we discard users that would cause the peak power constraint to became active. Hence we find the feasible set of powers p1 , . . . , pN for the baseline such that 90% of the users receive exactly 1 bps/Hz.

PC-CPA with relays: average power savings The peak power constraint of the base stations is fixed at pmax such that the baseline can deliver 1 bps/Hz at 10% outage. Since the relays are assumed to be inexpensive, we assume small peak power constraints for the relays. In our work, the peak power of the relays is fixed at 1 W. Let us consider a single instantiation of 57 users in the system. We start off similarly to the baseline system after discarding the same set of users. The base stations target the users to deliver the common rate of 1 bps/Hz. Only relays that have a better SINR to the base stations than the user are eligible to help the user. The other relays are always inactive. At time t = 0, all relays are inactive. The aim in this experiment is to

7.6 Orthogonal relaying

199

maintain a constant rate of 1 bps/Hz throughout the course of the simulation. When relay i is eligible to transmit at time t, we include relay i in the set of active relays A(t) and solve the LP (7.29). We stop when all the eligible relays are included in the set of active relays. The total power in the system when all eligible relays are active is noted for this instantiation. We repeat this experiment for all the K instantiations.

PC-CPA with relays: peak power savings The peak power constraints of the base stations are fixed at a value smaller than the baseline, say pmax . We assume that inexpensive relays are deployed in the system. Thus, the peak power constraints of the relays are fixed at 1 W. Since the peak power value of the base stations is reduced from the baseline and the common rate is fixed at 1 bps/Hz, the outage will be more than 10%. Let us consider a single instantiation of 57 users in the system. We start similarly to the baseline after discarding the same set of users. The base stations target the users to deliver the common rate of 1 bps/Hz. Only relays that have a better SINR to the base stations than the user are eligible to help the user. The other relays are always inactive. At time t = 0, all relays are inactive. Let relay i be eligible to transmit at time t. We include relay i in the set of active relays A(t) and solve the LP (7.35). We stop when all the eligible relays are included in the set of active relays. We repeat this experiment for all the K instantiations and the outage is calculated. If the outage is less than 10%, the peak power of the base stations reduces to pmax < pmax , otherwise the peak power value of the base stations increases to pmax > pmax and the above procedure is repeated until the outage is close to 10%.

7.5.5

Simulation results Power savings The average power saving over K = 200 instantiations is 3 dB and the peak power saving in the downlink when power control is employed is close to 2.6 dB.

Rate gains We have observed 34% improvement in the throughput for 90% of users in the system, with the baseline system being served at 1 bps/Hz. The results are summarized in Table 7.3.

7.6

Orthogonal relaying In Sections 7.4 and 7.5, we saw that in an interference-limited setting, the improvement in throughput was limited by the interference due to multiple transmissions in the cell. In some cases the transmissions from the base stations are redundant. For instance, for a user located at the edge of the cell, the received

200


Table 7.3. PC-CPA-based relaying (base station and relays employ power control) Peak power required to guarantee 1 bps/Hz at 10% outage; baseline (no relays)

Peak power required to guarantee 1 bps/Hz at 10% outage; with relays

Savings in dB

10 W

5.5 W

2.6

Common rate for 90% users; baseline (no relays)

Common rate for 90% users; with relays

Percentage rate increase

1 bps/Hz

1.34 bps/Hz

34%

power from the base station may be weak and the base station’s signal may be of little use. In that case, it might be better to turn the base station off since this may benefit the system overall in terms of reducing the interference levels. Moreover, the practical implementation of such collaborative schemes can be complex with the state of the art technology. Hence, we investigate how much gain due to collaborative addition can be obtained if we just use simple multihopping, where the base station transmits to a relay in one slot and then that relay passes on the message to the destination in the next time slot. In this section, we exploit the half-duplex property of the relays in a downlink cellular system to stagger the transmissions of the base station and relays over two time slots. A natural way to operate these relays is for them to receive in one time slot and transmit in another time slot. This gives us a natural orthogonality in the transmission scheme. Henceforth, we term this scheme orthogonal relaying.

7.6.1

Network operation and simulation aspects The simulation set-up is the same as that described in Section 7.2. Unlike CPA schemes, where the relay can start transmitting immediately after it decodes the message, relays can start transmitting only at specific times in the orthogonal relaying scheme. The system is assumed to be synchronous and time is divided into equal slots. The baseline and the system with relays are operated as follows.

Baseline The baseline system operates similarly to the P-CPA baseline as described in Section 7.4.1. All base stations transmit with peak powers and the users are required to receive a fixed sized file with a specified deadline. Satisfied users leave the system as soon as they receive the file. The associated base station sector is turned off. The users that do not receive the file are in outage. The peak transmit powers of the base stations are fixed such that 10% of the users over a large population of users are in outage. However, in the orthogonal relaying case, we do not discard the users in outage and rerun the simulations.

7.6 Orthogonal relaying

201

System with relays When relays are present in the system, time is divided into slots of equal durations, and the duration of a time slot is half of that in the baseline system. The operation of the system is periodic with odd and even time slots recurring at regular intervals. The base stations transmit in the odd time slots and the relays transmit in the even time slots. The peak power of the base stations is fixed as in the baseline and the peak power of the relays is fixed as 1 W.

r In the odd time slots, the base stations transmit at peak power. Relays are in receive mode in this time slot. The users and relays in each sector accumulate mutual information, depending on their channel qualities. If some of the users receive the desired rate from the base station transmission itself, those users are satisfied users and leave the system as soon as they receive the desired rate. The corresponding base stations and relays are turned off. Let us denote the 57 × 1 vector of rates obtained by users in the odd time slots by ro . r In the even time slots, only those users that have yet to receive the desired rate of 1 bps/Hz remain in the system. The base stations are turned off in this time slot. The relays that are required to help the users start transmitting simultaneously at the beginning of the even time slots. Simple power control is employed at the relay locations to reduce the interference caused to the other sectors. The power control is performed to achieve the desired residual common rate re = 1 − ro , where 1 is a 57 × 1 vector all 1’s vector (representing the 1 bps/Hz desired common rate). The users that require the relays to transmit more than their peak power constraint are discarded at the beginning of the even time slots. There may be cases where the user has a better channel to the base station than to the relay. Such users are not given the benefit of receiving the complete message from the base station. The base stations are switched off on the even time slots and are in outage if they do not receive the message at the end of the even time slots.

7.6.2

User discarding method Baseline The users that remain in the system are in outage. However, the users are not discarded in the baseline scheme.

System with relays The user elimination procedure is the same as that explained in Section 7.5.3. The users that violate the peak power constraint of the relays are discarded at the beginning of the even time slots. The discarded users do not receive the desired common rate at the end of odd and even time slots, and hence are said to be in outage. The system is operated such that there is 10% outage in the system over a large number of user instantiations. The peak power threshold of the relay nodes is adjusted such that the outage percentage is exactly 10%.

202


Table 7.4. Summary of gains due to relaying

7.6.3

Baseline

System with relays

57 sectors 1 user/sector

57 sectors 1 user/sector and 1 relay/sector

Peak power transmissions by base stations

Peak power transmissions by base stations and relays (CPA)

Base station power control

Base station and relays power control (PC-CPA)

Peak power transmissions by base stations

Relays power control to users (orthogonal relaying)

Results Power saving (baseline at 1 bps/Hz)

Common rate gain (baseline at 1 bps/Hz)

1.46 dB (peak)

25%

2.6 dB (peak) 3 dB (average)

34%

3 dB (average)

35%

Simulation results The average power saving in the base station locations is 3 dB, since the base stations transmit only for half the time. There is no peak power saving since the base stations transmit at peak power in the odd time slots. We obtain 35% rate gain due to orthogonal relaying when there is 10% outage in the system. It is interesting to note that simpler relaying methods, such as orthogonal relaying do nearly as well as the more complex forms of relaying, such as CPA schemes, in obtaining throughput gains and power savings. This observation is in agreement with the studies in simple linear settings [19, 27].

7.7

Conclusion We have presented a simulation study of the downlink of a cellular system with relays. We evaluated the power saving and common rate increase for users when a common rate of 1 bps/Hz is required by 90% of users in the system. We first described the CPA scheme of relay collaboration. In the CPA scheme, whenever the relay receives the complete message from the base station, it collaborates with the base station such that the mutual information at the user location corresponds to the sum of the received power at the user location, thus boosting the average rate. We observed that when the system is interference-limited the peak power savings are hard to come by. Consequently, the PC-CPA scheme along with a framework for power control was proposed. The power control framework can be posed as a formulation when the objective is to minimize peak power or to minimize average energy in the system. This formulation can be used to evaluate the average and peak power savings in the system. The peak power savings and the rate gains improve when power control is employed. We

References

203

then evaluated a simple multihopping scheme where the base stations and the relays transmit in orthogonal time slots. In the odd time slots, the base stations transmit at peak power and in the even time slots, the base stations are turned off and the relays employ simple power control to deliver the residual rate to the users. A summary of the results is given in Table 7.4.

References [1] Harmonized Contribution on 802.16j (Mobile Multihop Relay) Usage Models. http://ieee802.org/16. [2] Multi-hop relay system evaluation methodology. http://ieee802.org/16. [3] Y. Yang, H. Hu, J. Xu, and G. Mao, “Relay technologies for WiMAX and LTE-advanced mobile systems,” IEEE Commun. Magazine, 47(10): 100– 105, Oct. 2009. [4] L. Le and E. Hossain, “Multihop cellular networks: Potential gains, research challenges, and a resource allocation framework,” IEEE Commun. Magazine, 45(9): 66–73, Sep. 2007. [5] H. Viswanathan and S. Mukherjee, “Performance of cellular networks with relays and centralized scheduling,” IEEE Trans. Wireless Commun., 4(5): 2318–2328, Sep. 2005. [6] O. Oyman, J. N. Laneman, and S. Sandhu, “Multihop relaying for broadband wireless mesh networks: From theory to practice,” IEEE Commun. Magazine, 45(11): 116–122, Nov. 2007. [7] C. E. Perkins, Ad Hoc Networking. Addison-Wesley, 2001. [8] O. Oyman, “Oppurtunistic scheduling and spectrum reuse in relay-based cellular OFDMA networks,” in Proc. of IEEE Globecom, Washington DC, USA, 2007. IEEE, 2007. [9] E. C. van der Meulen, Transmission of Information in a T-terminal discrete memoryless channel. PhD thesis, University of California, Berkeley, 1968. [10] T. M. Cover and A. A. El Gamal, “Capacity theorems for the relay channel,” IEEE Trans. Inf. Theory, 25(5): 572–584, Sep. 1979. [11] G. Kramer, M. Gastpar, and P. Gupta, “Cooperative strategies and capacity theorems for relay networks,” IEEE Trans. Inf. Theory, 51: 3037–3063, Sep. 2005. [12] M. A. Khojastepour, A. Sabharwal, and B. Aazhang, “On the capacity of ‘cheap’ relay networks,” in Proc. of 37th CISS, Baltimore, MD, USA, 2003. The John Hopkins University, 2003. [13] G. Kramer, “Models and theory for relay channels with receive constraints,” in Proc. of Allerton Conf. on Commun., Control, and Comp., UIUC, IL, USA, 2004. University of Illinois at Urbana-Champaign, 2004. [14] D. Chen, M. Haenggi, and J. N. Laneman, “Distributed spectrum-efficient routing algorithms in wireless networks,” IEEE Trans. Wireless Commun., 7(12):5297–5305, Dec. 2008.

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[15] M. Sikora, J. N. Laneman, M. Haenggi, Jr., D. J. Costello, and T. E. Fuja, “Bandwidth- and power-efficient routing in linear wireless networks,” IEEE Trans. Inf. Theory, 52(6): 2624–2633, June 2006. [16] P. Bender, P. Black, M. Grob, R. Padovani, N. Sindhushayana, and A. Viterbi. “CDMA/HDR: A bandwidth-efficient high speed wireless data service for nomadic users,” IEEE Commun. Magazine, 38(7): 70–77, July 2000. [17] D. Bertsekas and R. Gallager, Data Networks. Prentice-Hall, 1992. [18] R. Pabst, B. H. Walke, D. C. Schultz, et al., “Relay-based deployment concepts for wireless broadband radio,” IEEE Commun. Magazine, 42(9): 80–89, Sep. 2004. [19] G. Foschini, A. Tulino, and R. Valenzuela, “Performance comparison for basic relay systems,” Tech. Memo, Bell Labs NJ, 2008. [20] T. M. Cover and J. A. Thomas, Elements of Information Theory. Wiley, 2006. [21] M. Katz and S. Shamai, “Transmitting to colocated users in wireless ad hoc and sensor networks,” IEEE Trans. Inf. Theory, 51: 3540–3563, Oct. 2005. [22] D. Blackwell, L. Breiman, and A. J. Thomasian, “Capacity of a class of channels,” Ann. Math. Stat., 30: 1229–1241, 1968. [23] I. Csiszar and P. Narayan, “Capacity of the gaussain arbitrarily varying channel,” IEEE Trans. Inf. Theory, 37: 18–26, Jan. 1991. [24] D. Tse and P. Viswanath, Fundamentals of Wireless Communication. Cambridge University Press, 2005. [25] K. Azarian, H. El Gamal, and P. Schniter, “On the achievable diversity-vsmultiplexing tradeoff in half-duplex cooperative channels,” IEEE Trans. Inf. Theory, 51: 4152–4172, Dec. 2005. [26] M. Chiang, P. Hande, T. Lan, and C. W. Tan, “Power control in wireless cellular networks,” Foundations and Trends in Networking, 4(2): 381–533, July 2008. [27] N. Jacobsen, “Practical cooperative coding for half-duplex relay channels,” in Proc. of CISS 2009, March 2009. The John Hopkins University, 2009.

8

Radio resource optimization in cooperative cellular wireless networks Shankhanaad Mallick, Praveen Kaligineedi, Mohammad M. Rashid, and Vijay K. Bhargava

8.1

Introduction Wireless cellular networks have to be designed and deployed with unavoidable constraints on the limited radio resources such as bandwidth and transmit power. With the boom in the number of new users and the introduction of new wireless cellular services that require a large bandwidth or data rate, the demand for these resources, however, is rising exponentially. Finding a solution to meet this increasing demand with the available resources is a challenging research problem. The primary objective of such research is to find solutions that can improve the capacity and utilization of the radio resources that are available to the service providers. Based on the concept of relay channels, cooperative communication1 has been found to greatly enhance the performance of a resource-constrained wireless network [2–6]. It can achieve benefits similar to those of the multipleinput multiple-output (MIMO) system without the need for multiple antennas at each node. By allowing users to cooperate and relay each other’s messages to the destination, cooperative communication also improves the transmission quality [7]. Because of the limited power and bandwidth resources of the cellular networks and the multipath fading nature of the wireless channels, the idea of cooperation is particularly attractive for wireless cellular networks. Proposed cooperative schemes or strategies, such as decode-and-forward (DF), amplify-and-forward (AF), and coded cooperation [4, 8–10], usually involve two steps of operation. In the first step, a user (called the source node), transmits its message to both the assigned partner (called the relay node) and to the destination. If the relay node employs a DF scheme, it will first decode and regenerate the message and then transmit it to the destination in the second step. When the regenerated message is encoded to provide additional error protection to the original message, it is referred to as coded cooperation. If an AF scheme is

1

The term cooperation was introduced in [1] in which the capacity of a three-node relay network was analyzed.


206


employed, the relay simply amplifies the received message and forwards it to the destination in the next step. At the destination, the signals from both the source and the relay are then combined for detection, using methods such as maximal ratio combining (MRC) or by selection combining. However, the benefits of a relay-based cooperation often depend on the channel quality between the source, relay, and destination involved in the transmission. This is because the transmission quality of a relayed message is limited by the channel signal-to-noise ratio (SNR). For example, a relay can fail to forward a message reliably to the destination if the received message from the source is already corrupted due to poor channel quality. Therefore, cooperation may not be always useful. In general, when the complete channel state information (CSI) between the source, relay, and destination is known to the system, relays should be selected to forward the source message only if the quality of the channels between source and relay and relay and destination meet certain criteria. Whenever cooperation is beneficial, the next goal is to allocate the limited resources (e.g., power, bandwidth) appropriately among the source and relay. Therefore, resource allocation among the cooperative nodes can be formulated as an optimization problem to exploit the maximum possible advantage of cooperation [11, 12]. The focus of this chapter is to formulate the resource allocation problems of different cooperative networks and strategies as optimization problems and to discuss their solution approaches. The chapter is organized as follows: Section 8.2 discusses the resource allocation problem for networks with a single source–destination pair. First the optimal power allocation is studied for the most basic three-node topology using different cooperation schemes, and the capacity or throughput gain is investigated. Then we consider the dual hop relay networks which contain multiple relays and study the relevant resource optimization problems in detail. Section 8.3 deals with the resource allocation problem of a cellular network with multiple source–destination pairs. Solution approaches using both centralized and distributed optimization algorithms are studied. The relay selection strategies for different networks are also discussed briefly in Section 8.4. Finally, a chapter summary is provided in Section 8.5.

8.2

Networks with single source–destination pair In this chapter, our strategy is to start with the problem of resource optimization in a simple cooperative architecture involving a single source–destination pair and then progress towards a more general system architecture. The simplest topology for a single source–destination is the three-node relay network shown in Figure 8.1. A more generic topology is the dual hop relay network which consists of multiple relays.

8.2 Networks with single source–destination pair

207

User 1 Feedback

(S)

(D)

hSD

Destination hSR hRD ack db e e F

(R)

User 2

Figure 8.1. A three-node relay network.

8.2.1

Three-node relay network Consider the three-node relay network shown in Figure 8.1, where we let user 1 be the source node (S) that intends to transmit a message to the destination (D) while user 2 serves as the relay node (R). Cooperation requires two time slots to send a message to destination, D. In the first time slot, source S transmits its message XS to both R and D. The received signals at R and D can be expressed as XR = hS R XS + ZR , XD 1 = hS D XS + ZD 1 , respectively, where hS R and hS D are the complex channel coefficients for the S–R and S–D links, and ZR and ZD 1 denote the independent and identically distributed (i.i.d.) circularly symmetric additive white Gaussian noise (AWGN) with zero mean and variance N0 . In the second time slot, relay R transmits the message (XR ) received in the first slot after either decoding and reencoding it or simply amplifying it. Depending on the cooperative scheme (DF or AF), let Y = f (XR ) be the transmitted message2 in the second slot. The received signal in D can be written as XD 2 = hR D Y + ZD 2 = hR D f (XR ) + ZD 2 , where hR D is the channel coefficient between the R–D pair and ZD 2 is the zero mean AWGN with variance N0 . In the following analysis, we assume that these coefficients are known (i.e., full CSI is available) to S, R, and D and the AWGN noise has unit variance, i.e., N0 = 1. The transmit powers of S and R are given by PS and PR . 2

For the AF scheme Y is X R corrupted with AWGN and for the DF scheme Y is simply X R .

208


Quality of Service (QoS), a measure of performance, reflects the transmission quality and the service availability of a transmission system. For example, channel capacity, SNR, outage probability or bit error rate (BER) can be one of the QoS measures. Our objective is to formulate the optimization problem so that the QoS performance of the network is optimal subject to some resource constraint. In the following we use the total power budget as the constrained resource of the network and the channel capacity (or, maximum achievable data rate) as the QoS measure. Therefore, the problem is to maximize the channel capacity given some total power constraint and the solution will provide the optimal allocation of PS and PR among the cooperative nodes. The solution for optimal power allocation depends on whether the direct S–D link is taken into account. If the messages from both the source and the relay are combined at the destination for detection, this is referred to as the case with diversity [13]. For the case without diversity, only the message from the relay (i.e., XD 2 ) is considered. In the following we study optimal power allocation for both the cases.

Case 1 With direct link First, let us formulate the capacity maximization problem taking the direct link into account to examine the optimal power allocation for the three-node network with DF cooperative strategy. In a two-time-slot operation, the capacity of the S–R link is given as [14] Chop1 =

1 2

log2 (1 + |hS R |2 PS ).

(8.1)

In the second time slot, the destination combines the messages from both the S–D and R–D links using MRC technique, and the capacity is given by Chop2 =

1 2

log2 (1 + |hR D |2 PR + |hS D |2 PS ).

(8.2)

The channel capacity in the DF cooperative scheme is limited by the minimum of the two hops: ; < CD F , div er sity = min 12 log2 (1 + |hS R |2 PS ), 12 log2 (1 + |hR D |2 PR + |hS D |2 PS ) . (8.3) Therefore the optimization problem becomes a standard max–min problem: ; maximize {P S ,P R }

min

1 2

log2 (1 + |hS R |2 PS ),

1 2

log2 (1 + |hS D |2 PS + |hR D |2 PR )

|hS D |2 , the capacity is maximized with equal capacity for the two hops, i.e. 1 2

log2 (1 + |hS R |2 PS ) =

1 2

log2 (1 + |hS D |2 PS + |hR D |2 PR ).

(8.5)

Since the objective is to maximize the capacity, the first inequality constraint of (8.4) should be met at equality. Using PS + PR = P0 in (8.5), we get the optimal power allocation as PS = P0

|hR D |2 |hS R |2 + |hR D |2 − |hS D |2

(8.6)

P R = P0

|hS R |2 − |hS D |2 . |hS R |2 + |hR D |2 − |hS D |2

(8.7)

and

From (8.6) and (8.7), we see that more power is allocated to the source than to the relay, which is justified since PS contributes both to the direct path and to the relay path. However, if |hS D |2 ≥ |hR D |2 we see that the capacity expressions (8.1) and (8.2) are both monotone increasing functions and the optimal power allocation that maximizes the objective function in (8.4) is PS = P0 and PR = 0. This result indicates that, if the direct channel has better quality than any of the S–R or R–D links, it is intuitive to allocate all available power to S alone. Now let us formulate the problem of optimal power allocation for the AF cooperative scheme. In this case, the message forwarded by the relay contains an amplified version of the noise along with the message transmitted originally by the source. As a result, the SNR at the destination node plays an important role in the optimal power allocation problem. The channel capacity of the two-hop AF scheme can be expressed as CA F ,div er sity =

1 2

log2 (1 + SN RD ),

(8.8)

where SN RD is the SNR at destination node given as [15] SN RD =

|hS R |2 PS |hR D |2 PR + |hS D |2 PS . 1 + |hS R |2 PS + |hR D |2 PR

(8.9)

For AF cooperation, optimizing the channel capacity is equivalent to SNR maximization. Therefore, the optimal power allocation problem for the AF scheme can be formulated as maximize {P S , P R }

|hS R |2 PS |hR D |2 PR + |hS D |2 PS 1 + |hS R |2 PS + |hR D |2 PR

subject to : PS + PR ≤ P0 , PS ≥ 0, PR ≥ 0.

(8.10)

210


Applying the Lagrange multiplier, the optimal power allocation of (8.10) is obtained as

PS =

|hS R |2 |hR D |2 P0 + |hS D |2 |hR D |2 P0 + |hS D |2 7 |hS R |2 P0 + 1 A+ |hS R |2 |hR D |2 A 2 |hR D | P0 + 1

(8.11)

and

PR =

|hS R |2 |hR D |2 P0 − |hS D |2 |hS R |2 P0 − |hS D |2 7 , |hR D |2 P0 + 1 2 2 A+ |hS R | |hR D | A |hS R |2 P0 + 1

(8.12)

where A = |hS R |2 |hR D |2 + |hS D |2 |hR D |2 − |hS R |2 |hS D |2 . Optimal power allocation holds if and only if A > 0 and |hS R |2 |hR D |2 P0 > |hS D |2 |hS R |2 P0 + |hS D |2 . Otherwise all available power should be allocated to the source alone, which indicates that the S–D link is better than the S–R or R–D link and that cooperation is not beneficial in such channel conditions. When |hS R |2 ≈ |hR D |2 and both are sufficiently larger than |hS D |2 , the ratio of PS and PR can be approximated as |hS R |2 |hR D |2 P0 + |hS D |2 |hR D |2 P0 + |hS D |2 PS ≈ . PR |hS R |2 |hR D |2 P0 − |hS D |2 |hS R |2 P0 − |hS D |2

(8.13)

Example 1 In this example, we compare the outage probabilities of the AF and DF schemes with equal and optimal power allocation methods, as shown in Figure 8.2. We consider that an outage occurs when the achieved rate is less than 1 (C < 1) at the destination. For simplicity, we assume that the relay node is located in the middle of the source and the destination and the complex channel coefficients hS R , hS D , and hR D are i.i.d. circularly symmetric Gaussian random variables with zero mean and variances, i.e., σS2 R = 1, σR2 D = 1, σS2 D = 1/(2α ), where α = 3 is the path loss coefficient. From Figure 8.2, we can see that optimal power allocation has significant SNR gain over the equal power allocation method. It is interesting to note that the outage probability of the AF scheme outperforms that of the DF scheme when the SNR value is sufficiently high (over 15 dB). This is because the DF scheme does not provide additional diversity gain. From the results we can conclude that, whenever there is diversity, it is always better to use the AF scheme over the DF cooperation.

211


Figure 8.2. Comparison of outage probabilities of AF and DF schemes with diversity.

Case 2 Without direct link Without diversity, the destination node receives only the relayed message from R. For DF cooperation, the channel capacity can be written as ;

< log2 (1 + |hS R |2 PS ), 12 log2 (1 + |hR D |2 PR ) . (8.14) The capacity maximization problem is thus a max–min problem. The maximum capacity is reached when the capacities of both hops are equal, i.e., CD F , w ithou t div er sity = min

1 2

1 2

log2 (1 + |hS R |2 PS ) =

1 2

log2 (1 + |hR D |2 PR ).

(8.15)

The optimal power allocation is obtained using PS + PR = P0 in (8.15) as P S = P0

|hR D |2 |hS R |2 + |hR D |2

(8.16)

P R = P0

|hS R |2 . |hS R |2 + |hR D |2

(8.17)

and

This result is also verified directly, by putting |hS D | = 0 in (8.6) and (8.7).

212


Figure 8.3. Comparison of outage probabilities of AF and DF schemes without diversity. Similarly for AF cooperation without diversity, the optimal power allocation is obtained by putting |hS D | = 0 in (8.11) and (8.12) as 7

PS = 1+

P0

(8.18)

|hS R |2 P0 + 1 |hR D |2 P0 + 1

and 7

PR = 1+

P0 |hR D |2 P0 + 1 |hS R |2 P0 + 1

Thus the ratio between PS and PR is given by 7 |hR D |2 P0 + 1 PS = . PR |hS R |2 P0 + 1

.

(8.19)

(8.20)

Example 2 The outage probabilities for AF and DF cooperation without diversity are compared in Figure 8.3. For each scheme, we plot the results obtained from equal and optimal power allocation methods. It is clear that optimal power allocation has approximately 3 dB SNR gain over the equal power allocation method for both the AF and DF schemes. Since there is no diversity, the DF scheme performs better than the AF scheme at low


X1 hs1 X2 X0

Source (S)

213

U1=f1(X1)

Relay 1 (R1)

hs2

h1D

U2=f2(X2)

h2D Relay 2 (R2) XN

hND

hSN

Z

Destination (D)

Relay N (RN) UN =fN (XN )

Feedback Figure 8.4. A dual-hop cooperative relay network.

to moderate SNR. However, at a very high SNR (over 30 dB), the performances of both the schemes are almost identical.

8.2.2

Dual-hop relay networks Now let us consider a two-stage cooperative network (also known as a parallel relay network) consisting of N relay nodes, denoted by Rk , k = 1, 2, . . . , N as shown in Figure 8.4. The complex channel coefficients from the source S to relay Rk and from Rk to destination D are given by hS k and hk D respectively. In such networks, S broadcasts its message in the first time slot and the set of relays {Rk , k = 1, 2, · · · , N } transmits simultaneously in the second slot. Here we assume all the channels are orthogonal and perfect CSI is available to all the nodes. The transmit powers of S and Rk are denoted by PS and Pk respectively. In this section, we focus on the power allocation among the relay nodes only. The power allocation among PS and PR can be determined using techniques similar to those derived in the previous section. The optimization problem is formulated as a capacity maximization problem but the total power constraint is imposed on the summation of relay powers, i.e., N k =1 Pk ≤ PR . In the following, we analyze the optimal power allocation for both AF and DF cooperation.

Case 1 AF scheme For the AF scheme, the capacity of the parallel relay channel is given as [16] CA F =

1 2

log(1 + SN RD ),

(8.21)

214


where

SN RD = PS

2

|hS D | +

N k =1

|hS k |2 |hk D |2 Pk |hS k |2 PS + |hk D |2 Pk + 1

.

(8.22)

The goal here is to optimize the power allocation among the parallel relay nodes so that the capacity is maximized. Optimizing CA F is equivalent to maximizing the SN RD . For a constant source power PS , we define 7 |hS k |2 |hk D |2 γk = , (8.23) |hS k |2 PS + 1 so that we can write N k =1

|hS k |2 γ 2 Pk |hS k |2 |hk D |2 Pk k = |hS k |2 PS + |hk D |2 Pk + 1 k =1 |hS k |2 + γk2 Pk N

(8.24)

and formulate the following optimization problem: maximize Pk

subject to:

N |hS k |2 γk2 Pk |hS k |2 + γk2 Pk k =1 N

Pk ≤ P R ,

k =1

Pk ≥ 0.

(8.25)

It can be easily shown that the optimization problem is convex since the objective function is now a concave increasing function of Pk and the constraints are linear. The solutions of any convex optimization problem can be easily obtained by available convex programming algorithms [17]. Among these algorithms, subgradient methods are the simplest and so are widely used. However, interior-point methods, bundle methods, and cutting-plane methods are also well known. The solution obtained using these algorithms does not provide any insight into the optimal power allocation among the relays though. Therefore, we solve the optimization problem of (8.25) using the Lagrange dual method. The Lagrangian of the problem is given by N N N |hS k |2 γk2 Pk (8.26) + λ k Pk − η Pk − PR , L(Pk , λ, η) = |hS k |2 + γk2 Pk k =1 k =1 k =1 where λ = λk ≥ 0, k = 1, 2, ..., N and η are the Lagrange multipliers corresponding to the inequality constraints on the relay power. From the Karush–Kuhn– Tucker (KKT) conditions, |hS k |2 γk2 (|hS k |2 + γk2 Pk ) − |hS k |2 γk4 Pk ∂L = + λk − η = 0 ∂Pk (|hS k |2 + γk2 Pk )2

(8.27)


215

and λk Pk = 0. By eliminating λk from (8.28), we get |hS k |2 γk2 (|hS k |2 + γk2 Pk ) − |hS k |2 γk4 Pk Pk = 0. η− (|hS k |2 + γk2 Pk )2

(8.28)

(8.29)

From (8.29) we see that if Pk = 0, then the expression |hS k |2 γk2 (|hS k |2 + γk2 Pk ) − |hS k |2 γk4 Pk η− (|hS k |2 + γk2 Pk )2 must be equal to zero. After simplification, we get the optimal power allocation among the relay nodes as

+ 1 |hS k |2 1 Pk = , (8.30) √ − γk η γk where [.]+ denotes the projection onto the feasible set of nonnegative orthants. Therefore, the optimal power allocation problem results in the following waterfilling solution [18]: ⎧ 1 1 1 |hS k |2 1 ⎪ ⎪ ( √ − ), if √ > ⎨ γk η γk η γk (8.31) Pk = ⎪ ⎪ ⎩ 0, else. The Lagrange multiplier, η, is chosen to meet the total power constraint of the relay nodes. Also note that the relay node Rk is allowed to transmit if and only if λk > η. Example 3 The sum capacities (or maximum achievable data rate) of the AF scheme with different numbers of relays are compared in Figures 8.5 and 8.6. For both the figures, we plot the results obtained from equal and optimal power allocation methods. In Figure 8.5, we assume that all the S–R and R–D channel coefficients are i.i.d. circularly symmetric Gaussian random variables with zero mean and unit variances. As in the previous examples, the direct S–D channel coefficient, hS D is assumed to have zero mean and variance σS2 D = 1/(2α ). In Figure 8.6, we assume that S–R and R–D channel coefficients are non i.i.d. Gaussian random variables. From Figures 8.5 and 8.6, it is clear that the rates achieved are much higher for optimal power allocation than for equal power allocation. As we increase the number of relays, the sum capacity increases. However, for the cases where some relay channels are better than others (in Figure 8.6), it is interesting to note that two relays with optimal power allocation can achieve a better rate than four relays with equal power allocation.


3

Sum capacity (bps/Hz)

2.5

2

1.5

1

4 relay equal power 4 relay optimal power 2 relay optimal power 2 relay equal power

0.5

0

1

2

3

4

5

6

7

8

9

10

Total relay power (watt)

Figure 8.5. Comparison of sum capacities of the AF scheme with i.i.d. channels.

3

2.5


216

2

1.5

1

4 relay equal power 4 relay optimal power 2 relay optimal power 2 relay equal power

0.5

0

1

2

3

4

5

6

7

8

9

10


Figure 8.6. Comparison of sum capacities of the AF scheme with non i.i.d channels.

217


Case 2 DF scheme A relay node can execute the DF scheme only if it is able reliably to decode the message received from the source node. Let us consider a set of relays denoted by ND F , among the N relay nodes, which are able to correctly decode the messages transmitted by the source. For given ND F , the dual-hop relay network with orthogonal channels is analogous to a multiple antenna system. The capacity of such networks can be written as [19]: CD F =

1 2

log(1 + |hS D |2 PS ) +

k ∈N D F

1 2

log(1 + |hk D |2 Pk ).

(8.32)

For optimal power allocation the DF scheme, the first task is to find the reliable relay nodes k ∈ ND F . We assume that a relay will be able to execute the DF strategy if it is able to reliably communicate with the source at a desired rate, rS . Therefore, a relay node k is reliable if the following condition is met: 1 2

log(1 + |hS k |2 PS ) ≥ rS .

(8.33)

Our goal is to find the optimal power allocation that maximizes the capacity of the network. However, the problem of maximizing the capacity under the relay power constraint, N k =1 Pk ≤ PR has its dual problem with the objective to communicate with the destination at the desired rate, rS using minimum relay power, Pk∗ . The analogous solutions of the two problems become identical when Pk∗ = PR . We use binary variables xk to indicate the reliable relays and formulate the following dual problem:

minimize

N

Pk

k =1

subject to:

N

1 2

log(1 + |hS D |2 PS ) +

1 2

log(1 + |hS k |2 PS ) > xk rS ,

k =1

1 2

log(1 + |hk D |2 Pk )xk ≥ rS ,

xk ∈ {0, 1}, Pk ≥ 0.

(8.34)

The formulated optimization problem is a mixed integer problem which is generally very difficult to solve. However, for severely restricted transmitter power or low SNR cases, i.e. Pk |hk D |2 1, the dual problem simplifies to the wideband

218


DF relay problem [20]: minimize

N

Pk

k =1

subject to:

N

1 2

|hS D |2 PS +

1 2

|hS k |2 PS > xk rS ,

1 2

k =1

|hk D |2 Pk xk ≥ rS ,

xk ∈ {0, 1}, Pk ≥ 0.

(8.35)

The solution of the above optimization problem is to choose a single relay which has the best channel gain towards the destination and allocate the total relay power to it. This is due to the fact that, at low SNR (Pk |hk D |2 1), a waterfilling solution finds the relay which has the best channel gain to the destination node. This means that the selective relaying scheme is optimal for the DF strategy for dual-hop relay networks with multiple relays. Therefore, the optimal power allocation among multiple relays becomes a single relay optimization problem: minimize

P S + Pk

subject to:

1 2

|hS D |2 PS +

1 2

|hS k |2 PS ≥ xk rS ,

1 2

|hk D |2 Pk xk ≥ rS ,

xk ∈ {0, 1}, Pk ≥ 0, PS ≥ 0.

(8.36)

As in the three-node case, one can show that cooperation with relay k is beneficial if and only if |hS k |2 > |hS D |2 and |hk D |2 > |hS D |2 . Otherwise it is optimal to allocate all the power to the source for direct transmission. The optimal power allocation is obtained using the first and second constraints of (8.36) with equality: rS |hS k |2

(8.37)

rS − PS∗ |hS D |2 . |hk D |2

(8.38)

PS∗ = and Pk∗ =

219


0.7

0.6


0.5

0.4

0.3

0.2

DF optimal power (best relay) DF equal power (2 relay) DF equal power (4 relay)

0.1

0

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5


Figure 8.7. Comparison of sum capacities of DF scheme in the low SNR regime. The optimal total power is then 5 PS∗ + Pk∗ = rS

6 |hS D |2 . + − |hS k |2 |hk D |2 |hS k |2 |hk D |2 1

1

(8.39)

The best relay will be the one among the set of useful relays which minimizes the total power PS∗ + Pk∗ . If the set of useful relays RU = {k ∈ ND F | |hS k |2 > |hS D |2 , |hk D |2 > |hS D |2 } is nonempty, then the optimal relay selection criterion is 5 6 1 1 |hS D |2 ∗ k = argmin . + − |hS k |2 |hk D |2 |hS k |2 |hk D |2 k ∈R U

(8.40)

The maximum capacity of the primal problem for the dual-hop DF scheme in the low-SNR regime can thus be approximated as CD F ≈

1 2

|hS D |2 PS +

1 2

|hk ∗ D |2 PR .

(8.41)

Example 4 Similarly to the previous example, we compare the sum capacities of DF scheme for the dual-hop network with optimal and equal power allocation in Figure 8.7. The results are shown for the cases of severely restricted transmitter power or the low-SNR regime. We assume that the different S–R and R–D channels have different channel variances.

220


Relay Base station (BS)

Relay

User near BS

User near cell edge Figure 8.8. Typical cooperative cellular network with multiple users.

Unlike that for the AF scheme, the sum capacity of the DF scheme does not depend on the number of relays at low SNR. Since the DF scheme does not provide additional diversity gain, it is optimal to find the best relay and allocate total relay power to it.

8.3

Multiuser cooperation In the previous section, we analyzed the problem of resource allocation for a single source–destination pair. Now we examine the resource allocation problem for multiuser (or multisource) cooperative networks. Consider the case of cellular networks shown in Figure 8.8, where some relays are deployed to assist the users located at cell edges for both uplink and downlink transmissions. Since the number of relays is smaller than the number of users in a practical scenario, each relay is assigned to assist more than one user. To formulate the power allocation problem for multiuser networks we choose one of two QoS measures, namely the minimum rate of the users (max–min fairness) or the weighted sum rates of the users (weighted-sum fairness). Therefore, the problem is to maximize either the minimum rate of the users or the weighted-sum rates given total relay power as the constraint. In the following, we will see that both the problems are convex and the problem can be solved using centralized or distributed algorithms.

8.3 Multiuser cooperation

8.3.1

221

System model Consider a multiuser network where M source nodes Si , i ∈ {1, 2, ..., M } transmit messages to their corresponding destination nodes Di , i ∈ {1, 2, ..., M }. There are N relay nodes Rk , k ∈ {1, 2, ..., N } in the network. The set of relays assisting the transmission of Si is denoted by R(Si ). The set of sources using the Rk relay is denoted by S(Rk ). Thus we can write S(Rk ) = {Si | Rk ∈ R(Si )},

(8.42)

which means one relay can forward the messages of several users. For this section we consider that no direct link exists between any source–destination (Si –Di ) pair. We also assume all the channels are orthogonal and perfect CSI is available to all the nodes. In a multiuser cooperative network with the AF scheme, each source Si transmits a message to its chosen relays in the set R(Si ) in the first time slot, and each relay amplifies and forwards its received message to Di in the second time slot. The transmit powers of the source Si and its assisting relays Rk ∈ R(Si ) are denoted by PS i and PRS ki respectively. Consider that in the first time slot, source Si broadcasts the message Xi with unit energy to the relays Rk ∈ R(Si ). The received message at the relay Rk can be written as XRS ik = PS i hSRik Xi + ZR k , Rk ∈ R(Si ). (8.43) In the second time slot, the relay Rk amplifies the received message and relays it to the destination node Di . The received message at Di is given by [21]

i XD Rk

= > > => ?

PRS ki PS i Si i ˆ hD " " R k hR k Xi + Z D i , " S i "2 PS i "hR k " + 1

Rk ∈ R(Si ),

(8.44)

i where hSRik and hD R k denote the complex channel coefficients for the Si –Rk and Rk –Di links, and ZR k and ZD i are the zero mean AWGN with unit variance. The modified AWGN at Di is denoted by ZˆD i with equivalent variance " " " i "2 PRS ki "hD Rk " . 1+ " " " S i "2 PS i "hR k " + 1

Assuming that MRC is employed at the destination node Di , the combined SNR at Di can be written similarly, as given by [22]: " " " " " S i "2 " D i "2 S i "hR k " "hR k " PR k PS i SN RD i = . (8.45) " " " " " S i "2 " D i "2 S i R k ∈R(S i ) "hR " PS i + "hR " PR + 1 k k k

222


The above expression for SN RD i is similar to that of (8.22) used in the previous section for the dual-hop relay network with the AF scheme. The rate ri of user i is given by ⎛ ⎞ " " " " " S i "2 " D i "2 S i "hR k " "hR k " PR k PS i 1 1 ⎜ ⎟ ri = log2 (1 + SN RD i ) = log2 ⎝1 + " " " " ⎠. " D i "2 S i " S i "2 2 2 R k ∈R(S i ) "hR " PS i + "hR " PR + 1 k k k (8.46) Similarly to the single-user case, it can be shown that, for a constant source power PS i , the rate expression (8.46) is a concave increasing function with respect to PRS ki , Rk ∈ R(Si ). Using this fact, the optimal power allocations for both the max–min fairness and weighted-sum fairness schemes can be calculated as shown in the following subsection.

8.3.2

Centralized power allocation Max–min fairness For the rate expression given in (8.46), the power allocation problem under the max–min rate can be formulated as min ri

maximize

Si

subject to:

PRS ki ≤ PRmax , k

k = 1, 2, ..., N,

S i ∈S(R k )

PRS ki ≥ 0,

(8.47)

where PRmkax is the maximum (or total) power of the relay Rk . The first constraint can also be written equivalently as a constraint on the maximum sum of powers transmitted by the corresponding assisted source nodes. The set of linear inequality constraints with positive variable in (8.47) is compact and nonempty. Hence the optimization problem set is always feasible. Moreover, since the objective function is an increasing function of power, the first inequality constraint should meet with equality at the optimal point. The convex optimization problem can be written in its standard form: minimize

−t

subject to: t − ri ≤ 0 ,

PRS ki ≤ PRmkax ,

i = 1, 2, ..., M, k = 1, 2, ..., N,

S i ∈S(R k )

PRS ki ≥ 0, t ≥ 0,

(8.48)

where t is a slack variable. The solution of this problem gives the optimal power allocation among the relays that maximizes the worst-user rate. In the special


223

case, in which all the users share the same set of relays the rates of all users are equal at the optimal point. This is easily understood from the max–min problem of single-user case where the capacity is maximized with equality at the optimal point.

Weighted-sum fairness The problem of the max–min rate-based power allocation is that it degrades the sum capacity (or total network throughput). This is because it tends to improve the performance of the worst-user rate by allocating more power to the poor links. The weighted-sum rate maximization can potentially achieve certain fairness for different users by allocating large weights to the users in unfavorable channel conditions while maintaining good network performance. Let wi denote the weight allocated to user i, then the weighted-sum rate power allocation problem can be formulated as maximize

M

wi ri

i= 1

subject to:

PRS ki ≤ PRmkax ,

k = 1, 2, ..., N,

S i ∈S(R k )

PRS ki ≥ 0.

(8.49)

The solution of this convex optimization problem gives better network throughput, which indicates that the weighted-sum-rate-based power allocation favors users with good channel conditions. However, it does not severely penalize users with bad channel conditions either. In fact, because the objective function (weighted-sum rate) is concave and increasing with respect to the allocated powers, the increment in the function value is higher when the power is low. Therefore to maximize the objective function value, it is obvious to allocate more power to ‘bad’ users operating at low SNR.

8.3.3

Distributed power allocation The centralized allocation discussed in the previous subsection may not be very practical for a number of reasons. Firstly, it requires a large signaling overhead since the channel gain estimations between various S–R and R–D have to be transmitted to the base station, which allocates power based on these estimates. Moreover, the wireless channels are time varying and frequency selective. Therefore, the channel gain information needs to be constantly updated, which requires a lot of data to be transmitted to the base station using the control channels. In fact, in mobile communication systems with constant changes in the channels between various devices, such a centralized power allocation scheme could become impractical. Secondly, these schemes are highly complex and would create a large computational load at the base station. Thus, it is very important

224


to devise distributed schemes in which each relay calculates its own optimal power allocation based on the information available from neighboring nodes and hence reduces the overall signaling overhead as well as the large computational complexity in the base station. Several distributed power allocation schemes for cooperative communication systems have been discussed in the literature. The distributed power allocation scheme for the multiuser AF relay network was developed in [21] using the Lagrange dual decomposition method. For the DF scheme, the distributed power allocation problem with partial CSI was addressed in [23] and computationally efficient optimal schemes were proposed. Both relay selection and power allocation for AF wireless networks with reduced complexity were investigated in [24]. In the following we discuss the distributed power allocation strategy for both AF and DF schemes.

Case 1 AF scheme The centralized optimization problem for power allocation based on weightedsum rate maximization is given in (8.49). Here we solve the same problem in a distributed manner. The main idea is to separate the original problem in (8.49) into independent subproblems using the Lagrange dual decomposition method. The Lagrangian of problem (8.49) is L(PRS ki , λ) =

M

wi ri −

i=1

N

⎛

⎞

λk ⎝

PRS ki − PRmkax ⎠ ,

(8.50)

S i ∈S(R k )

k =1

where λ = [λ1 , λ2 , ..., λN ] represents the Lagrange multipliers corresponding to the N constraints of (8.49). Using (8.42) we can write the following: N

λk

k =1

PRS ki =

S i ∈S(R k )

M

λk PRS ki .

(8.51)

i=1 R k ∈R(S i )

The Lagrangian in (8.50) is rewritten using (8.51) as L(PRS ki , λ) =

M

⎣wi ri −

⎤ λk PRS ki ⎦ +

R k ∈R(S i )

i=1

=

⎡

M

Li (PRS ki , λ) +

i=1

N

N

λk PRmkax

k =1

λk PRmkax ,

(8.52)

k =1

where Li (PRS ki , λ) corresponds to the ith value of the Lagrangian. The corresponding Lagrange dual function is given by g(λ) = max L(PRS ki , λ). S

P R i ≥0 k

(8.53)


225

This dual function can be obtained by solving M separate subproblems corresponding to M different users as maximize Li (PRS ki , λ) subject to: PRS ki ≥ 0, Rk ∈ R(Si ).

(8.54)

Since the original problem given in (8.49) is convex, strong duality holds and we can get the optimal power allocation by solving the dual problem: minimize

g(λ)

subject to: λk ≥ 0, k = 1, 2, ..., N.

(8.55)

Let the solution of the optimization problem in (8.54) be L∗i (λ), which corresponds to the optimal value of Li (PRS ki , λ). Then the dual problem can be rewritten as minimize

M i=1

L∗i (λ) +

N

λk PRmkax

k =1

subject to: λk ≥ 0, k = 1, ..., N.

(8.56)

The distributed power allocation algorithm aims to solve (8.54) and (8.56) sequentially. Let the Lagrange multiplier λk ≥ 0 denote the price per unit power at relay k. Therefore λk PRS ki represent the total price that user i must pay for using PRS ki power at each relay Rk ∈ R(Si ). Thus each user tries to maximize the weighted rate minus the total price it has to pay given the price coefficients at the relays. Since the dual function g(λ) is differentiable, the problem can be solved iteratively by the gradient projection method. The receiver of user i finds its optimal power with given λ from the assisting relays Rk ∈ R(Si ) as ⎧ ⎫ ⎨ ⎬ λk [t]PRS ki (λ[t]) . (8.57) PRS ki (λ[t + 1]) = arg max wi ri − ⎩ ⎭ R k ∈R(S i )

The receiver of user i then sends this information to all the relays allocated to source i. Based on PRS ki values received from destinations, the relays update their dual variable λk as follows: ⎡ ⎛ ⎞ ⎤+ PRS ki (λ[t])⎠⎦ , (8.58) λk [t + 1] = ⎣λk [t] − δ ⎝PRmkax − S i ∈S(R k )

where t is the iteration index, [.]+ denotes the projection onto the feasible set of nonnegative orthants, and δ is the step size parameter. Update equation (8.58) can be interpreted as the price (λk ) change by Rk depending on the requested power levels from its users. The price increases when the power allocated to the relay exceeds its maximum limit. This price-based distributed algorithm requires

226


Figure 8.9. Price-based distributed power allocation algorithm. message passing only between each receiver and its assisting relays. The overall structure of the distributed power allocation is shown in Figure 8.9.

Example 5 In Figure 8.10, we compare the worst-user rate for both the weighted-sum and max–min fairness algorithms for a network with number of source nodes, M = 8 and number of relays, N = 4. The equal power allocation among the relays is also included for reference. We see that the worst user obtains the best rate under the max–min fairness scheme and the worst rate under weighted-sum scheme with equal weight coefficients. However, Figure 8.11 shows the weighted-sum scheme results in maximum capacity or network throughput. The max–min scheme targets improving the performance of the worst user, which results in a significant loss in the sum capacity of the whole network.

Case 2 DF scheme Distributed power allocation strategies for the two-hop DF scheme were investigated in [23]. Here the relay decides its power so that the destination achieves the target SNR assuming that it is the only relay to the destination. The relay


227

-

Figure 8.10. Comparison of the worst-user rate for the weighted-sum rate and max–min rate algorithms.

Figure 8.11. Comparison of the sum capacity for the weighted-sum rate and max–min rate algorithms.

228


decides to forward the received message from the source to the destination if its channel gain hk D satisfies |hk D |2 > γ,

(8.59)

where γ is a given threshold value. The transmit power of the relay is given by Pk∗ =

(SN Rtar g et − Ps |hS k |2 )+ . |hk D |2

(8.60)

The distributed power allocation algorithm is formulated as follows: E[Pk ] minimize Ps + k ∈N R (P s )

subject to: Prob (SN RD ≤ SN Rtar g et ) ≤ ρtar g et , Ps |hk D |2 ≥ SN Rtar g et ,

k ∈ NR ,

(8.61)

where NR denotes the set of reliable relays which satisfy (8.61). SN RD is the SN R at destination node and ρtar g et is the target outage probability. Note that, even though a relay ultimately determines its own power, it does not take much of the computational load. This scheme, however, requires knowledge of all the channels gains at the receiver. Therefore, several suboptimal schemes should be derived, in which the source can calculate γ and Ps based on the channel characteristics without requiring feedback from the receivers.

8.4

Relay selection Until now we have assumed that the relays are assigned a priori to power allocation. The joint relay selection and power allocation problem is a mixed integer optimization problem and is very difficult to solve. Therefore, in most of the literature, the problem is divided into two subproblems [25]. The relays are chosen assuming fixed powers (e.g., equal power allocation) at the relays. Once the relays are selected, the techniques mentioned in previous sections of this chapter are used to allocate power to the selected relays. In this section, some of the relay selection algorithms are presented. In spite of assuming fixed power at the relays, relay selection is still an NPhard problem and the optimum solution can only be achieved through exhaustive search [22]. Several greedy algorithms for relay selection for DF systems have been proposed in the literature. The general strategy is to select the best relay or a group of relays which satisfies a certain performance improvement over the direct S–D link [26]. In [27], a relay is selected based on the amount of time taken to deliver a fixed number of messages. Two optimal algorithms are provided where in the first one the relays are adaptively selected and in the second one the optimal number of relays is predetermined without relying on

8.4 Relay selection

229

the specific network realization. Alternatively, in [24], a relay is selected if it offers an increase in capacity compared with source destination channel. In [28], a distributed algorithm is presented to select the ‘best’ relay that provides the best end-to-end path between the source and the destination. Each relay is assigned a timer with initial value inversely proportional to either hk = min(|hS k |2 |, |hk D |2 ) or hk = 2|hS k |2 |hk D |2 /(|hS k |2 + |hk D |2 ). The relay with the highest value of hk is considered to be the one with the best end-to-end path between source and destination. All relays start their timers simultaneously with different initial values which depend upon the channel realizations. The relay whose timer expires first (i.e., the one with maximum hk ) starts relaying the message from the source as soon as its time expires. All the relays listen to the other relays and, therefore, know whether some other relay has started forwarding the message or not. When they recognize that a particular relay has started transmission, they do not forward the source message to the destination. Joint relay selection and power allocation algorithms were studied in [29] for multisource AF systems. The following max–min optimization problem formulated: ⎛ maximize min Si

1 ⎜ log2 ⎝1 + 2

subject to:

Rk

⎞ " " " " " S i "2 " D i "2 S i "hR k " "hR k " PR k PS i xSRik ⎟ " "2 " "2 ⎠ " Si " " i " Si Si P x + 1 "hR k " PS i + "hD " Rk Rk Rk

PRS ki ≤ PRmkax ,

Si

xSRik = xSmi ax ,

Rk

PRS ki ≥ 0, xSRik ∈ {0, 1}.

(8.62)

This is a nonconvex optimization problem and hence a unique analytical solution cannot be achieved. Therefore, a suboptimal solution was proposed by relaxing the integrality constraints on xSRik and allowing them to take all values in the interval [0, 1]. The relaxed optimization problem is convex and can be easily solved using convex programming techniques. A rounding technique is then used to obtain a suboptimal solution for the original optimization problem from the solution of the relaxed optimization problem. Joint relay selection and resource allocation is still an open research issue. The challenge is to develop low-complexity schemes that treat all users fairly and that can be implemented feasibly without the requirement of significant additional system resources.

230


8.5

Conclusion We have studied the problem of radio resource allocation in cooperative wireless networks. Our objective was to show how the usage of the available radio resources in these networks can be maximized by using different optimization techniques. In formulating these optimization models, we have taken into consideration the architecture and various cooperation schemes deployed in these networks along with the constraints on the available radio resources such as bandwidth and transmit power. In a cooperative network, relay nodes play a vital role in achieving the intended benefit of cooperative communication. The performance of the entire network depends on how these relays are selected for individual communications between source and destination nodes and how resource is allocated on the links between the relays and the communicating nodes. Jointly optimizing relay selection and resource allocation is an NP-hard problem and is often handled as two separate subproblems. Although the bulk of this chapter has been devoted to analyzing different optimization-based approaches for resource allocation once relays are selected, we have also highlighted the different relay selection methods that are proposed in the literature and several suboptimal methods to solve these subproblems jointly. Resource optimization in cooperative wireless networks remains, however, an open research problem and demands in-depth future research.

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9

Adaptive resource allocation in cooperative cellular networks Wei Yu, Taesoo Kwon, and Changyong Shin

9.1

Introduction The cellular structure is a central concept in wireless network deployment. A wireless cellular network comprises base stations geographically located at the centre of each cell serving users within the cell boundary. The assignment of the users to the base stations depends on the relative channel propagation characteristics. As a mobile device can usually receive signals from multiple base stations, the mobile is typically assigned to the base station with the strongest channel gain. Signals from all other base stations are regarded as intercell interference. However, at the cell edge, it is often the case that the propagation path-losses from two or more base stations are similar. In this case, the signal-to-noise-andinterference ratio (SINR) could be close to 0 dB, even if the mobile is assigned to the strongest base station. To avoid excessive intercell interference in these cases, traditional cellular networks employ a fixed frequency reuse pattern so that neighboring base stations do not share the same frequency. In this manner, neighboring cells are separated in frequency so that cell-edge users do not interfere with each other. The traditional fixed frequency reuse schemes are effective in minimizing intercell interference, but are also resource intensive in the sense that each cell requires a substantial amount of nonoverlapping bandwidth, so that only a fraction of the total bandwidth can be made available for each cell. Consequently, the standardization processes for future wireless systems have increasingly targeted maximal frequency reuse, where all cells use the same frequency everywhere. In these systems, it is crucial to manage intercell interference using dynamic power control, frequency allocation, and rate allocation methods. Wireless channels are fundamentally impaired by fading, propagation loss, and interference. Intensive research has been focused on the mitigation of short-term fading, where spatial, temporal, and frequency diversity techniques have been devised to combat the short-term variation of the channel over time. Large-scale fading, propagation loss, and intercell interference, however, call for different approaches. As large-scale channel and interference characteristics can often be Cooperative Cellular Wireless Networks, eds. Ekram Hossain, Dong In Kim, and Vijay K. Bhargava. Published by Cambridge University Press. C Cambridge University Press, 2011.

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estimated at the receivers and made available at the transmitter, rather than combating large-scale fading the right approach is to adapt to it. To this end, cooperative communication has emerged as a promising future technology for dealing with the large-scale channel impairments. This chapter considers two types of cooperative networks that specifically address the issues of intercell interference and path-loss.

r Base station cooperation This type of cooperative network explores the possibility of coordinating multiple base stations. In a traditional cellular network, each base station operates independently. In particular, each base station adapts to the channel propagation condition within each cell without considering the intercell interference it causes the neighboring cells. The intercell interference is always treated as part of the background noise. A network with base station cooperation is a network in which the transmission strategies among the multiple base stations are designed jointly. In particular, the base stations may cooperate in their power, frequency, and rate allocations in order to jointly mitigate the effect of intercell interference for users at the cell edge. Such a cooperative network can also be thought of as an adaptive frequency reuse scheme where the frequency usage and transmission power spectrum are designed specifically according to the mobile locations and user traffic patterns. r Relay cooperation This type of cooperative network explores the use of relays to aid the direct communication between the base station and the remote subscribers. The path-loss is a fundamental characteristic of the wireless medium. The path-loss exponent, which is determined by the physics of electromagnetic wave propagation environment, typically ranges from 2 to 6. Consequently, propagation distance is a crucial factor that affects the capacity of the wireless channel. The use of cooperative relays in a cellular network can be thought of as a method for reducing the propagation distance. Instead of adding more base stations to the network (which is costly), the idea of a cooperative relay network is to deploy relay stations within each cell so that the mobile users may connect to the nearest relay, rather than the base station which may be far away. Relay deployment substantially improves the area-spectral efficiency of the network. In both types of cooperative networks, resource allocation is expected to be a crucial issue. In a network with base station cooperation, base stations must jointly determine their respective power and bandwidth allocation for the purpose of minimizing intercell interference. In a cooperative relay network, power and bandwidth assignments need to be made for each of the base-station-to-relay and relay-to-mobile links. The optimal allocation of these network resources has a significant impact on the overall network performance. This chapter provides an optimization framework for power, bandwidth, and rate allocation in cooperative cellular networks. The network is assumed to employ orthogonal frequency division multiple access (OFDMA) which provides

9.2 System model

235

flexibility in power, subchannel, and rate assignment for each link. This chapter covers the theory and practice of cooperative network design, and makes a case that cooperative communication is a key future technology that could significantly improve the overall capacity of wireless networks. Throughout this chapter, it is assumed that the network employs an initial channel estimation phase so that the frequency selective channel gain between any arbitrary transmitter and receiver pair can be estimated and made known throughout the network. The assumption of channel knowledge is necessary in order to optimize the allocation of power, bandwidth, and rate in the network. In this chapter it is further assumed that channel estimation is perfect. In practical situations where channel estimation error exists, robust optimization design is needed. The impact of imperfect channel knowledge on the resource allocation of cooperative cellular networks has been dealt with in [1, 2], but is not directly addressed in this chapter. It should be noted that in this chapter we consider cooperative networks in which transmitting nodes cooperate in their transmission strategies only (e.g., power, bandwidth allocation), but not in actual signals. It is possible to envision a network-wide cooperative system where all the antennas from all the base stations are pooled together as a single antenna array at the signal level. Such a network multiple-input multiple-output (MIMO) system is capable of achieving the ultimate area-spectral efficiency limit of the network, but is outside of the scope of this chapter.

9.2

System model In this chapter we consider wireless cellular networks employing an OFDMA scheme, where the total bandwidth is divided into a large number of subchannels, and where arbitrary scheduling, as well as power, frequency, and rate allocation, may be made for any transmitter–receiver pair throughout the network. The flexibility of the OFDMA system in assigning resources throughout the network is one of its key advantages, but it also presents a challenge in resource optimization, as the number of optimization variables is typically quite large in a realistic network. This section presents a system model for the OFDMA network.

9.2.1

Orthogonal frequency-division multiplexing (OFDM) The OFDM scheme was originally conceived as a way to combat the multipath or frequency-selective nature of the wireless channel. By utilizing an N -point inverse fast Fourier transform (IFFT) at the transmitter and an N -point fast Fourier transform (FFT) at the receiver, the available frequency band is divided into N orthogonal subchannels on which independent data transmissions take place. The orthogonalization of frequency dimensions relies on the use of a cyclic


Frequency

236

3 2 3

2 4 1 1

3 1 3 1 2 2 1 1 2

3 2 3 2

2 3 2 1 4

1 1 1 1 4

1 2 2 2 2

4 2 4 2 1 1 4 1 2 2 4 4 2 4 3 2 3 Time

Figure 9.1. In an OFDMA system, the time and frequency dimensions are partitioned and can be assigned arbitrarily to multiple users in the cell.

prefix, and on the assumption that the channel is stationary within each OFDM symbol, an assumption which is made throughout this chapter. The OFDM system can also be thought of as a multiple-access scheme, in which multiple users may occupy orthogonal frequency subchannels without interfering with each other. For example, in a cellular network, different mobile users may communicate with the base station on nonoverlapping sets of frequency tones, so that different users’ signals are separated in frequency. This is known as OFDMA. The idea of OFDMA can also be extended to a cooperative relay network in which different transmitter–receiver pairs in the network use nonoverlapping sets of frequency tones. Orthogonalization within each cell is, in general, a good idea, as whenever a receiver is close in range to a nonintended transmitter, orthogonalization is needed to avoid mutual interference. The use of OFDM enables orthogonalization in the frequency domain, which along with scheduling (which is essentially orthogonalization in the time domain) allows an arbitrary division of orthogonal dimensions among users within each cell. The assignment of dimensions can be visualized in a time–frequency map as shown in Figure 9.1. It is implicitly assumed in the preceding discussion that when multiple transmitter–receiver pairs use OFDMA, the FFT at each receiver orthogonalizes not only the intended transmit signal, but also all the interfering signals. For this to happen, the received OFDM symbols from all transmitters must be symbol synchronized, as otherwise a leakage would occur from one tone to its neighboring tones [3]. For the downlink cellular setting, symbol synchronization is automatic. For the uplink, transmit timing offset can be introduced to ensure synchronization at the receiver. A more challenging case is the relay cooperative network, where it is possible to have one relay communicating with a mobile on one set of frequency tones, while another relay communicates with a different mobile on adjacent tones. In this case, simultaneous symbol synchronization at

9.2 System model

237

two different receivers becomes difficult. It is possible to use advanced techniques (such as a cyclic suffix in addition to a cyclic prefix [4]) to correct for these effects. For simplicity, in the rest of this chapter it is assumed that leakage of this type is sufficiently small that its effect can be ignored.

9.2.2

Adaptive power, spectrum, and rate allocation An OFDM system allows arbitrary assignment of power, modulation format, and rates across the frequency domain for each transmitter–receiver pair. Assuming a fixed type of modulation, e.g., quadrature amplitude modulation (QAM), and a fixed target probability of error, the maximum bit rate in each OFDM tone is a function of the SINR on that tone. The overall achievable rate of the link is the sum of the bit rates across the tones, which can be expressed as R=

SINR(n) , log 1 + Γ n =1 N

(9.1)

where SINR(n) is the ratio of the received signal power to the noise and interference power at the receiver in tone n, and Γ is the SNR gap, which is a measure of the efficiency of the particular modulation and coding scheme employed. With strong coding, Γ can be made to be close to the information-theoretical limit of 0 dB. In practical wireless systems, Γ can range from around 6 dB to 12 dB. The exact value of Γ depends on the modulation scheme, coding gain, and the probability-of-error target. The use of the SNR gap to relate the SINR with the transmission rate is an approximation which is accurate for moderate and high SNRs. The exact relation between the SINR and the rate depends on a detailed probability-oferror analysis, and would give rise to complex functional forms. The advantage of using the SNR gap approximation is that the resulting functional relation is amenable to analytic optimization, and it closely resembles the Shannon capacity formula for the additive white Gaussian noise channel. Note that because of the presence of intercell and intracell interference within the network, the SINRs of different links in a cellular network are interdependent. For this reason, the optimization of achievable rates over all users across the network is, in general, a nontrivial problem.

9.2.3

Cooperative networks In this chapter we consider two types of cooperative cellular networks: networks where multiple base stations from different cells may cooperatively set their power allocation across the frequency tones; and networks where relay stations may be deployed to transmit and receive information from the mobile users. It is assumed that an OFDMA scheme is used within each cell, and no two links within each cell can use the same frequency tone at the same time. This

238


eliminates intracell interference. Intercell interference is still present especially for cell-edge users. Given a fixed frequency and power allocation for all transmitters, the SINR for each link in every frequency tone can be easily computed as a function of the transmit powers and the direct and interfering channel pathlosses. The network optimization problem is that of coordinating the allocation of frequency tones and time slots to different links within each cell and the allocation of power across time and frequency subject to total and peak power constraints, so that an overall network objective function is maximized.

9.3

Network optimization

9.3.1

Single-user water-filling The OFDM transmit power optimization problem for a single link has a classic solution known as water-filling. In this section, we briefly review the optimization principle behind water-filling and set the stage for subsequent development for multiuser network optimization. For the single-link problem where the noise and interference are assumed to be fixed, the optimization of the achievable rate subject to a total power constraint can be formulated as N

|h(n)|2 P (n) log 1 + Γσ 2 (n) n =1

maximize

N

subject to :

P (n) ≤ Ptotal ,

n =1

0 ≤ P (n) ≤ Pm ax ,

(9.2)

where the optimization is over P (n), the transmit power on the frequency tone n. The channel path-loss |h(n)|2 and the combined noise and interference σ 2 (n) are assumed to be fixed. The optimization is subject to a total power constraint Ptotal and a per-tone maximum power-spectral-density (PSD) constraint Pm ax . The water-filling solution arises from solving the above optimization problem via its Lagrangian dual. Let λ be the dual variable associated with the total power constraint, then the Lagrangian of the above optimization problem is N N |h(n)|2 P (n) −λ (9.3) log 1 + P (n) − Ptotal . L(P (n), λ) = Γσ 2 (n) n =1 n =1 The constrained optimization problem is now reduced to an unconstrained one in which λ can be interpreted as the power price. Optimizing the above Lagrangian subject to peak power constraints by setting its derivative to be zero gives

Γσ 2 (n) 1 − P (n) = λ |h(n)|2

P m a x , 0

(9.4)

9.3 Network optimization

239

Figure 9.2. Single-user water-filling solution.

where [·]ba denotes a limiting operation with lower bound a and upper bound b. The optimal λ can then be found based on the total power constraint, either by a bisection or by using algorithms based on the sorting of the subchannels by their effective noises. Equation (9.4) is the celebrated water-filling solution for transmit power optimization over a single link. The name water-filling comes from the interpretation that the effective noise and interference Γσ 2 (n)/|h(n)|2 can be thought of as the bottom of a bowl, 1/λ can be thought of as the water level, and the power allocation process can be thought of as that of pouring water into the bowl. The optimal power is the difference between the water level and the bottom of the bowl, as illustrated in Figure 9.2. The fundamental reasons that an (almost) analytic and exact solution exists for this problem are that the objective function of the optimization problem (9.2) is a concave function of the optimization variables and the constraints are linear. Therefore, convex optimization techniques such as Lagrangian dual optimization can be applied. Modern wireless communication systems often implement adaptive power control and adaptive modulation schemes that emulate the optimal water-filling solution. It should be noted that the exact shape of the optimal power allocation is not important. If one approximates the optimal solution by a constant power allocation where all subchannels that would receive positive power in the optimal solution receive equal power in this approximate solution, the value of the objective function would be close to the optimum [5, 6]. This is because the waterfilling relation, i.e., (9.4), operates on a linear scale on P (n), while the rate expression, i.e., (9.2), is a logarithmic function, which is not sensitive to the exact value of P (n) when it is large. Thus, in the implementation of water-filling in practice, while it is important to identify the minimum channelgain-to-noise ratio beyond which transmission should take place, the exact value of P (n) is not as important.

240


In a cellular setting, whenever a particular cell implements power adaptation, it changes its interference pattern on its neighbors. Thus, when every cell implements water-filling at the same time, the entire network effectively reaches a simultaneous water-filling solution, where the optimal power allocation in each cell is the water-filling solution against the combined noise and interference from all other cells. Such a simultaneous water-filling solution can typically be reached via an iterative water-filling algorithm in a system-level simulation where the water-filling operation is performed on a per-cell basis iteratively [7]. Mathematically, the most general condition for the convergence of such an iterative algorithm is not yet known, but iterative water-filling has been observed to converge in most practical situations.

9.3.2

Network utility maximization In a network with multiple users, the transmit power, bandwidth, and rate allocation problem becomes considerably more complicated, as the achievable rates of various users become interdependent. There are several consequences of such interdependency. First, the improvement in the rate of one user generally comes at the expense of other users in the network. For example, in a multicell OFDMA setup, to improve the rate of one user, one has to increase either its frequency allocation or its transmit power. The former comes at the expense of the bandwidth allocation for other users within the cell. The latter comes at the expense of more interference for users in adjacent cells. In both cases, there is a tradeoff between the rates of various users. The concept of rate region is often used to characterize such a physical-layer tradeoff among the rates of various users as a function of their power and bandwidth allocations. Further, in a realistic network with many users running different applications, the same rate improvement often brings a different amount of benefit to different users depending on the application layer characteristics. For example, a rate improvement could result in higher video quality for one user engaged in a video-on-demand service, or a faster file transfer by a different user. The network must decide which of the two alternatives is preferable. Such a choice depends not only on the nature of the application, but also on revenue considerations. Therefore, a tradeoff also exists in the application layer. Network utility maximization (NUM) is an optimization framework that captures both the physical-layer and the application-layer tradeoffs [8]. In this framework, each user has an associated utility, which is a function of its (windowed) ¯ i ). The utility is an increasing function and is average rate, denoted as Ui (R ¯ i for the assumed to be concave; it captures the desirability of having a rate R user i. The NUM problem is that of maximizing the sum of the utilities over all users in the network, subject to the achievability of these rates in the physical


241

layer, i.e., maximize

K

¯i ) Ui (R

i=1

subject to:

(R1 , R2 , · · · , RK ) ∈ R,

(9.5)

where the constraint is that each instantaneous rate-tuple must be inside R, the achievable rate region at each time instance, which is defined as the convex hull of the union of all achieveable rate-tuples. It is implicitly assumed in the above problem formulation that the utility functions for different users in the network are independent. This is a realistic assumption for the case where each user runs a separate application. In a specialized network, such a sensor network, where users collaborate in a specific task, it is conceivable that the utility of the network could depend jointly on all the ¯2 , . . . , R ¯ K ). A generalization of ¯1 , R rates, i.e., the objective is to maximize U (R NUM in this setting has been treated in [9].

9.3.3

Proportional fairness ¯i ) = A common choice of the utility function is the logarithm function, i.e., Ui (R ¯ log(Ri ). The choice of log-utility leads to a proportional fair rate allocation, which is described in detail below. The network’s objective is to maximize the sum utility of the average rates of different users in the network. The averaging is typically done in a windowed fashion, or more commonly, exponentially weighted as ¯ i + αRi , ¯ i = (1 − α)R R

(9.6)

where 0 < α < 1 is the forgetting factor. Assuming that αRi is small, the new contribution of the instantaneous rate Ri to the overall utility can be approximated as " ∂Ui "" ¯ ¯ (αRi ). (9.7) Ui (1 − α)Ri + αRi ≈ Ui (1 − α)Ri + ∂Ri "R i = R¯ i Under this approximation, the maximization of the sum utility, which is equivalent to the maximization of the incremental utility, becomes the maximization of the weighted sum rate, where the weights are determined by the derivative of the utility function evaluated at the present average rate. When the utility function is the logarithm function, the equivalent maximization problem reduces to maximize

K

wi Ri

i=1

subject to:

(R1 , R2 , · · · , RK ) ∈ R,

(9.8)

242


¯ i . This is a weighted rate sum maximization problem for the where wi = 1/R instantaneous rates with weights equal to the inverse of the average rates. As these weights fluctuate, and as the rate region R changes over time (due to, for example, user mobility and the fading characteristics of the underlying fading channel), the above optimization problem needs to be solved repeatedly. The proportional fair rate allocation was originally devised in the context of user scheduling [10]. The above discussion shows that it is also applicable to the power allocation problem. The use of proportional fairness utility is not the only way to reduce the network utility maximization to a weighted rate maximization problem. Alternatively, one may consider a system in which each user has an associated input queue, and where weights of the weighted rate sum maximization problem are determined as a function of the input queue length of each respective user [11, 12]. The important point is that in either approach, the application layer demand for rates (expressed in either the utility function or the queue length) is decoupled from the physical layer provision of rates. In both cases, the physical-layer problem is reduced to a weighted rate sum maximization problem.

9.3.4

Rate region maximization The reduction of the network utility maximization problem to a weighted rate sum maximization problem is a crucial step in the development of resource allocation algorithms for OFDMA networks. In an OFDMA network, the rate of each link is the sum of bit rates across the frequency tones. The reduction of the maximization of a nonlinear utility function of link rates to a weighted rate sum maximization essentially linearizes the objective function and decouples the objective function on a per-tone basis, which simplifies the problem significantly. The rate region maximization problem also often has constraints that couple across the frequency tones. For example, each user may have a power constraint across the frequency. In addition, there is typically the constraint that no two users should occupy the same frequency tone within each cell. To solve the rate region maximization problem efficiently, it is important to decouple these constraints across the frequency tones as well. A key technique for achieving decoupling is to utilize the Lagrangian duality theory in optimization. For example, consider the case where N

|hii (n)|2 Pi (n) log 1 + Ri = Γ( j = i |hj i (n)|2 Pj (n) + σ 2 (n)) n =1

(9.9)

subject to a power constraint N n =1

Pi (n) ≤ Pi,total ,

(9.10)


243

where Pi (n) denotes the transmit power of user i in tone n, and hij (n) is the complex channel gain from the transmitter of user i to the receiver of the user j. The weighted rate sum maximization problem subject to the power constraint can be solved by dualizing with respect to the power constraint. This results in a dual function g(λi ) defined as N 4 g(λi ) = max wi Ri − λi . (9.11) Pi (n) − Pi,total P i (n )

n =1

The point is that when the objective function is a weighted rate sum and the constraint is linearized via the use of Lagrangian dual variable λi , the above optimization problem reduces to N per-tone problems: 4 |hii (n)|2 Pi (n) − λi Pi (n) . (9.12) max wi log 1 + Γ( j = i |hj i (n)|2 Pj (n) + σ 2 (n)) P i (n ) Just as in single-user water-filling, where the solution to a convex optimization problem reduces to solving the problem for each λ, then finding the optimal λ, similar algorithms based on λ search can be applied here. The reduction to an N per-tone optimization problem ensures that the computational complexity for each step of this optimization problem with fixed λi is linear in the number of tones. The theoretical justification for the above duality approach is convexity. For convex optimization problems where the feasible set has a nonempty interior (which is almost always true in engineering applications), the maximum value of the original objective is equal to the minimum of the dual optimization problem min g(λi ).

λ i ≥0

(9.13)

The optimum λi can be found using search methods such as the ellipsoid method (which is a generalization of bisection search to higher dimensions) or the subgradient method (see, for example, [13]). An interesting fact is that this duality technique remains applicable even when the functional form of the rate expression is nonconvex as is the case in (9.9), as long as the OFDM system has a large number of dimensions in the frequency domain, which allows an effective convexification of the achievable rate region as a function of the power allocation. More rigorously, under general conditions, the duality gap between the original optimization problem and its dual goes to zero as the number of OFDM tones goes to infinity [13, 14]. This fact allows the duality technique to be used in a wide variety of applications. To summarize, under the NUM framework, the network optimization problem for an OFDMA network under per-user power constraints reduces to a per-tone weighted sum rate maximization problem with a linear power penalty term. The weights in weighted rate sum maximization are determined by the utility function. The power penalty weighting can be found using a generalization of bisection.

244


Figure 9.3. A multicell network in which the base stations cooperate in user scheduling and power allocation across the frequency spectrum.

The rest of this chapter is devoted to two examples of cooperative OFDMA networks where the adaptive scheduling, and power, frequency, and rate allocation problem can be solved efficiently using this methodology.

9.4

Network with base station cooperation

9.4.1

Problem formulation Consider an OFDMA-based cellular network as shown in Figure 9.3 in which the base stations cooperate in setting their downlink transmit power, and the mobiles likewise jointly set their uplink transmit power in order to avoid excessive interference between the neighboring cells. The optimal design of this multicell cooperative network becomes that of designing a joint scheduling and power allocation scheme that decides in each frequency tone:

r Which user should be served in each cell? r What are the appropriate uplink and downlink transmit power levels? Scheduling can be thought of either as the optimal partitioning of the frequency among the users within each cell, or as the optimal assignment of users in each time slot for each frequency tone. Scheduling and power allocation need to be considered jointly in order to reach an optimal solution for the entire network. Assuming a proportional fairness objective function, the network optimization problem for the downlink is a weighted rate sum maximization problem max

K L l=1 k =1

wD ,lk RD ,lk ,

(9.14)

9.4 Network with base station cooperation

245

where RD ,lk is the instantaneous downlink rate of the kth user in the lth cell in a network consisting of L cells with K users per cell. The weights wD ,lk = ¯ D ,lk are the proportional fairness variables determined by the exponentially 1/R weighted average rates. Let k = fD (l, n) be the downlink scheduling function, which assigns a user k to the nth frequency tone in the lth base station. The downlink rate expression RD ,lk is then PDn ,l |hnllk |2 , (9.15) log 1 + RD ,lk = Γ(σ 2 + j = l PDn ,j |hnjlk |2 ) n ∈Dl k

where the summation is over frequency tones assigned to the kth user in the lth cell, i.e., Dlk = {n|k = fD (l, n)}. Here, hnjlk is the channel transfer function from the jth base station to the kth user in the lth cell and in the nth tone, and PDn ,l is the downlink power allocation for the lth base station in the nth tone. The optimization is over PDn ,l . The weighted rate maximization problem is to be solved under the per-base-station power constraint for the downlink N

Pl (n) ≤ Pl,total

(9.16)

n =1

as well as possibly peak power constraints: m ax 0 ≤ PDn ,l ≤ SD .

(9.17)

In addition, there is the OFDMA constraint that no two users should occupy the same frequency tone within each cell. Finally, note that a similar optimization problem with corresponding rate and power expressions can be written for the uplink. The joint scheduling and power allocation problem formulated above has been studied in several works [15–17], in which key ideas such as iterative optimization of scheduling and power allocation and numerical methods for power adaptation have been proposed. The following section outlines the approach based on these works and provides a performance projection for networks with base station power cooperation.

9.4.2

Joint scheduling and power allocation The dual decomposition technique outlined in the previous section can be used to tackle the joint scheduling and power allocation problem above. The key fact is that after dualizing with respect to the total power constraint, the optimization problem decouples on a tone-by-tone basis: PDn ,l |hnllk |2 − λD ,l PDn ,l , wD ,lk log 1 + maximize Γ(σ 2 + j = l PDn ,j |hnjlk |2 ) l

subject to:

m ax 0 ≤ PDn ,l ≤ SD

∀l,

(9.18)

246


where the optimization is over both the power variables PDn ,l as well as the scheduling function k = fD (l, n) across the L base stations for a fixed tone n. The duality theory for OFDMA networks states that if the above per-tone optimization problem can be solved exactly for each set of fixed λD ,l s, an ellipsoid or subgradient search over λD ,l in an outer loop can be carried out to find the optimal λD ,l , which then leads to the global optimum of the overall network optimization problem. The optimization problem (9.18) is a mixed integer programming problem with nonconvex objective function. Finding the global optimum for such an optimization problem is known to be a difficult task. However, many approximation algorithms that can reach at least a local optimum exist. Although strictly speaking, the duality theory for OFDMA networks requires the global optimum solution of the per-tone optimization problem, the local optimum solution already works quite well in practice. The rest of this section focuses on solving (9.18) using local optimum approaches. Observe first that for the downlink, the scheduling step and the power allocation step can be carried out separately. This is because the scheduling choice at one base station does not affect the amount of intercell interference at the neighboring cells. The intercell interference is a function of the power allocation only. Thus, an iterative algorithm can be devised so that one can find the best schedule for a fixed power allocation, then find the best power allocation for the fixed schedule [15]. The iteration always increases the objective function monotonically, so it is guaranteed to converge to at least a local optimum of the joint scheduling and power allocation problem. For the downlink, because the intercell interference is independent of the scheduling decisions at each cell, finding the best schedule for a fixed power allocation is a per-cell optimization problem. In other words, each base station only needs to find the user in each tone that maximizes the weighted rate. This amounts to a simple search among the K users in each cell. For a fixed user schedule, the optimal power allocation problem becomes that of solving (9.18) for the set of scheduled users in each tone. This is a nonconvex problem with potentially multiple local optima. The first-order condition for this optimization problem can be found by taking the derivative of the objective function and setting it to be zero:

PDn ,l |hnllk |2

wD ,lk |hnllk |2 = tnD ,j l + λD ,l , n n 2 2 + Γ(σ + j = l PD ,j |hj lk | )

(9.19)

j = l

where k = fD (l, n) for l = 1, . . . , L,

tnD ,j l

Γ|hnlj k |2 = wD ,j k n PD ,j |hnjj k |2

(SINRnD ,j )2 1 + SINRnD ,j

,

(9.20)


247

Figure 9.4. Water-filling where the water-filling level is modified by the tnD ,j l pricing terms. and SINRnD ,j =

PDn ,j |hnjj k |2 Γ(σ 2 + i = j PDn ,i |hnij k |2 )

(9.21)

with k = fD (j, n). The first-order condition gives a water-filling like condition if the terms tnD ,j l are considered to be fixed. In this case, (9.19) suggests that the following power allocation is a local optimum of the per-tone optimization problem: 6S Dm a x 5 2 n n 2 + P |h | ) Γ(σ w D ,j j lk D ,lk j = l PDn ,l = − , (9.22) n |hnllk |2 j = l tD ,j l + λD ,l 0

where k = fD (l, n). Note that this is similar to the single-user water-filling power allocation (9.4), except that the power is allocated with respect to the combined noise and interference, and that the water-filling level λD ,l is modified by the additional tnD ,j l terms. This process is called modified water-filling [18] and is illustrated in Figure 9.4. The tnD ,j l term can be interpreted as a summary of the effect of allocating additional power at the lth base station on the downlink rate at the neighboring jth cell. A larger value of tnD ,j l signals a larger interference effect from the lth cell to the jth cell. The multiuser water-filling condition in (9.22) implies that when interference is present, the water-filling level needs to be modified. The water-filling level should decrease if the effect of interference is strong, which suggests that the power allocation should be reduced. Note that the water-filling level is also affected by the proportional fairness weights wD ,lk . A larger weight suggests a higher water-filling level. The terms tnD ,j l also have a pricing interpretation [19–22], which comes from the fact that tnD ,j l is the derivative of the jth base station’s data rate with respect to the lth base station’s power, weighted by the proportional fairness variable.

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A higher value of tnD ,j l suggests that the lth base station must pay a higher price for allocating its power in tone n, which is reflected in the modification of the water-filling level. The water-filling condition (9.22) suggests that one way to coordinate multiple base stations in a cooperative cellular network is to allow base stations to exchange values of tnD ,j l with their neighbors. Note that the value of tnD ,j l depends on the ratio of the direct and the interfering channel gains, which can be easily estimated using pilot signals. Knowing tnD ,j l , each base station may use (9.22) to update its power allocation. This results in an iterative process. When it converges, it reaches a local optimum of the weighted rate sum maximization problem (9.18). This procedure is known as the modified iterative water-filling algorithm [18]. In practice, it may be necessary to damp the iteration to ensure convergence [17]. Alternatively, one may resort to a direct numerical optimization of (9.18) [16, 17]. Starting from an initial power allocation, one may compute a gradient or Newton’s increment direction for the optimization objective, then successively improve the objective function until a local optimum is reached. The gradient can be computed locally at each base station based on the pricing terms tnD ,j l . To summarize, the coordination of base stations for the downlink can be efficiently implemented using an approach that iterates between coordinated scheduling and coordinated power allocation. The scheduling step for the downlink can be efficiently implemented on a per-cell basis; the power allocation step can be implemented if certain exchange of pricing information is allowed among the base stations. This iterative process, together with an outer loop that finds the optimal power prices λD ,l , reaches a local optimum of the weighted rate sum maximization problem. Much of the discussion in this section is also applicable to the uplink, except that optimal scheduling is no longer a per-cell problem. In the uplink, the assignment of users in each cell directly affects the interference in neighboring cells, so an optimal uplink scheduler needs to consider the effect of the interference as well. However, there is evidence suggesting that if one uses identical scheduling for both the uplink and the downlink, the network often already performs very well [17]. This can be justified in part by the fact that there is a duality between uplink and downlink channels. The capacity regions of the uplink and downlink channels are identical under the same power constraint.

9.4.3

Performance evaluation To illustrate the performance of the proportionally fair joint scheduling and power allocation method described in Section 9.4.2, we present simulation results for a multicell network with base station cooperation. The simulated network consists of 19 cells hexagonally tiled with 40 users per cell, occupying a total bandwidth of 10 MHz partitioned into 256 subchannels using OFDMA. For

249


Table 9.1. Uplink (UL) and downlink (DL) sum rates over 19 cells with 40 celledge users per cell with proportional fairness joint scheduling and cooperative power allocation among the base stations [17] 2.8 km

1.4 km

Base to base distance

UL

DL

UL

DL

Fixed power spectrum Adaptive power spectrum Improvement

125 Mbps 185 Mbps 48%

129 Mbps 181 Mbps 40%

137 Mbps 228 Mbps 66%

142 Mbps 227 Mbps 60%

simplicity, a maximum transmit PSD of −27 dBm/Hz is imposed at both the base stations and the remote users, but no total power constraint is imposed. A multipath fading channel model is used with 8 dB of log-normal shadowing. The channel path-loss is modeled as a function of distance d as 128.1 + 37.6 log10 (d) (in decibels). The background noise level is assumed to be −169 dBm/Hz. The joint proportionally fair scheduling and adaptive power allocation is expected to provide the largest improvement in performance for users at the cell edge where intercell interference is dominant. To illustrate the performance gain for cell-edge users, in the simulation users are placed at the cell edge on purpose. Table 9.1 illustrates a comparison of the achievable sum rates over all users in 19 cells for the adaptive power allocation algorithm vs. the constant transmit PSD scheme with proportionally fair scheduling. These results were originally reported in [17] and are consistent with other studies in this area [16]. It can be seen that depending on the base station to base station distance, a sum rate improvement of 40–60% is possible. The improvement is larger when the base stations are closer, because in this case the intercell interference is also larger. It is worth emphasizing that the sum rate improvement reported in Table 9.1 is for cell-edge users. If averaged over all users uniformly placed over the cell, the sum rate improvement would have been about 15–20%. Figure 9.5 illustrates the convergence behavior of the joint proportional fair scheduling and power allocation algorithm. Each iteration here consists of either an adaptive power allocation step or a scheduling step. Up to ten subiterations are performed within each power allocation step. The sum rates of each of the 19 cells are plotted. Note that the proportional fairness weights are also updated in each iteration. These weights ensure that the rates are allocated to all users with fairness. The simulation results clearly illustrate the value of coordinating base station PSDs in an interference-limited multicell environment. The projected performance improvement is obtained by allowing base stations to exchange pricing information with each other, and by iteratively converging to a joint networkwide optimum.

250


45

Downlink sum rate per cell (Mbps)

40 35 30 25 20 15 10 5 0

0

20

40

60

80 Iterations

100

120

140

160

Figure 9.5. Convergence of downlink sum rates in each of the 19 cells using modified iterative water-filling with proportional fairness joint scheduling and power allocation.

9.5

Cooperative relay network Base station cooperation addresses the intercell interference problem for cell-edge users in a cellular network, but the cell-edge users’ performances are also fundamentally affected by path-loss, which is distance-dependent, and shadowing. A viable approach for dealing with path-loss is to deploy relay stations throughout the cell, so that a mobile user may connect to the base station via a relay, thereby reducing the effective path distance. This section addresses the network optimization problem for the cooperative relay network. The resource allocation problem for the cooperative relay network has attracted much attention in the wireless cellular communication literature (e.g., [23–26]). There are many different ways in which a relay may help the communication between a transmitter and receiver pair (also known as the source and the destination in the relay literature). In a decode-and-forward protocol, the relay decodes the message from the source then reencodes and transmits to the destination. Alternatively, a relay may amplify and forward, or quantize its observation and forward it to the destination. In general, decode-and-forward is a sensible strategy when the relay is located closer to the source than to the destination, while amplify-and-forward and quantize-and-forward are more suitable when the relay is closer to the destination. However, the question of which strategy is the most suitable is a complicated one, as it also depends on the power allocation at the source and at the relay, as well as the end-user’s rate requirement or utility function. An

9.5 Cooperative relay network

251

optimization framework for choosing the best cooperation strategy has been dealt with for a single-relay link in [27], but the general optimization of relay strategies for a cellular network is likely to be quite hard. In the chapter we focus instead on a simplified model where only the decodeand-forward protocol is used. This is done for the following reasons. First, the primary focus of this chapter is the use of relay for enhancing cellular coverage at the cell edge, in which case a sensible relay location within the cell is somewhere close to the half-way point between the base station and the cell edge. In this case, for both uplink and downlink transmissions, the lengths of both the source–relay and the relay–destination paths are about the same, making decode-and-forward a suitable strategy. Second, decode-and-forward offers a digital approach to relaying. It eliminates the noise enhancement problem inherent in amplifying, or quantizing the relay observation. Third, in this chapter we consider the deployment of fixed infrastructure-based relay stations. These relay stations typically have the computational resources to perform decoding and reencoding. Further, as the primary focus here is the use of relays to combat distancedependent path-loss, in this chapter attention is restricted to a two-hop relay strategy, where the direct path from the source to the destination is ignored (as it is typically very weak). In the first hop, the source transmits information to the relay. In the second hop, the relay decodes and retransmits the same information to the destination. Under these assumptions, the capacity of a single source–relay–destination link is simply the minimum of the source–relay and the relay–destination link capacities. The characterization of capacity becomes more involved if one considers the possibility that a single relay deployed in a cellular network may help multiple mobiles at the same time. Further, each mobile has a choice of either connecting to the base station directly, or through relays. The mobile may even choose to use different relays for different frequency tones. These possibilities are coupled with the allocation of power across the frequency tones. In the rest of this section we use the network optimization framework introduced earlier and provide a solution based on the duality theory to solve the bandwidth, rate, and power allocation problem for OFDMA relay networks. The methodology used here is the one proposed in [23] and [26].

9.5.1

Problem formulation Consider a wireless cellular network in which each cell is equipped with M relay stations located somewhere between the base station and the cell edge and at angles 360/M degrees apart from each other. There are K mobiles in each cell. Each mobile may connect either directly to the base station or through one of the relays in each frequency tone, (but the mobile may possibly use different relays in different tones.) There are a total of M + 1 links emanating from each mobile. These mobile-originated links, plus the M links connecting the relays

252


h(1,1) h(2,0) h(0,1) h h(3,2) (0,2)

h(0,3) h(5,0)

h(4,2)

h(5,2)

Figure 9.6. A cooperative relay network in which the mobiles may connect directly to the base station or through the relays. to the base station, give a total of K(M + 1) + M links in the entire cellular network. Label the base station as node 0, and the mobiles as nodes k = 1, . . . , K. Label each link by a pair of indices as follows: the base-station–relay links are labeled (0, m), with m = 1, . . . , M ; the mobile–base-station links are labeled (k, 0) and the mobile–relay links are labelled (k, m) with k = 1, . . . , K and m = 1, . . . , M . This labeling convention is illustrated in Figure 9.6. We consider a setup in which each cell employs an OFDMA scheme. Further, it is assumed that in each frequency tone, at most one link may be active at any given time. This assumption allows the intracell interference to be avoided completely, and simplifies the numerical solution considerably. For simplicity, we also assume that scheduling and power allocation are done on a per-cell basis (i.e., without base station cooperation). The problem formulation presented here can be extended to a more general setting where spatial reuse is enabled within each cell, or where intercell cooperation is enabled across the cells, but the resulting optimization problem would become considerably more complex. Consider now the uplink scenario. Define the scheduling function as a mapping from the frequency tone to the link index, i.e., fU (n) = (i, j). With the assumptions stated above, the achievable rate for each link (i, j), denoted rU,(i,j ) , can be expressed as n n 2 PU,(i,j ) |h(i,j ) | , (9.23) log 1 + rU,(i,j ) = Γσn2 n ∈U( i , j )

where the summation is over all frequency tones assigned to that link, i.e., n n 2 U(i,j ) = {n|(i, j) = fU (n)}, P(i,j ) denotes the transmit power, |h(i,j ) | denotes


253

the channel gain for the link (i, j) at tone n, and σn2 denotes the combined intercell interference and noise. The achievable rate for each user, denoted Rk , is the sum of achievable rates of all links emanating from the mobile, i.e., RU,k =

M

rU,(k ,j ) .

(9.24)

j =0

At each relay, a flow conservation constraint must be satisfied so that all the incoming traffic can be forwarded to the base station. This results in M constraints as follows: K

rU,(k ,m ) ≤ rU,(0,m ) .

(9.25)

k =1

The above equation is an example of the general flow conservation formulation [23, 26]. It is now straightforward to write down the uplink per-cell optimization problem for the cooperative relay network, which consists of both the allocation of power and bandwidth for each link, and the routing of the information within each cell. Under the network utility maximization framework, the optimization problem can be reduced to a weighted rate sum maximization problem across ¯ U,k : the K users with weights wU,k = 1/R maximize

K

wU,k

subject to :

rU,(k ,m )

,

m =0

k =1 K

M

rU,(k ,m ) ≤ rU,(0,m )

∀m = 1, · · · , M,

max pnU,(0,m ) ≤ PU,R ,m

∀m,

k =1 N n =1 N M

max pnU,(k ,m ) ≤ PU,M ,k

m =0 n =1 max 0 ≤ pnU,(k ,m ) ≤ SU,(k ,m ) pnU,(k ,m ) pnU,(k ,m ) = 0,

∀k, ∀k, m,

∀n,

∀(k, m) = (k , m )

∀n, (9.26)

where rU,(k ,m ) is as expressed in (9.23), and the optimization is over power max allocations pnU,(k ,m ) , subject to the per-mobile total power constraint PU,M ,k , max the per-relay total power constraint PU,R ,m , as well as the peak PSD constraints max at both the mobiles and the relays SU,(k ,m ) . The last constraint ensures that no two links share the same frequency tone within each cell. Note that the downlink problem can be formulated in a similar fashion.

254


9.5.2

Joint routing and power allocation The network utility maximization problem for the cooperative relay network is essentially a joint routing and power allocation problem, as each mobile has the option of either transmitting information bits directly to the base station or routing through one or more of the relays. One way to solve this problem is to dualize with respect to the flow conservation constraint (9.25) using dual variables µm , so that the objective function becomes a new weighted rate sum maximization problem over all link rates (rather than the end-user rates in (9.26)). The new objective function is K k =1

wU,k

M

rU,(k ,m )

M

−

m =0

m =1

=

M m =1

µm

K

rU,(k ,m ) − rU,(0,m )

k =1

µm rU,(0,m ) +

M K

(wU,k − µm )rU,(k ,m ) , (9.27)

k =1 m =0

subject to the peak and total power constraints in (9.26). Let g(µ1 , · · · , µM ) denote the maximum value of (9.27) subject to the power constraints for any fixed set of µm . Because of the zero-duality-gap property of the OFDMA system, the solution of the original problem then reduces to the maximization of g(µ1 , · · · , µM ) over all µm . The dual variables, µm , enter the new objective function as weights to the weighted rate sum maximization problem over the link rates. Roughly speaking, a higher value for µm indicates congestion in the link between the base station and the mth relay and that more rate should be allocated to that link to release congestion. A lower value of µm indicates the opposite. The weighted link rate sum maximization problem subject to the power constraints can itself be solved by yet another dual decomposition step with respect to the total power constraints, as treated earlier in this chapter. In this case, the optimization problem is again decoupled on a tone-by-tone basis. Because of the assumption that only one link may be active in any given time slot and frequency tone, the weighted rate sum maximization then reduces to the selection of the best link for each frequency tone, which involves a simple search. Finally, the optimization of g(µ1 , · · · , µM ) over all µm can be handled by either an outer loop using the ellipsoid or the subgradient method. The search over the optimal set of µm balances the incoming and outgoing flows at each relay.

9.5.3

Performance evaluation The optimization framework described above can be used to evaluate the effectiveness of deploying relay stations in a cellular network. To take into account the cost of relay deployment, the performance of a baseline system with a cell diameter of 1.4 km is compared with a relay network in which the cell area is doubled

255


Table 9.2. The achievable minimum and sum rates for a seven-cell network: the baseline vs. relay scenarios (RS) with a varying number of relays per cell and relay locations [26] Scenario Relays per cell Relay distance Mobiles per cell Cell diameter (km) Cell area (km2 ) Mininum rate (Mbps) Sum rate (Mpbs)

Baseline

RS 1

RS 2

RS 3

RS 4

0 n/a 9 1.4 1.54 0.193 96.4

3 r 18 1.98 3.08 0.583 75.4

4 r 20 1.98 3.08 0.972 80.2

5 r 20 1.98 3.08 0.705 72.7

3 r 18 1.98 3.08 0.578 87.2

2 3

2 3

2 3

1 3

(with diameter 1.98 km), but with three, four or five relays deployed within each cell. The rationale is that if a relay station costs roughly 13 – 15 of a base station, then the deployment cost of both systems would be approximately the same. In both cases, the achievable uplink transmission throughput is computed for a seven-cell system with users uniformly placed within the area. The user densities in both cases are the same. When the relays are deployed, they are located between 13 r and 23 r from the base station, symmetrically in the angular direction. Again, standard cellular channel models are used with both distance-dependent path-loss and log-normal shadowing components. The simulation setting is as presented in [26]. The simulation methodology presented in the previous section is for a weighted rate–sum maximization problem formulation. However, instead of maximizing a proportionally fair utility function, the numerical results in this section pertain to a maximization of the minimum rate over all users in the system (similar to [23]), which requires a slight modification of the optimization problem (9.26). First, the additional constraint that each user must have a rate larger than some minimal rate Rmin , where Rmin is a constant added. Then, the resulting optimization problem is solved with successively larger Rmin until the problem becomes infeasible. The largest such Rmin is the maximum minimal rate. In practice, the maximum Rmin can be found efficiently using a bisection. For simplicity, the adaptive scheduling and power and rate allocation here are implemented on a per-cell basis. For simulation purposes, the network throughput is computed using an iterative approach, in which the intercell interference is updated in each iteration, and the cellular network eventually reaches an equilibrium. Table 9.2 shows the maximum minimal rates for the baseline network without relays and for a number of relay scenarios. These results were first presented in [26]. The most interesting feature here is that the addition of relays to the infrastructure improves the minimal rate dramatically; however, it does not make

256


much difference at all in the sum rate. This illustrates that the benefit of relays is concentrated on users at the cell-edge. As far as the sum rate is concerned, when the users are uniformly distributed throughout the cell, the sum rate is dominated by the rates of those users closest to the base station, which are not helped by the relays.

9.6

Conclusion In this chapter we have presented a network utility maximization framework for cooperative networks employing OFDMA. It has been shown that the objective of maximizing the sum of utilities of multiple users in a multicell network can be efficiently carried out using a number of techniques, including proportional fairness scheduling, dual optimization, the descent method for local optimization, and the network flow conservation principle. A central observation here is that because the OFDM scheme partitions the frequency domain into many parallel subchannels, the NUM problem often decomposes into a tone-by-tone optimization problem, which is considerably easier to solve. In this chapter we have focused on two types of cooperative networks and formulated the corresponding joint scheduling, power adaptive and rate allocation problem in each case. For networks with base station cooperation, it has been shown that adaptively adjusting power allocation across the base stations has the effect of reducing intercell interference, hence improving the throughput of the cell-edge users in the network. The cell-edge performance can also be reduced by deploying relays throughout the cells. The relays have the effect of enhancing the coverage at the cell edge, which improves the minimal service rate within each cell. Base station cooperation and relay deployment are technologies with the potential to significantly enhance the performance of the traditional wireless cellular network structure, especially at the cell edge. The benefits brought by these cooperative techniques are particularly valuable to network service providers, because cell-edge users are the bottleneck in the current generation of wireless networks.

References [1] I. C. Wong and B. L. Evans, “Optimal resource allocation in the OFDMA downlink with imperfect channel knowledge,” IEEE Trans. Commun., vol. 57, no. 1, pp. 232–241, Jan. 2009. [2] Y. Cui, V. K. N. Lau, and R. Wang, “Distributive subband allocation, power and rate control for relay-assisted OFDMA cellular system with imperfect system state knowledge,” IEEE Trans. Wireless Commun., vol. 8, no. 10, pp. 5096–5102, Oct. 2009.

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10 Cross-layer scheduling design for cooperative wireless two-way relay networks Derrick Wing Kwan Ng and Robert Schober 10.1

Introduction Background. The degrees of freedom introduced by multiple antennas at the transmitters and receivers of wireless communication systems facilitate multiplexing gains and diversity gains [1, 2]. A wireless point-to-point link with M transmit and N receive antennas constitutes an M -by-N multiple-input multipleoutput (MIMO) communication system. The ergodic capacity of an M -by-N MIMO fading channel increases almost linearly with min{M, N } provided that the fading meets certain mild conditions [2, 3]. Hence, it is not surprising that MIMO has attracted a lot of research interest since it enables significant performance and throughput gains without requiring extra transmit power and bandwidth. However, limitations on the number of antennas that a wireless device is able to support as well as the significant signal processing power and complexity required in MIMO tranceivers limit the gains that can be achieved in practice. To overcome the limitations of traditional MIMO, the concept of cooperative communication has been proposed for wireless networks such as fixed infrastructure cellular networks and wireless ad-hoc networks [4, 5]. The basic idea of cooperative communication is that the single-antenna terminals of a multiuser system can share their antennas and create a virtual MIMO communication system. Thereby, three different types of cooperation may be distinguished, namely, user cooperation, base station (BS) cooperation, and relaying. Theoretically, user cooperation and BS cooperation are able to provide huge performance gains, when compared with noncooperative networks. However, the required information exchange between users and BSs may make these options less attractive in practice. In contrast, cooperative relaying with dedicated relays requires significantly less signaling overhead and allows for low-cost implementations while achieving significant coverage extensions, diversity gains, and throughput gains compared with noncooperative transmission. Therefore, cooperative relaying has attracted significant interest from both academia and industry. In theory, relays can transmit and receive signals at the same time and over the same frequencies; this is known as full-duplex relaying. However, building such relays requires Cooperative Cellular Wireless Networks, eds. Ekram Hossain, Dong In Kim, and Vijay K. Bhargava. Published by Cambridge University Press. C Cambridge University Press, 2011.

260

Cross-layer scheduling design for cooperative wireless relay networks

Figure 10.1. One-way half-duplex relaying system.

Figure 10.2. Two-way half-duplex relaying system.

precise and expensive components which is undesirable in practice. Alternatively, relays may operate in a one-way half-duplex mode as shown in Figure 10.1, i.e., relays do not receive and transmit simultaneously at the same time and frequency. These relays are also referred to as cheap relays in the literature [6]. The main disadvantage of one-way half-duplex relaying is a loss in throughput compared with full-duplex relaying. Fortunately, this throughput loss can be recovered by two-way half-duplex relaying [12–15]. Compared with traditional one-way half-duplex relaying [16–18], two-way half-duplex relaying achieves higher power and spectral efficiencies, by allowing simultaneous message exchanges between a BS and the users, see Figure 10.2. Both amplify-and-forward (AF) and decodeand-forward (DF) protocols can be used for two-way half-duplex relaying. The AF protocol may be more appealing in practice because of its simple transceiver design. Cross-layer design. Combining cross-layer design with cooperative relaying has become an active research area [7–11]. Orthogonal frequency division multiple access (OFDMA) is a particularly attractive multiple access technique because of

10.1 Introduction

261

its flexibility in resource allocation and its robustness against multipath fading. Cross-layer design can lead to significant improvements in the overall system performance by facilitating the exchange of useful information between different layers of the protocol stack. The effect of cross-layer design on quality of service (QoS) provisioning in multiuser systems is an interesting, yet challenging, topic. Intuitively, by allocating resources to users with better channel qualities, the scheduler can maximize the overall system throughput and exploit the so-called multiuser diversity (MUD) gain. However, it may degrade other QoS metrics such as delay and fairness, since users are suspended from transmission when their channels are poor. Next generation wireless communications systems are expected to provide resource-hungry services such as video streaming and real-time video conferencing with certain QoS requirements. The combination of OFDMA/OFDM with two-way half-duplex relaying may be instrumental in meeting these requirements, particularly for users at the cell edge. In [32, 33], best-effort resource allocation for two-way half-duplex relay-assisted OFDMA and OFDM systems for homogeneous users is studied. In these works, perfect global channel state information (CSI) of each link is assumed to be available at the BS such that optimal resource allocation can be performed. However, in practice, users are heterogeneous with different QoS requirements, such as the maximum tolerable outage probability and minimum required data rate, which best-effort resource allocation cannot guarantee. Besides, perfect CSI at the transmitter (CSIT) cannot be achieved in practice for the relay-to-user links due to the mobility of the users. When the CSIT is imperfect, there is a finite probability that the scheduled data rate exceeds the instantaneous channel capacity despite the use of strong forward error correction (FEC) codes, causing the transmitted packet to be corrupted which is known as channel outage. The conventional performance measure, ergodic capacity, fails to account for the penalty of channel outage. Furthermore, the asymmetric nature of fading in the BS-to-relay and relay-touser links in relay networks has often been overlooked in the system modeling, e.g., [12–18, 32, 33]), which may lead to inaccurate results with regard to the performance gain achievable with relays in a practical system. In addition, though the multiuser diversity capacity gain has been known to scale with the number of users K in the order of O(log log K) [26, 34] in Rayleigh faded single-hop systems with perfect CSIT, it is not clear how the system performance scales with the number of users and relays in a two-way half-duplex relay-assisted OFDMA system with imperfect CSIT and asymmetric fading links. Furthermore, existing works such as [32–36] focus on centralized resource allocation at the BS. As the numbers of users, relays, and subcarriers in the system increase, the overhead in collecting CSI for scheduling becomes significant and the computational complexity increases exponentially at the BS which limits the scalability of the system in practice. Contributions. Motivated by the aforementioned prior works, we propose and analyze in this chapter a novel cross-layer scheduling design for two-way

262


half-duplex relay-assisted OFDMA systems. In particular, we focus on the following issues:

r We consider cross-layer scheduling for an AF two-way half-duplex relayassisted OFDMA system when both delay-sensitive users and non-delaysensitive users are coexisting in the system. The considered problem is formulated as a mixed integer and nonconvex optimization problem which takes into account imperfect CSIT and the heterogeneous data rate requirements of users. After a proper transformation of the original nonconvex problem into a convex one, dual decomposition is used to derive a novel distributed iterative resource allocation algorithm with closed-form solutions for the power, data rate, and subcarrier allocation. The proposed algorithm’s fast convergence and robustness to quantization effects in the information exchanged between the BS and the relays in each iteration make it attractive for implementation. r We investigate the asymptotic behavior of the system goodput of proportional fair (PF) schedulers in a two-way half-duplex relay system with respect to the numbers of non-delay-sensitive users and relays by using tools from extreme value theory. Closed-form asymptotic order growth expressions are derived which reveal that an extra gain from a large number of users and relays can be achieved only under certain conditions. These expressions also allow us to quantify the penalties on the system performance caused by imperfect CSIT and a line-of-sight (LoS) path. r We propose an efficient computational burden reduction scheme which is aimed at alleviating the computational load at each relay. The proposed scheme preserves the essential MUD gain for various scheduling policies, such as maximum system goodput scheduling and PF scheduling. On the other hand, the computational load can be explicitly controlled by adjusting a corresponding threshold. Simulation results demonstrate significant computational savings at the cost of a small performance degradation. Organization. The rest of the chapter is organized as follows. In Section 10.2, we discuss some basic concepts in cross-layer scheduler design. In Section 10.3, we outline the model for the considered two-way half-duplex relay-assisted OFDMA system, and in Section 10.4, we formulate the cross-layer design for this system as an optimization problem. In Section 10.5, the problem considered is solved by dual decomposition, and in Section 10.6, we analyze the asymptotic order growth of the system goodput for large numbers of users and relays and introduce a computational burden reduction scheme. Simulation results for the distributed algorithm are provided in Section 10.7 and some conclusions are drawn in Section 10.8. Notation. E[·] and (·)∗ denote statistical expectation and complex conjugation, respectively. A complex Gaussian random variable with mean µ and variance σ 2 is denoted by CN (µ, σ 2 ), and ∼ means “distributed as”. 1(·) denotes an indicator function which is 1 when the event is true and 0 otherwise. O(g(x)) denotes an asymptotic upper bound. Specifically, f (x) = O(g(x)) if limx→∞ |f (x)/g(x)| ≤ W

10.2 Cross-layer scheduling design – some basic concepts

263

Figure 10.3. Traditional OSI reference model [19]. for W ∈ (0, ∞). Moreover, Q(c, d) is the first-order Marcum Q-function, I0 (·) is the zeroth order modified Bessel function of the first kind, J0 (·) is the zeroth order Bessel function of the first kind. u(·) is the unit step function and (x)+ = max{0, x}. Finally, all logarithms, unless further specified in the subscript, are assumed to have base e.

10.2

Cross-layer scheduling design – some basic concepts Traditional communication systems can be viewed as a hierarchy of layers, which is known as the open system interconnection (OSI) reference model (Figure 10.3). A layer is a collection of conceptually similar system functions which provide services to other layers. For example, the duty of the physical (PHY) layer is to transmit a bit stream over a given physical channel with a target bit error rate (BER), while the media access control (MAC) layer is charged with giving multiple users access to the channel and error checking. The layering concept emphasizes the isolation of the different layers which means that each layer is optimized individually without considering the requirements of other layers. In other words, a layer treats the other layers as black boxes when performing its own duty. This isolated approach provides a higher flexibility for the deployment of new protocols and simplifies debugging and standardization compared with a joint optimization of all layers. However, while the rigid separation of layers is well suited for time-invariant wire-line communication channels, it is not

264


Figure 10.4. Timing diagram for cross-layer scheduling.

compatible with the requirements of next generation wireless communications systems. Current and future wireless communication systems not only have to support concurrent transmission of real-time voice and video data, but also non-real-time services such as email and web surfing. In practice, these services require different levels and different types of QoS. For instance, real-time video conferencing is a delay-sensitive application but it is relatively robust with respect to decoding errors. On the other hand, email is a delay nonsensitive application but does not tolerate even a single bit error. Unfortunately, the PHY layer as it is defined in the OSI model does not guarantee any QoS since it does not receive any side information regarding QoS requirements from the upper layers. Therefore, cross-layer design/optimization is essential for a better utilization of the limited system resources, while guaranteeing the required QoS for each application at the same time. We would like to point out that it is a common misconception that cross-layer design is aimed at removing the concept of layering and performing an overall optimization of the communication system. Instead, the crux of cross-layer design is to enhance the system performance by allowing minimal information exchange between the layers.

10.2.1

Utility function-based cross-layer optimization In each scheduling slot, the scheduler selects the users for the next transmission frame and determines their power and rate allocation based on the information available at the scheduler such as the CSI of all users and the length of their queues (Figure 10.4). Ideally, a cross-layer scheduler should exploit both the


265

information from the PHY layer and that from the layers above the MAC layer in order to achieve the best possible performance. In the literature, utility-functionbased cross-layer optimization [20, 21] is one of the widely used methods for solving resource allocation problems. There are two main functionalities of the utility function U(·). First, it captures the essential scheduling criteria by using the available cross-layer information building a bridge between different layers. Second, it maps the users’ utilization of the system resources into a level of satisfaction providing a tangible performance metric. In the following, we briefly discuss two utility functions commonly used for cross-layer scheduling. Maximum throughput scheduler. In most wireless applications, the aggregate data rate of users is the most important figure of merit for evaluation of the system performance from the service provider’s point of view. Considering a system with K users, the corresponding utility function can be expressed as 6 5K K (10.1) Rk = E rk , UThp (R1 , . . . , RK ) = k =1

k =1

where Rk = E[rk ] is the average throughput of user k and rk is the instantaneous throughput of user k in each time slot. Schedulers designed to maximize the above utility function achieve the highest average system capacity and are referred to as maximum throughput schedulers. Proportional fair (PF) scheduler. Although the maximum throughput scheduler results in the optimal utilization of the system resources, it does not take into account fairness in the scheduling process. Users with poor channel conditions may suffer from starvation since they are rarely selected for transmission which is undesirable from the users’ point of view. Therefore, PF scheduling [1, 2] was proposed to resolve the fairness issue. PF schedulers are popular because they allow a balance to be struck between overall system capacity and fairness among users, and they have been implemented in third generation (3G) cellular systems for delay-tolerant applications. The corresponding utility functions are given by UPF,1 (R1 , . . . , RK )

K

˜k ) log2 (R

(10.2)

6 K rk . ≈E ˜k R k =1

(10.3)

≈

k =1

and

5

UPF,2 (R1 , . . . , RK )

˜k The utility functions in both (10.2) and (10.3) achieve proportional fairness. R is the approximation of Rk . In order to implement PF schedulers, the system has ˜ k . For the (n + 1)th scheduling slot, the average to keep track of the value of R

266


˜ k [n + 1] of user k can be updated as follows: data rate R ⎧ 1 ˜ 1 ⎪ ⎪ Rk [n] + rk [n] , k = k∗ , ⎨ 1− tc tc ˜ Rk [n + 1] = 1 ˜ ⎪ ⎪ 1− Rk [n] , k= k∗ , ⎩ tc

(10.4)

where tc is the time constant for the averaging window and k ∗ is the selected user at the (n + 1)th time slot.

10.2.2

Quality-of-service (QoS) measure The increasing demand for high-data-rate wireless service networks imposes great challenges on cross-layer optimization since operators are required to satisfy the diverse QoS requirements of heterogeneous user populations. Different QoS measures have to be incorporated in the cross-layer optimization in order to overcome these challenges. While many different QoS measures have been considered in the literature, we discuss here only the two most important ones. Minimum data rate requirement. In practical systems, users are usually heterogeneous with different minimum data rate requirements imposed by the maximum delay constraints for the respective applications they are running. One way to handle these requirements, is to incorporate data rate constraints in the formulation of the cross-layer optimization problem [22]. Intuitively, the scheduler will first try to serve the delay-sensitive users which have nonzero data rate constraints. Once these users are served, the remaining resources will be allocated to the non-delay-sensitive users. However, it is clear that this kind of resource allocation results in a degradation of the overall system performance since the scheduler loses degrees of freedom in the user selection. Frame error rate (FER). Although at the PHY layer the BER is usually considered as a performance measure, at the MAC layer the FER is more relevant. In general, the FER is hard to calculate analytically and typically results in complicated expressions which are not useful for cross-layer scheduling design. However, in slow fading channels, if channel capacity achieving codes are used for error protection (such as, e.g., turbo codes or low-density parity-check codes (LDPCs)), the outage probability is a good approximation for the FER [23, 24]. This connection between the outage probability and FER can be often exploited to arrive at a simple resource allocation algorithm.

10.2.3

Multiuser diversity gain In a multiuser wireless communication system, different users experience different fading conditions. When the number of users in the system is large, there is a high probability that at least one user has a very good channel at any time. This


267

effect is known as multiuser diversity [25]. It can be exploited by scheduling a user for transmission only when his/her channel is in a favorable condition. Therefore, the average system throughput increases with the number of users if only good users are selected for transmission in each scheduling slot. This performance gain plays an important role in the cross-layer scheduling design. In the following, we present a simple example to illustrate the concept of multiuser diversity in a system with scheduling and resource adaptation. Example 10.1 We consider a wireless system with five users having infinite backlog in their buffers as illustrated in Figure 10.5. We assume that only one user is scheduled in each scheduling slot and the channel state of each user is either good or bad with equal probability. If the channel states of the users are perfectly known at the transmitter and a capacity achieving code is applied for error protection, then 6 bps/Hz and 1 bps/Hz can be successfully delivered1 to scheduled users having good and bad channels, respectively. We consider first a simple round-robin (RR) scheduling2 scheme where users take turns to access the channel periodically regardless of their actual channel states. Since all users have the same channel access probability, the average system throughput of this scheduling scheme is 6 × 12 + 1 × 12 = 3.5 bps/Hz. On the other hand, by taking advantage of CSIT, the scheduler can select a user whose channel is in the good state (provided there is such a user) which results in maximum throughput scheduling. The average system throughput of the latter scheduling scheme is 215 × 1 + (1 − 215 ) × 6 = 5.84375 bps/Hz. Maximum throughput scheduling tries to operate the system at the peak transmission rate based on CSIT knowledge and the resulting performance gain is the multiuser diversity gain. In the following, we will quantify the multiuser diversity gain for maximum throughput scheduling for a large number of users based on extreme value theory. Asymptotic multiuser diversity gain. Extreme value theory is a branch of statistics which deals with the extreme value, such as the maximum or the minimum, of a set of random variables. It has been widely used for analyzing the asymptotic performance of maximum throughput scheduling [26, 27]. In the following, we introduce a fundamental theorem from extreme value theory. Theorem 10.1 (Generalized extreme value distribution [28]) Let x1 , x2 , . . . , xZ , be a sequence of Z independent and identically distributed (i.i.d.) random 1 2

Spectral efficiencies of 6 bps/Hz and 1 bps/Hz correspond to 64-ary quadrature amplitude modulation (64-QAM) and binary phase shift keying (BPSK), respectively. RR is the simplest scheduling technique for scheduling users and is widely used in TDMA systems such as GSM.

268


(6 bps/Hz) (1 bps/Hz)

feedback b

Figure 10.5. An example for cross-layer scheduling with two channel states.

variables and let xmax denote the maximum among the Z random variables, i.e., xmax = max(x1 , x2 , . . . , xZ ).

(10.5)

If there exist some constants aZ ∈ R, bZ > 0 and some nondegenerate distribution G(x) such that the distribution of aZ (xmax − bZ ) converges to G(x), then G(x) must be one of the following three standard extreme value distributions: Gumbel distribution, Fréchet distribution, and Weibull distribution. Next, in the following lemma, we introduce a sufficient condition on the distribution of xi such that the limiting maximum distribution is a Gumbel distribution with cumulative distribution function (CDF) G(x) = Pr{X ≤ x} = exp(− exp(−x)),

x ∈ R.

(10.6)

Lemma 10.1 (Sufficient conditions for converging to Gumbel distribution [28]) Let {x1 , x2 , . . . , xK } be a sequence of K positive i.i.d. random variables with probability density function (PDF) f (·) and twice differentiable CDF F (·). Let xmax = max{x1 , x2 , . . . , xK } denote the maximum among the K random variables. If the reciprocal hazard function g(x) satisfies lim g(x) = lim

x→∞

x→∞

1 − F (x) = c, f (x)

(10.7)

269


6

Average system throughput (bps/Hz)

5

4

3

2 Simulation at SNR = 10 dB Asymptotic trend at SNR = 10 dB Simulation at SNR = 5 dB Asymptotic trend at SNR = 5 dB Simulation at SNR = 0 dB Asymptotic trend at SNR = 0 dB

1

0

0

10

20

30

40

50 60 Number of users

70

80

90

100

Figure 10.6. Average system throughput vs. number of users for a Rayleigh fading channel and different received SNRs. where c is a constant, then xmax − lK converges to a Gumbel distribution where lK is given by F (lK ) = 1 − 1/K. This suggests that xmax grows like lK for K → ∞. Now, let us consider K Rayleigh distributed channel gain coefficients, {h1 , h2 , . . . , hK }, i.e., {|h1 |2 , |h2 |2 , . . . , |hK |2 } are exponentially distributed with unit mean. By evaluating the corresponding reciprocal hazard function, it can be shown that (1 − F (x))/f (x) = 1 and lK = log K. Therefore, by selecting the maximum channel gain among K users, the multiuser gain grows in the order of log K. Figure 10.6 depicts the system goodput as a function of the number of users K assuming that all users have i.i.d. Rayleigh fading channels. Both simulation results and analytical results obtained by exploiting the asymptotic growth of the maximum channel gain are shown. If the maximum throughput scheduler is used for scheduling, it can be observed from Figure 10.6 that the multiuser diversity provides a significant throughput gain as the number of users increases. However, as the number of users becomes large the growth rate of the multiuser diversity gain decreases since the average system throughput grows with the number of users in the order of log log(K). Now, that we have established the basic idea behind cross-layer scheduling, we will focus in the remainder of this chapter on a particular application, namely cross-layer scheduling for a two-way half-duplex AF relay-assisted OFDMA network.

270


1 2

Figure 10.7. Relay-assisted packet transmission system model with K = 9 users, A = 3 sectors, and M = 3 relays.

10.3

Network model for relay-assisted OFDMA system In this section, we first establish the adopted system and channel models, and subsequently discuss the CSI model assumed for cross-layer scheduling.

10.3.1

System model We consider a single-antenna two-way half-duplex relay OFDMA network which consists of one BS, M relays, and K mobile users which belong to one of two categories, namely, delay-sensitive users and non-delay-sensitive users. Without loss of generality, we assume that the first K1 users are delay-sensitive users belonging to set D = {1, 2, . . . , K1 } and the remaining K − K1 users are nondelay-sensitive users belonging to set N = {K1 + 1, K1 + 2, . . . , K}. A single cell with two ring-shaped boundary regions as shown in Figure 10.7 is studied. The cell coverage is divided into A equal size sectors and each user is assigned to a group of GRj > 0 relays such that M = A j =1 GRj . In this chapter, we focus on the cross-layer scheduling design for relay-assisted users and we assume that the resource allocation for non-relay-assisted users (e.g., users close to the BS) is done separately.3 In the model considered, there is no direct link between the BS and the users due to path-loss and heavy blockage. We adopt the frame structure 3

We note that a joint resource allocation for relay-assisted and non-relay-assisted users would entail a significantly higher computational complexity at the BS than separate resource allocations.

10.3 Network model for relay-assisted OFDMA system

271

Figure 10.8. Frame structure and CSI correlation model.

of IEEE 802.16m [30] where a superframe is divided into F frames (Figure 10.8). The channel is assumed to be slowly time varying over a superframe but to remain constant within a frame. In each scheduling slot, at the beginning of each superframe, scheduling and resource allocation are performed. In each frame, the information exchange between the BS and the users via the relays is accomplished in two phases. In the first phase, the BS and the users transmit their signals to the relay stations through a multiple access channel. Then, in the second phase, the relay stations amplify the previously received signals and forward them to the corresponding users.

10.3.2

Channel model We consider an OFDMA system with nF subcarriers. The channel impulse response is assumed to be time-invariant (slow fading) within a frame. In the first phase of frame t ∈ {1, . . . , F }, the received symbol in subcarrier i ∈ {1, . . . , nF } at relay m ∈ {1, . . . , M } for user k ∈ {1, . . . , K} is given by @ @ (t,k ) (t,k ) (t) (t) (t,k ) (t,k ) (t,k ) (t,k ) (t,k ) PB R m ,i lB R m HB R m ,i Xi + PU R m ,i lU R m HU R m ,i Wi +ZR m ,i , YR m ,i = (10.8) (t,k )

(t,k )

where PB R m ,i and Xi are the transmit power and the transmit symbol for the link between the BS and relay m in subcarrier i in the first phase of transmission (t) of frame t, respectively. lB R m represents the path-loss between the BS and relay (t,k )

(t,k )

(t,k )

, and lU R m are defined in a similar manner as the m. Variables PU R m ,i , Wi corresponding variables for the BS-to-relay links except that the signaling direction is from the users to the relays. ZR m ,i is the additive white Gaussian noise (t) (t,k ) (AWGN) in subcarrier i at relay m, and HB R m ,i and HU R m ,i are, respectively the small-scale fading coefficients between the BS and relay m and between relay m and user k in subcarrier i. In practice, different links in a relay network can experience asymmetric fading conditions [37]. For instance, a strong LoS propagation channel is expected between the BS and the relays, since they are placed

272


Phase 1

Phase 2

Broadcasts to the BS and users

Signals from the BS and users

f tr t

Figure 10.9. Subcarrier mapping in a two-way half-duplex relay OFDMA system for users 1, 2, and 3. in relatively high positions in practice and the number of blockages between them (t) is limited. Hence, HB R m ,i is modeled as Rician fading with Rician factor κ, i.e., (t) (t,k ) HB R m ,i ∼ CN ( κ/(1 + κ), 1/(1 + κ)). On the other hand, we model HU R m ,i as (t,k )

Rayleigh-distributed, i.e., HU R m ,i ∼ CN (0, 1), since the users are generally surrounded by a large number of scatterers. In order to optimize the system performance [33], the signals received at relay m from the BS and user k in subcarrier i are mapped to subcarrier p ∈ {1, . . . , nF } in the second transmission phase as shown in Figure 10.9. Furthermore, the signal in subcarrier p is forwarded @ to the destination after being amplified by a gain factor

(t,k )

(t,k )

GR m ,i,p PR m ,p , where

(t,k )

PR m ,p is the transmit power of relay m in subcarrier p for user k and the BS, and (t,k )

GR m ,i,p normalizes the input power of the relay. Since the channel is assumed to be time-invariant for the two transmission phases, channel reciprocity is preserved. Therefore, the signal received at user k in subcarrier p from relay m in frame t is given by @ (t,k ) (t,k ) (t,k ) (t,k ) (t,k ) Y˜U m ,p = GR m ,i,p PR m ,p lU R m HU R m ,p @ (t,k ) (t) (t) (t,k ) (t,k ) PB R m ,i lB R m HB R m ,i Xi × + Im ,i + ZR m ,i + Zp(k ) , (10.9) (t,k )

where Im ,i =

@

(t,k )

(t,k )

(t,k )

(t,k )

PU R m ,i lU R m HU R m ,i Wi (k ) Zp

represents the self-interference of

user k in subcarrier i and is the AWGN at user k in subcarrier p. For simplicity and without loss of generality, we assume a normalized noise variance

10.3 Network model for relay-assisted OFDMA system

273

of N0 = 1 at all transceivers. By estimating the channel coefficients in each frame and exploiting the channel reciprocity, the self-interference is perfectly known (t,k ) at user k and can be subtracted from Y˜U m ,p [12]. Therefore, the received signal after self-interference cancellation can be written as @ (t,k ) (t,k ) (t,k ) (t,k ) (t,k ) YU m ,p = GR m ,i,p PR m ,p lU R m HU R m ,p @ (t,k ) (t) (t) (t,k ) × PB R m ,i lB R m HB R m ,i Xi + ZR m ,i + Zp(k ) . (10.10) Similarly, the received signal at the BS in subcarrier p from user k is given by @ (t,k ) (t,k ) (t,k ) (t) (t) YB m ,p = GR m ,i,p PR m ,p lB R m HB R m ,p @ (t,k ) (t,k ) (t,k ) (t,k ) × PU R m ,i lU R m HU R m ,i Wi + ZR m ,i + Zp , (10.11) where Zp is the AWGN at the BS in subcarrier p. Following [12], the gain is chosen as |GR m ,i,p |−1 = 1 + PB R m ,i lB R m |HB R m ,i |2 + PU R m ,i lU R m |HU R m ,i |2 . (t,k )

10.3.3

(t,k )

(t)

(t)

(t,k )

(t,k )

(t,k )

(10.12)

Channel state information (CSI) In the system considered, both the BS and the users exchange information with the help of relays. As mentioned before, we assume the CSI of all links to be constant for the duration of one frame. Thus, the BS, the relays, and all (scheduled) users can accurately estimate the CSI of their links using training symbols in each frame for relaying and signal detection purposes. For scheduling, we assume that the relays perfectly know the path-losses of their respective BS-to-relay and relay-to-user links due to accurate long-term measurements. Furthermore, to perform scheduling for the next superframe, the relays estimate the small-scale fading coefficients of their respective BS-to-relay and relay-to-user links based on training symbols sent by the BS and all users at the beginning of the scheduling slot (Figure 10.8). Since we assume that both the BS and the relays are static, the associated channel is time-invariant and is assumed to remain constant for the duration of the entire superframe. In contrast, due to the mobility of the users, the CSI of the relay-to-user links changes slowly and the CSIT of these links used for scheduling becomes outdated over the duration of a superframe. To capture this effect, we model the CSI of the relay-to-user links using Jake’s model [38]. For simplicity, we assume that each scheduling slot has the length of one frame. As illustrated in Figure 10.8, the correlation between the scheduling slot (frame 0) and frame t in subcarrier i of the link between relay m and user (t,k ) (0,k ) k is given by E[HU R m ,i (HU R m ,i )∗ ] = ρ(t × τ ) with ρ(τ ) = J0 (2πfD τ ), where τ and fD are the time duration of one frame and the maximum Doppler frequency, (t,k ) respectively. Therefore, for scheduling purposes, the actual CSI, HU R m ,i , in frame t ∈ {1, . . . , F } for the link between user k and relay m in subcarrier i can be

274


expressed as (t,k )

HU R m ,i = (t,k )

ˆ (t,k ) + ∆H (t,k ) , 1 − σe2 (t)H U R m ,i U R m ,i

(10.13)

(0,k )

ˆ where H U R m ,i = HU R m ,i is the outdated CSI used for scheduling at the beginning (t,k )

of the superframe. Here, ∆HU R m ,i ∼ CN (0, σe2 (t)) represents the CSIT error with (0,k )

(t,k )

variance σe2 (t) = 1 − ρ2 (t × τ ) and E[HU R m ,i ∆HU R m ,i ] = 0.

10.4

Cross-layer design for two-way relay-assisted OFDMA systems In this section, we introduce the system goodput as a performance measure for cross-layer scheduling and formulate the cross-layer optimization problem.

10.4.1

Instantaneous channel capacity and system goodput Given perfect CSI at the receiver (CSIR), the downlink (DL) instantaneous channel capacity between the BS and user k in using subcarrier pair (i, p) through relay m in frame tis given by the mutual information which can be expressed as (t,k ) (t,k ) 1 CD L m ,i,p ≈ 2 log2 1 + ΓDLm ,i,p with equivalent DL SNR (t,k )

ΓDLm ,i,p = (t,k )

(t)

(t)

(t,k ) (t,k )

(t,k )

PB R m ,i lB R m |HB R m ,i |2 PR m ,p lU R m |HU R m ,p |2 (t,k )

(t)

(t)

(t,k )

(t,k )

(t,k )

(t,k ) (t,k )

(t,k )

PB R m ,i lB R m |HB R m ,i |2 + PU R m ,i lU R m |HU R m ,i |2 + PR m ,p lU R m |HU R m ,p |2

,

(10.14) 1 2

where the approximation and the prelog factor in the channel capacity equation are due to a high-SNR assumption and the two channel uses necessary for transmitting one message, respectively. Similarly, the channel capacity for the end-to-end uplink (UL) from user k in using subcarrier pair (i, p) through relay (t,k ) (t,k ) m in frame t is given by CU L m ,i,p ≈ 12 log2 (1 + ΓULm ,i,p ) with equivalent UL SNR (t,k )

ΓULm ,i,p = (t,k )

(t,k )

(t,k )

(t,k ) (t)

(t)

PU R m ,i lU R m |HU R m ,i |2 PR m ,p lB R m |HB R m ,p |2 (t,k )

(t)

(t)

(t,k )

(t,k )

(t,k )

(t,k ) (t)

(t)

PB R m ,i lB R m |HB R m ,i |2 + PU R m ,i lU R m |HU R m ,i |2 + PR m ,p lB R m |HB R m ,p |2

.

(10.15) Now, we are ready to define the instantaneous goodput (bps/Hz successfully delivered) of DL and UL transmission for user k who is assigned to relay m as (k )

ρD L m (k ) ρU L m

=

nF F nF 1 (t,k ) (t,k ) (t,k ) (t,k ) s r 1(rD L m ,i,p ≤ CD L m ,i,p ), Fn F t=1 i=1 p=1 m ,i,p D L m , i , p

=

nF F nF 1 (t,k ) (t,k ) (t,k ) (t,k ) s r 1(rU L m ,i,p ≤ CU L m ,i,p ), Fn F t=1 i=1 p=1 m ,i,p U L m ,i,p

(10.16)

10.4 Cross-layer design for two-way relay-assisted OFDMA systems

275

(t,k )

where Fn F = F × nF , sm ,i,p ∈ {0, 1} is the subcarrier pair allocation indicator, (t,k )

(t,k )

and rD L m , i , p and rU L m , i , p are the transmission data rates for DL and UL, respectively. The average weighted system goodput, which is defined as the total average number of bps/Hz successfully decoded at the BS and the K users via the M relays (averaged over multiple scheduling phases), is given by 5 M 6 (k ) (k ) (k ) w (ρD L m + ρU L m ) , (10.17) Ug oodpu t (P, R, S) = E m =1 k ∈Um

where P, R, and S are the power, rate, and subcarrier allocation policies, respectively. Um is the set of users associated with relay m and w(k ) is a positive constant that can be used to enforce certain notions of fairness such as proportional fairness and max–min fairness [39].

10.4.2

Cross-layer design problem In practice, a channel outage occurs in slow fading channels whenever the data rate exceeds the channel capacity. Furthermore, users are heterogeneous with different data rate requirements. Therefore, a practical scheduler has to be able to fulfill the different data rate requirements of the users as well as their channel outage probability requirements. This leads to the following optimization problem.

Problem (Cross-layer optimization problem) The optimal power allocation policy, P ∗ , rate allocation policy, R∗ , and subcarrier allocation policy, S ∗ , are given by

subject to:

(P ∗ , R∗ , S ∗ ) = arg max Ug oodpu t (P, R, S), P,R,S 0 / (t,k ) (t,k ) C1: Pr rD L m ,i,p > CD L m ,i,p |Ξm ≤ ε, ∀k, t, m, i, p, / 0 (t,k ) (t,k ) C2: Pr rU L m ,i,p > CU L m ,i,p |Ξm ≤ ε, ∀k, t, m, i, p, C3: C4:

M m =1 M

(k )

(k )

ρD L m + ρU L m

nF nF F

m =1 k ∈Um t=1

≥ R(k ) , (t,k )

∀k ∈ D ∩ U m ,

(t,k )

(t,k )

(t,k )

sm ,i,p (PU R m ,i + PB R m ,i + PR m ,p ) ≤ PT , i=1 p=1 (t ,k )

Pm , i , p

C5:

nF M

(t,k )

sm ,i,p = 1, ∀p, t,

m =1 k ∈Um i=1

C6:

nF M

(t,k )

sm ,i,p = 1,

m =1 k ∈Um p=1 (t,k ) C7: sm ,i,p ∈ {0, 1}, ∀m, i, p, k, t, (t,k ) (t,k ) (t,k ) C8: PB R m ,i , PU R m ,i , PR m ,p ≥ 0,

∀i, t,

∀m, i, p, k, t.

(10.18)

276


ˆ U R m , Lm ] is the CSI matrix, where H ˆ U R m , HB R m , and Lm Here, Ξm = [HB R m , H (k ) ˆ are vectors which contain the estimated CSIT, HU R m ,j , for all links from relay m to users k ∈ Um , the actual CSIT, HB R m ,i , for the link between the BS and relay m, and the path-loss for all links involving relay m, respectively. D ∩ U m is (t,k ) (t,k ) (t,k ) (t,k ) the intersection of sets Um and D, and Pm ,i,p = PU R m ,i + PB R m ,i + PR m ,p is the power usage for one subcarrier pair. Furthermore, C1 (C2) represents the outage probability requirement of the DL (UL) for user k in each frame and limits the maximum outage probability to ε. This constraint is used as a measure for the QoS with respect to the FER which can be well approximated by the channel outage probability if capacity achieving codes are applied [23, 24]. C3 enforces the minimum required data rate for delay-sensitive users which are chosen by the application layer. C4 is the joint power constraint for the BS, relays, and users with total maximum power PT . Although the BS, relays, and users have different power supplies in practice, a joint power optimization provides insight into the power usage of a whole communication link (both UL and DL) rather than the per-hop required power. Furthermore, the global CSI of the entire system is needed in all devices in order to derive the optimal power allocation if separate power constraints are used [32], which would limit the system’s scalability due to significant signalling overheads. Constraints C5, C6, and C7 are imposed to guarantee that each subcarrier pair is only used by one user in each frame.

10.5

Cross-layer optimization solution In this section, the problem considered is solved by dual decomposition and a novel distributed iterative scheduling algorithm is derived to reduce the computational complexity at the BS.

10.5.1

Transformation of the optimization problem The problem considered is a mixed combinatorial and nonconvex optimization problem. The combinatorial nature of the problem is due to the integer constraint for subcarrier allocation while the nonconvexity is caused by the power allocation variables in the objective function. In general, a brute force approach is needed to obtain the globally optimal solution. However, such a method does not provide any system design insights and has limited scalability. In order to obtain an insightful iterative solution, we first assume that the ratio between the DL and UL transmitted power is fixed, i.e., (t,k )

PB R m ,i (t,k )

P(B + U ) m ,i

(t,k )

(t,k )

(t,k )

(t,k )

(t,k )

= αm ,i P(B + U ) m ,i , PU R m ,i = (1 − αm ,i )P(B + U ) m ,i , (10.19) (t,k )

(t,k )

= PB R m ,i + PU R m ,i ,

277

10.5 Cross-layer optimization solution

(t,k )

where 0 < αm ,i < 1 controls the transmit power ratio between UL and DL, and (t,k )

P(B + U ) m ,i represents the power consumption on subcarrier i by the BS and user k. We introduce the following useful lemma. Lemma 10.2 (High-SNR power consumption) Assuming a high SNR, the optimal power allocation for the BS, relay m, and user k in using subcarrier pair (i, p) in frame t is given by (t,k )

(t,k )

PR m ,p

(t,k )

=

Pm ,i,p Pm ,i,p (t,k ) , P(B + U ) m ,i = , 2 2

=

(1 − αm ,i )Pm ,i,p αm ,i Pm ,i,p (t,k ) , PB R m ,i = . 2 2

(t,k )

(t,k ) PU R m ,i

(t,k )

(t,k )

(t,k )

(10.20)

Proof. Please refer to the Appendix at the end of this chapter. A key step in solving the optimization problem in (10.18) is to incorporate the outage probability constraints in C1 and C2 into the objective function. In general, a very tedious expression will be obtained if we try to incorporate the inequality in C1 and C2 into the objective function and it is virtually impossible to obtain a tractable resource allocation solution. To obtain first-order design insight and a simple resource allocation algorithm, we restrict the problem such that the constraints in C1 and C2 are fulfilled with equality for the optimal solution. Simulations (not shown here) suggest that C1 and C2 are always satisfied with equality for the low outage probabilities required in practical applications (e.g., ε ≤ 0.1). We are now ready to introduce the following lemma. Lemma 10.3 (Equivalent data rate incorporating outage probability) For a given outage probability ε in C2, the equivalent UL data rate in using subcarrier pair (i, p) is (t,k )

C2 ⇒ rU L m ,i,p =

1 (t,k ) log2 1 + ΛUL m ,i,p , ∀i, p 2

(10.21)

with equivalent UL receive SNR (t,k )

ΛULm ,i,p = (t,k )

(t,k )

(t,k )

−1(t,k )

(t)

(t)

Pm ,i,p (1 − αm ,i )lU R m FU R m ,i (ε)lB R m |HB R m ,p |2 (t,k ) (t)

(t)

(t,k )

(t,k )

−1(t,k )

(t)

(t)

2 αm ,i lB R m |HB R m ,i |2 + (1 − αm ,i )lU R m FU R m ,i (ε) + lB R m |HB R m ,p |2

, (10.22)

−1(t,k )

where FU R m ,i (ε) is the inverse CDF of a noncentral chi-square random variable ˆ (t,k ) |2 /σe2 (t). Here, with two degrees of freedom and noncentrality parameter |H U R m ,j 2 σe (t) is the estimation error variance defined in (10.13).

278


On the other hand, for a given outage probability ε in C1, the equivalent DL data rate in using subcarrier pair (i, p) is (t,k ) (t,k ) (10.23) C1 ⇒ rD L m ,i,p = 12 log2 1 + ΛDLm ,i,p (t,k )

with equivalent DL receive SNR ΛDL m ,i,p at user k given by ⎧ (t,k ) (t,k ) (t) (t) (t,k ) −1(t,k ) ⎪ Pm ,i,p αm ,i lB R m |HB R m ,i |2 lU R m FU R m ,i (ε) ⎪ ⎪ , if i = p, ⎪ ⎪ (t,k ) (t) (t) ⎪ 2 + (2 − α(t,k ) )l(t,k ) F −1(t,k ) (ε) ⎨ 2 αm l |H | ,i B R m m ,i B R m ,i U R m U R m ,i (t,k ) ΛDLm ,i,p = (10.24) (t,k ) (t,k ) (t) (t) −1(t,k ) 2 ⎪ Pm ,i,p αm ,i lB R m |HB R m ,i | (FU R m ,i,p (ε))2 ⎪ ⎪ ⎪ , if i = p, ⎪ ⎪ −1(t,k ) ⎩ 2 α(t,k ) l(t) |H (t) |2 + (F (ε))2 m ,i

B Rm

B R m ,i

U R m ,i,p

−1(t,k )

where FU R m ,i,p (ε) is the inverse CDF of a random variable which is the ratio of two independent nonidentical Rice distributed random variables (10.42). Proof. Please refer to the appendix. A new objective function which incorporates the outage of both UL and DL can be obtained by substituting (10.21) and (10.23) into the original objective function (10.17). The next step in solving the problem is to handle the combi(t,k ) natorial constraint in C7. We adopt a time-sharing approach4 by relaxing sm ,i,p (t,k )

to be a real value between 0 and 1 instead of a Boolean, i.e., 0 ≤ sm ,i,p ≤ 1. Furthermore, since the power constraint is instantaneous, average weighted system goodput maximization is equal to the instantaneous weighted goodput maximization in each scheduling slot. Thus, the cross-layer scheduling optimization problem is transformed into the following convex optimization problem. Problem (Transformed cross-layer optimization problem) arg max

P,R,S

(t,k ) nF nF M F w(k ) sm ,i,p m =1 k ∈Um t=1 i=1 p=1

subject to: C4:

2Fn F

nF nF M F m =1 k ∈Um t=1

(t,k ) (t,k ) P˜(B + U ) m ,i + P˜R m ,p ≤ PT , C3, i=1 p=1

C5, C6,

(t ,k ) P˜m , i , p

(t,k )

C7: 0 ≤ sm ,i,p ≤ 1, C8:

(t,k ) C˜m ,i,p

∀m, i, p, t, k,

(t,k ) (t,k ) (t,k ) P˜B R m ,i , P˜U R m ,i , P˜R m ,p

≥ 0,

∀m, i, p, t, k,

(10.25)

(t,k ) (t,k ) (t,k ) (t,k ) (t,k ) where C˜m ,i,p = log2 (1 + ΛDL m ,i,p /sm ,i,p ) + log2 (1 + ΛUL m ,i,p /sm ,i,p ) is the data (t,k ) rate incorporating the effects of outage and time sharing. P˜(B + U ) m ,i = (t,k ) (t,k ) (t,k ) (t,k ) (t,k ) (t,k ) (t,k ) (t,k ) s P , P˜ =s P , and P˜ =s P are auxiliary m ,i,p

4

(B + U ) m ,i

R m ,p

m ,i,p

R m ,p

m ,i,p

m ,i,p

m ,i,p

In which the authors showed that this relaxation is asymptotically optimal w.r.t. the number of subcarriers.

279

10.5 Cross-layer optimization solution

(t,k ) (t,k ) (t,k ) power variables, and P˜m ,i,p = P˜(B + U ) m ,i + P˜R m ,p is the total power usage of subcarrier (i, p) in frame t for user k. Since the Hessian matrix of the objective function in (10.25) is negative semidefinite, the problem is jointly concave w.r.t. the optimization variables, and the duality gap is equal to 0 under some mild conditions [40]. Thus, centralized numerical methods such as the interior-point method can be used to solve the above problem. However, for centralized methods, the overhead required for collecting the CSI of all links and the computational complexity at the BS grows exponentially w.r.t. the number of subcarriers and users. Therefore, an optimal distributed iterative solution with reduced signaling overhead in the CSI collection and lower computational complexity will be derived in the next section.

10.5.2

Dual problem formulation In this subsection, the transformed cross-layer scheduling optimization problem is decomposed into one master problem (solved at the BS) and several subproblems (solved at each relay) by using dual decomposition. For this purpose, we first need the Lagrangian function of the primal problem. Upon rearranging terms, the Lagrangian is given by L(λ, β, δ, υ, P, R, S) = (t,k ) nF nF M F M sm ,i,p (w(k ) + δk ) (t,k ) C˜m ,i,p − R(k ) δk 2F n F m =1 t=1 i=1 p=1 m =1 k ∈Um

+

nF F

k ∈Um

(t)

(βi

(t)

+ υi ) − λ

nF nF M F

(t,k ) P˜m ,i,p + λPT −

m =1 k ∈Um t=1 i=1 p=1

t=1 i=1 nF nF M F

(t)

(t,k )

(βp(t) + υi )sm ,i,p ,

(10.26)

m =1 k ∈Um t=1 i=1 p=1

where λ is the Lagrange multiplier corresponding to the joint power constraint and δ is a vector of Lagrange multipliers corresponding to the data rate constraint with elements δk , k ∈ {1 . . . K}, with δk = 0 for non-delay-sensitive users. Furthermore, Lagrange multiplier vectors β and υ are associated with the sub(t) (t) carrier usage constraints and have elements βp , p ∈ {1, . . . , nF }, and υi , i ∈ {1, . . . , nF }, t ∈ {1, . . . , F }, respectively. Thus, the dual problem is min

max

λ,β,δ,υ≥0 P,R,S

10.5.3

L(λ, β, δ, υ, P, R, S).

(10.27)

Distributed solution – subproblem for each relay station By dual decomposition, relay station m can solve the following subproblem without any assistance from other relays. max

P,R,S

Lm (λ, β, δ, υ, P, R, S),

280


where Lm (λ, β, δ, υ,P, R, S) = (t,k ) nF nF F sm ,i,p (w(k ) + δk ) (t,k ) (t,k ) (t) (t,k ) C˜m ,i,p− λP˜m ,i,p − (βp(t) + υi )sm ,i,p . 2F n F t=1 i=1 p=1 k ∈Um

(10.28) Using standard optimization techniques and the Karush–Kuhn–Tucker (KKT) condition, the optimal power allocation in high SNR for subcarrier pair (i, p) is given by + 1 (w(k ) + δk ) 1 ∗(t,k ) (t,k ) ∗(t,k ) (t,k ) ˜ − Pm ,i,p = sm ,i,p Pm ,i,p = sm ,i,p − , (t,k ) (t,k ) λ 2ΛUL m ,i,p 2ΛDL m ,i,p (10.29) where δk is equal to 0 for non-delay-sensitive users, i.e., δk = 0, ∀k ∈ N . Power allocation (10.29) can be interpreted as a multilevel water-filling scheme as the water levels of different users can be different. Specifically, the water levels of delay-sensitive users, i.e., (w(k ) + δk /λ), are generally higher than those of nondelay-sensitive users, in order to satisfy constraint C3 in (10.18). To obtain the optimal subcarrier allocation, we take the derivative of the subproblem with (t,k ) respect to sm ,i,p and substitute the optimal power allocation (10.29) into the derivative. The resulting subcarrier pair selection determined by relay station m is given by ⎧ (t,k ) (t,k ) (t) (t) ΛUL m ,i,p ΛDL m ,i,p ⎪ 2(βp + υi ) ∗(t,k ) ⎨ ˜ + + , 1, if Cm ,i,p ≥ ∗(t,k ) (t,k ) (t,k ) sm ,i,p = w(k ) + δk 1 + ΛUL m ,i,p 1 + ΛDL m ,i,p ⎪ ⎩ 0, otherwise, (10.30) ∗(t,k )

(t,k )

(t)

(t)

where C˜m ,i,p = C˜m ,i,p |P˜ ( t , k ) = P˜ ∗( t , k ) . The dual variables βp and υi m ,i,p

can be inter-

m ,i,p

preted as the shadow price associated with the usage of subcarrier pair (i, p) in frame t. Dual variable δk forces the scheduler to assign more subcarrier pairs to delay-sensitive users by lowering the price for satisfying the data rate requirements. The Lagrange multipliers λ, β, δ, and υ are provided by the BS in each iteration. Finally, by substituting (10.20) and (10.29) into the equivalent packet ∗(t,k ) outage constraints in (10.21) and (10.23), the optimal rate allocation rD L m ,i,p ∗(t,k )

and rU L m ,i,p can be calculated.

10.5.4

Solution of the master problem at the BS To solve the master problem at the BS, each relay calculates the local resource ∗(t,k ) ∗(t,k ) ∗(t,k ) ∗(t,k ) usages and passes this information, i.e., rD L m ,i,p , rU L m ,i,p , sm ,i,p , and Pm ,i,p , to the BS. Since the dual function is differentiable, the gradient method can be used to solve the minimization in (10.27) at the BS. Thus, the solution is given

281

10.6 Asymptotic performance analysis

by 5 βp(t) (n

+ 1)

βp(t) (n)

=

− ξ1 (n) 1 −

5 (t) υi (n

+ 1)

/ δk (n + 1)

=

=

6+ (t,k ) sm ,i,p

m =1 k ∈Um i=1

− ξ2 (n) 1 −

nF M

∀p, t, (10.31)

, 6+

(t,k ) sm ,i,p

∀i, t, (10.32)

,

m =1 k ∈Um p=1

0+ δk (n) − ξ3 (n) ∆R(k ) 1 ∆R(k ) < 0 , ∀k ∈ D ∩ U m ,

5 λ(n + 1)

(t) υi (n)

=

nF M

λ(n) − ξ4 (n) PT −

M

nF nF F

(10.33)

6+ (t,k )

Pm ,i,p

,

(10.34)

m =1 k ∈Um t=1 i=1 p=1

where ∆R(k ) is the difference between the scheduled data rate and the target (k ) (k ) (k ) ). data rate for delay-sensitive user k, i.e., ∆R(k ) = M m =1 (ρD L m + ρU L m − R Index n is the iteration index, ξ1 (n), ξ2 (n), ξ3 (n), and ξ4 (n) are positive step sizes, and convergence to the optimal solution is guaranteed under some mild conditions on the step sizes [41]. The overall algorithm tries to select the best user who can maximize the outage incorporated data rate for both DL and UL while any selected subcarrier pair is eventually occupied by one user only. In summary, in each iteration, the BS broadcasts the Lagrange multipliers, which indicate the price of global resource usage for all relays. Then each relay solves the subproblem based on its local CSI and passes the solution back to the BS. Finally, the BS updates the Lagrange multipliers according to (10.31)–(10.34) and broadcasts them to all relays in the next iteration. This process is repeated until convergence or the maximum number of iterations are reached.

10.6

Asymptotic performance analysis and computational complexity reduction scheme In this section, we analyze the asymptotic order growth of the average system goodput with respect to the numbers of non-delay-sensitive users KN = K − K1 and relays M . In addition, an efficient computational complexity reduction scheme is proposed for the relays in order to achieve the simplicity required for a practical implementation.

10.6.1

Asymptotic analysis of system goodput The schedulers sacrifice system performance in order to fulfill the data rate requirements of the delay-sensitive users, since system resources are allocated to them regardless of their actual channel conditions. In contrast, non-delaysensitive users allow a more flexible resource allocation which benefits the overall

282


system performance. Therefore, in this section, we analyze the asymptotic order growth of the average weighted system goodput w.r.t. the numbers of non-delaysensitive users KN = K − K1 and relays M . In order to obtain a tractable result, we assume that the distances between the BS and each relay are identical and that relays do not perform subcarrier mapping, and we focus on the study of PF schedulers with long-term fairness consideration. PF scheduling provides a good compromise between maximizing system capacity and achieving fairness among users and has been implemented in practical systems such as the high-speed downlink packet access (HSDPA). For long-term fairness, the path-loss of the users is disregarded by the PF scheduler and the user selection is based only on the instantaneous i.i.d. small-scale fading channel gain [29]. In other words, the near–far effect is omitted and each user is served at its own peak channel gain, and therefore each user has the same channel access probability. The analysis is divided into two cases. In case I a large number of non-delaysensitive users KN and a growing number of relays M such that their ratio can be written as limK N ,M →∞ KN /M → ∞ are considered. In case II a large number of relays M and a growing number of non-delay-sensitive users KN with ratio limK N ,M →∞ M/KN → ∞ are studied. The results are summarized in the following theorem. Theorem 10.2 (Asymptotic system goodput for PF scheduler in high SNR5 ) log M . (10.35) Case I: Ug oodpu t (P, R, S) = O log2 κ+1 Case II: Ug oodpu t (P, R, S) for 0 ≤ σe2 (·) < 1. = O log2 (1 − σe2 (F × τ )) log KN (10.36) Proof. Please refer to the Appendix. Theorem 10.2 illustrates that the asymptotic growth of the average system goodput is indeed the asymptotic growth of the cut-set bound of a twoway relay channel [14] in both cases. If KN and M do not satisfy either limK N ,M →∞ M/KN → ∞ or limK N ,M →∞ KN /M → ∞, the gain achieved by either large KN or large M will be quickly saturated due to noise amplification in the AF relays. On the other hand, both Case I and Case II demonstrate the benefits of using two-way half-duplex relays which are able to recover the spectral efficiency loss of 12 asymptotically when compared with one-way half-duplex relays. Moreover, the terms κ + 1 and 1 − σe2 (F × τ ) act as penalties on the system performance introduced by the LoS path and the imperfect CSIT, respectively. Thus, we need an exponentially larger number of non-delay-sensitive users KN 5

For a better illustration of the effect of imperfect CSIT and LoS path on the system performance, we preserve some terms which do not grow with either K N or M .

10.7 Results and discussions

283

and relays M to compensate the penalties on the system performance caused respectively by an LoS path and imperfect CSIT.

10.6.2

Scheme for reducing computational burden at each relay In this section, a novel computational burden reduction scheme is introduced to reduce the computational load of the relays. In general, the distributed resource allocation and scheduling algorithm alleviates the computational burden at the BS by distributing computation to the relays. However, the relays may not be able to handle the additional computational complexity when the number of users is large, since relays have usually limited computational power. Therefore, a computational burden reduction scheme for the relays is needed. Our proposed scheme offers two advantages. First, it preserves the desirable properties of the scheduler under various scheduling policies. In other words, the essential gain achieved by MUD is preserved as will be demonstrated in the simulation section. Second, the total computational load can be conveniently controlled by adjusting a corresponding threshold. We assume that subcarrier mapping is not performed such that the combination of subcarrier pairs in the view of each relay increases linearly w.r.t. nF instead of n2F . As can be observed from (10.30), the subcarrier selection criterion at the relays is based on the data rate incorporating outage and the global (t) (t) resource usage which is reflected in the shadow price, i.e., βp and υi . For a reasonably large number of users K, due to MUD, the probability that a user with ∗(t,k ) a small value of C˜m ,i,p is assigned any subcarrier pairs is low. Hence, computing and allocating any resources to them is wasteful and should be avoided. In the proposed computational burden reduction scheme, the scheduler only considers subcarrier i of user k for scheduling when the following condition is fulfilled: 4 Θ th 4nF +4 (t,k ) −1(t,k ) ( w k + δ k ) ( 1 −ε ) 2 , (10.37) lU R m FU R m ,i (ε) ≥ PT where Θth is a threshold. Since only some users are considered for scheduling, the computational burden for the calculation of the resource allocation is reduced. Threshold Θth allows us to trade performance for complexity. The larger Θth , the fewer the subcarriers that are considered, which leads to a lower complexity but may cause some degradation in performance. For the derivation of (10.37), please refer to the Appendix.

10.7

Results and discussions In this section, we evaluate the system performance using simulations. A single cell with two ring-shaped boundary regions is considered. The outer boundary and the inner boundary have radii of 1 km and 500 m, respectively. The M relay stations are equally distributed in the area between the inner and the

284


outer boundaries, which is divided into A sectors of equal sizes. Each user is served by GRj = M/A, 1 ≤ j ≤ A, relays. In a superframe, there are N = 5 frames and each frame has a length of 2 ms. The number of subcarriers is nF = 128 with carrier center frequency 2.5 GHz and the 3GPP path-loss model is (t,k ) adopted [42]. αm ,i = 2/3 such that the transmit power of the BS is twice that of the mobile users. The small-scale fading coefficients of the BS-to-relay links are modeled as i.i.d. Rician random variables with Rician factor κ = 6 dB, while the small-scale fading coefficients of the relay-to-user links are i.i.d. Rayleigh random variables. The target packet outage probability is set to ε = 0.01 for illustration. The quantizer used to quantize the information exchanged between the relays and the BS in each iteration of the distributed resource allocation algorithm is designed offline using the Lloyd–Max algorithm. We study the performance of the maximum system goodput and PF schedulers. Maximum goodput scheduling can be obtained by using weights wk = 1, ∀k, while PF scheduling is performed by adapting the weights of each user according to [29]. The average weighted system goodput is obtained by counting the number of packets successfully decoded by all users averaged over both the macroscopic and microscopic fading.

10.7.1

Convergence of the distributed resource allocation algorithm Figures 10.10, 10.11, and 10.12 illustrate the evolution of the Lagrange multi(1) pliers λ, β1 , and δ1 for the distributed maximum goodput and PF scheduling algorithms over time for different maximum transmit powers Pt . There are K = 15 users, A = 3 sectors, and M = 3 relays and the packet outage probability was chosen to be ε = 0.01. Each user has mobility 5 km/h and there are three delay-sensitive users with data rate requirement R(k ) = 1 bps/Hz. The results are averaged over 1000 independent adaptation processes. As can be observed from Figures 10.10–10.12, the proposed distributed algorithm converges fast and typically achieves 90–95% of the optimal value within ten iterations even if the value of the dual variables which are exchanged between the BS and relays are quantized to 3 bits.

10.7.2

Average system goodput vs. transmit power and user mobility Figure 10.13 illustrates the average weighted system goodput vs. the transmit power for M = 3 relays and A = 3 sectors. In the cell, there are K = 15 users with mobilities of 5 km/h. Three users are delay-sensitive with data rate requirement R(k ) = 1 bps/Hz, ∀k ∈ D, while the remaining users are non-delay-sensitive. We study the performance of maximum system goodput and PF scheduling with the proposed distributed algorithms. For comparison, we also simulate the centralized schedulers associated with the scheduling algorithms considered. The centralized scheduler is implemented at the BS which is assumed to have the global CSI of the entire network and resource allocation is performed by using a brute force search. It can be observed that the performance of the proposed distributed


285

PT=38 dBm, PT=38 dBm, PT=38 dBm, PT=35 dBm, PT=35 dBm, PT=35 dBm, PT=35 dBm, PT=38 dBm, PT=38 dBm, PT=35 dBm, PT=35 dBm, PT=35 dBm,

Figure 10.10. Dual variable λ vs. the number of iterations with K = 15 users, A = 3 sectors, M = 3 relays, and packet outage probability ε = 0.01. Each user has mobility 5 km/h and there are three delay-sensitive users with data rate requirement R(k ) = 1 bps/Hz.

(1)

Figure 10.11. Dual variable β1 vs. the number of iterations with K = 15 users, A = 3 sectors, M = 3 relays, and packet outage probability ε = 0.01. Each user has mobility 5 km/h and there are three delay-sensitive users with data rate requirement R(k ) = 1 bps/Hz.

286


Figure 10.12. Dual variable δ1 vs. the number of iterations with K = 15 users, A = 3 sectors, M = 3 relays, and packet outage probability ε = 0.01. Each user has mobility 5 km/h and there are three delay-sensitive users with data rate requirement R(k ) = 1 bps/Hz.

algorithm closely approaches the optimal centralized scheduling algorithm for both maximum goodput and PF scheduling after only ten iterations, which confirms the practicality of the distributed algorithm. On the other hand, although a better performance can be achieved when subcarrier mapping is implemented at the relays, it provides less than 1 dB gain in terms of system goodput at the cost of a higher implementation complexity. Therefore, subcarrier mapping should be avoided if the system is operating in high SNR and the computational complexity is a concern. We also study the impact of the proposed computational burden reduction scheme and quantization of the information exchanged between the BS and the relays in each iteration of the distributed algorithm on the system performance. In particular, three bits are used for quantization and the threshold Θth , defined in Section 10.6.1, is chosen such that the relays only need to process 20% of the CSI coefficients. It can be observed that the quantization and the computational burden reduction scheme cause only a small loss in performance while significantly reducing the required signaling overhead and computational complexity. It is not surprising that the maximum goodput scheduler has a better performance than the PF scheduler in terms of the average weighted system goodput. Nevertheless, the maximum goodput scheduler results in a extremely unfair resource allocation, since only users with good channel conditions (users who are located near the relays) are selected for transmission. In contrast, the PF scheduler maintains fairness among users by sacrificing performance. Figure 10.13 also shows the performance of a baseline one-way half-duplex relay [16] in which subcarrier mapping is performed and a brute force approach

287

(bps/Hz)


PT

Figure 10.13. Average weighted system goodput vs. the total transmit power for different scheduling algorithms with K = 15 users, A = 3 sectors, M = 3 relays, and packet outage probability ε = 0.01. Each user has a mobility of 5 km/h and there are three delay-sensitive users with data rate requirement R(k ) = 1 bps/Hz.

is used for resource allocation. The proposed scheduler achieves a substantial gain in average weighted system goodput when compared with the baseline scheme, especially in the high transmit power regime. This is because the proposed scheduler acquires a better spectral efficiency by utilizing simultaneous message exchanges between the BS and users, while the one-way half-duplex relay uses two phases to transmit only one message.

288


Figure 10.14. Average weighted system goodput vs. the user mobility. A = 3 sectors, M = 3 relays, packet outage probability ε = 0.01, and K = 15 users. There are three delay-sensitive users in the system. Each curve corresponds to different transmit power levels and different data rate requirements for the delaysensitive users. Figure 10.14 illustrates the average system goodput vs. the user mobilities for K = 15 users where three users are delay-sensitive with different data rate requirements. It can be observed that as the speed of the users increases, the system performance decreases since the corresponding CSI at the proposed schedulers becomes more outdated, and the schedulers have to be conservative in the


289

resource allocation in order to satisfy the outage probability requirements of each user. In addition, the PF scheduler is more sensitive to the CSIT quality degradation due to the mobility of the users when compared with the maximum goodput scheduler, since the PF scheduler only considers the small-scale fading in the long run while the maximum goodput scheduler considers both the path-loss and small-scaling fading. It can be observed that the average weighted system goodput diminishes as the data rate requirements become more stringent, since most of the resources are consumed by the delay-sensitive users regardless of their actual channel quality. In other words, the degrees of freedom in the resource allocation decrease when the delay-sensitive users become more resource hungry, and hence the performance gain achieved by multiuser diversity diminishes. In contrast, the non-delay-sensitive users cannot be served even if they have very good channel conditions, because the scheduler needs to fulfill the data rate requirements of the delay-sensitive users.

10.7.3

Asymptotic system goodput performance of PF scheduling In this section, we focus on the asymptotic performance of PF scheduling with respect to the numbers of users K and relays M for A = 3 sectors. All users in the system have a mobility of 5 km/h. There are three delay-sensitive users with data rate requirement R(k ) = 1 bps/Hz, ∀k ∈ D, and KN = K − 3 nondelay-sensitive users. The number of iterations for the distributed scheduler is set to 20 and subcarrier mapping is not performed. Figure 10.15 illustrates the average system goodput vs. the number of relays for K = 300 users and different transmit powers. As expected, the average system goodput grows with order O (log2 (log M /(κ + 1))) which matches the predicted asymptotic trend closely. Although the asymptotic expressions in Theorem 10.2 are derived for non-delaysensitive users, they can be used to approximate the system performance in the considered case as well. This is because the performance can again be mainly attributed to the non-delay-sensitive users since they provide more degrees of freedom for the resource allocation. Figure 10.16 illustrates the average system goodput as a function of the number of users K for M = 300 relays for different total transmit powers and each user has a mobility of 5 km/h. As be observed, the average system goodput can follows the order growth of O log2 (1 − σe2 (F × τ )) log KN closely. This result suggests that in order to fully exploit the MUD gain in the considered system, the number of relay stations should grow faster than the number of users to compensate for the noise amplification in the AF process at the relay, which corresponds to an impractical scenario. We also study in Figures 10.15 and 10.16 the impact of the proposed computational burden reduction scheme and quantization on the system performance. It can be observed that both techniques do not change the asymptotic trend of the system performance which confirms that the proposed computational burden

290


PT =38 dBm

(bps/Hz)

PT =35 dBm

PT =32 dBm

PT t PT t PT t PT t PT t PT t

M

Figure 10.15. Average weighted system goodput of PF scheduler vs. the number of relays M with K = 300 users. Tthree users are delay-sensitive with data rate requirements R(k ) = 1 bps/Hz, ∀k ∈ D. The cell is divided into A = 3 sectors, each user has mobility of 5 km/h, and the packet outage probability requirement is ε = 0.01. reduction scheme is able to preserve the essential multiuser diversity gain even if the scheduler takes into account only 20% of the users for resource allocation.

10.8

Conclusion We have explored some basic ideas in cross-layer scheduling design and technical challenges arising in practical implementations of cross-layer scheduling. In particular, we have studied the cross-layer scheduling design for two-way half-duplex AF relay-assisted OFDMA systems. The problem considered has been formulated as a mixed combinatorial and nonconvex optimization problem, in which imperfect CSIT and heterogeneous user QoS requirements have been taken into consideration. After a proper transformation, dual decomposition has been used to derive an optimal, iterative, and distributed resource allocation solution, which requires only local CSI at each relay. Furthermore, an efficient computational burden reduction scheme has been proposed, which reduces the computational

10.8 Conclusion

291

PT =38 dBm

PT =35 dBm

PT =32 dBm

PT PT PT PT PT PT

Figure 10.16. Average weighted system goodput of PF scheduler vs. the number of users K with M = 300 relays. There are three delay-sensitive users with data rate requirements R(k ) = 1 bps/Hz, ∀k ∈ D. The cell is divided into A = 3 sectors, each user has mobility of 5 km/h and packet outage probability requirement ε = 0.01. complexity at the relays significantly, while preserving the essential gain obtained from multiuser diversity. In addition, the asymptotic order growth of the average system goodput in terms of the number of users and relays has been derived to obtain useful system design insights. Our simulation results have demonstrated the excellent performance of the proposed schedulers which approach the optimal centralized solution within a small number of iterations.

Appendix

Proof of Lemma 10.2 For convenience of notation, we define |H1 |2 , |H2 |2 , |H3 |2 , and |H4 |2 to represent (t) (t) (t) (t) (t,k ) (t,k ) (t,k ) (t,k ) lB R m |HB R m ,p |2 , lB R m |HB R m ,i |2 , lU R m |HU R m ,p |2 , and lU R m |HU R m ,i |2 , respec2 2 tively. Without loss of generality, we assume that |H1 | ≥ |H2 | ≥ |H3 |2 ≥ |H4 |2 . (t,k ) (t,k ) Furthermore, for high SNR, log2 (1 + ΓDLm ,i,p ) and log2 (1 + ΓULm ,i,p ) can be (t,k )

(t,k )

approximated as log2 (ΓDLm ,i,p ) and log2 (ΓULm ,i,p ), respectively. By applying (10.20) in (10.14) and (10.15), upon rearranging terms, the channel capacity becomes

(t,k )

(t,k )

CD L m ,i,p + CU L m ,i,p ≈ ; (t,k ) 2(t,k ) (t,k ) (t,k ) 2 2 2 2 1 2 log2 (αm ,i − αm ,i ) + 2 log2 (PR m ,p P(B + U ) m ,i ) + log2 (|H1 | |H2 | |H3 | |H4 | ) (t,k ) (t,k ) (t,k ) (t,k ) (t,k ) − log2 αm ,i P(B + U ) m ,i |H2 |2 + (1 − αm ,i )P(B + U ) m ,i |H4 |2 + PR m ,p |H3 |2 < (t,k ) (t,k ) (t,k ) (t,k ) (t,k ) − log2 αm ,i P(B + U ) m ,i |H2 |2 + (1 − αm ,i )P(B + U ) m ,i |H4 |2 + PR m ,p |H1 |2 ⎛ ⎞ (t,k ) (t,k ) (t,k ) 2(t,k ) PR m ,p P(B + U ) m ,i log ((αm ,i − αm ,i )|H1 |2 |H2 |2 |H3 |2 |H4 |2 ) ⎠+ 2 ≥log2 ⎝ (t,k ) (t,k ) 2 P +P R m ,p

(B + U ) m ,i

− log2 (|H1 | ). 2

(10.38)

It is interesting to note that on the right hand side of (10.38), (t,k ) (t,k ) (t,k ) (t,k ) log2 PR m ,p P(B + U ) m ,i /(PR m ,p + P(B + U ) m ,i ) is the only term related to the (t,k )

(t,k )

power allocation variables and it is jointly concave w.r.t. PR m ,p and P(B + U ) m ,i . (t,k )

(t,k )

(t,k )

Therefore, for a given power Pm ,i,p = PR m ,p + P(B + U ) m ,i and using standard (t,k )

(t,k )

optimization techniques, the optimal values of PR m ,p and P(B + U ) m ,i can be shown (t,k )

to be identical and are given by Pm ,i,p /2. On the other hand, using an approach similar to that above, we can show that the obtained power allocation also max(t,k ) (t,k ) imizes the cut set bound [14], i.e., log2 (PR m ,p P(B + U ) m ,i ), which is a capacity upper bound for the relay channel.

Appendix

293

Proof of Lemma 10.3 We assume that the subcarrier pair (i, p) is used for transmission in the first and second time slots through relay m for user k. Then, the outage probability in C2 (t,k ) for the UL data rate rU L m ,i,p is given by ⎤ ⎡ 1 (t,k ) (t,k ) Pr ⎣rU L m ,i,p > log2 1 + ΛUL m ,i,p |Ξm ⎦ 2 6 5 (t) (t) (t) (t) z(lB R m |HB R m ,i |2 + lB R m |HB R m ,p |2 ) (t,k ) 2 = Pr |HU R m ,i | ≤ |Ξm (t) (t) (t,k ) (lB R m |HB R m ,p |2 − z)lU R m (t) (t) (t) (t) z(lB R m |HB R m ,i |2 + lB R m |HB R m ,p |2 ) (t,k ) (10.39) = FU R m ,i (t) (t) (t,k ) (lB R m |HB R m ,p |2 − z)lU R m (k )

(t,k )

(t,k )

where z = 2(22r m , i , j − 1)/Pm ,i,p , and FU R m ,i (·) denotes the CDF of a noncentral chi-square random variable with two degrees of freedom and noncentrality (k ) 2 ˆ (t,k ) |2 /σ 2 (t). Note that P (t,k ) l(t) |H (t) parameter |H e U R m ,i R m ,p B R m B R m ,p | > z since rm ,i,j will not exceed the channel capacity of the BS-to-relay links as the corresponding perfect CSI is available at the scheduler. Using the above result, the target outage probability in constraint C2 in (10.18) is equivalent to (t) (t) (t) (t) z(lB R m |HB R m ,i |2 + lB R m |HB R m ,p |2 ) (t,k ) = ε (10.40) C2 ⇒ FU R m ,i (t) (t) (t,k ) (lB R m |HB R m ,p |2 − z)lU R m (t)

⇒ ⇒

(t)

(t)

(t)

z(lB R m |HB R m ,i |2 + lB R m |HB R m ,p |2 ) (t) (lB R m

(t) |HB R m ,p |2

−

(t,k ) z)lU R m

−1(t,k )

= FU R m ,i (ε)

(t,k ) (t,k ) rU L m ,i,p = log2 1 + ΛUL m ,i,p ,

−1(t,k )

(t,k )

where FU R m ,i (·) represents the inverse function6 of FU R m ,i (·). On the other (t,k )

hand, in order to obtain the DL data rate rD L m ,i,p which incorporates outage, we need first to derive the PDF of the outage event. For the case of i = p, since there is only one random variable in the view of the scheduler, we can use the same approach as for the UL to find the outage incorporated data rate. (t,k ) (t,k ) For the case of i = p, we first define random variables Xm ,p = |HU R m ,p |2 and (t,k )

(t,k )

Ym ,i = |HU R m ,i |2 , which are noncentral chi-square distributed with two degrees ˆ (t,k ) |2 and s2y = |H ˆ (t,k ) |2 , and of freedom, noncentrality parameters s2x = |H U R m ,p

U R m ,i

variances σx2 and σy2 , respectively. Conditional on the power allocation variables, the CSI of the BS-to-relay link and the imperfect CSI of the relay-to-user link, upon rearranging terms, the outage probability of the DL transmission is given 6

The inverse of the noncentral chi-square CDF is commonly implemented as an inbuilt function in software such as MATLAB.

294


by

= ⎛= > (t,k ) (t,k ) ⎞ > (t,k ) (t,k ) (t,k ) > m ,i ηm ,i,p > m ,i lU R Xm ,p m ⎠ < ? (t,k ) Pr ⎝? (t,k ) (t,k ) (t,k ) (t,k ) m ,i + θm ,i Ym ,i m ,i − ηm ,i,p = ⎛ > (t,k ) (t,k ) ⎞ (t,k ) > m ,i ηm ,i,p Am ,i,p ⎠, = Pr ⎝ (t,k ) < ? (t,k ) (10.41) (t,k ) Bm ,i,p m ,i − ηm ,i,p @ @ (t,k ) (t,k ) (t,k ) (t,k ) (t,k ) (t,k ) (t,k ) (t,k ) Am ,i,p = m ,i lU R m Xm ,p , Bm ,i,p = m,i + θm,i Ym,i ,

where (t,k )

(t,k ) (t)

(t)

m ,i = αm ,i lB R m |HB R m ,i |2 , (t,k )

(t ,k )

(t,k )

(t,k )

ηm ,i,p = (22r D L m , i , p − 1)2/Pm ,i,p ,

(t,k )

(t,k )

(t,k )

and

(t,k )

θm ,i =

(t,k )

(1 − αm ,i )lU R m . Note that in (10.41) m ,i > ηm ,i,p as rD L m ,i,p will not exceed the channel capacity of the BS-to-relay links since the corresponding perfect (t,k ) (t,k ) (t,k ) (t,k ) CSI is available at the schedulers. Let ZU R m ,i,p = Am ,i,p /Bm ,i,p , where Am ,i,p (t,k )

and Bm ,i,p are Rician random variables with two degrees of freedom, noncen(t,k ) (t,k )

(t,k )

(t,k )

trality parameters s2a = m ,i lU R m s2x and s2b = m ,i + θm ,i s2y , and variances (t,k ) (t,k )

(t,k )

σa2 = ( m ,i lU R m )2 σx2 and σb2 = (θm ,i )2 σy2 , respectively. Thus, the CDF of (t,k )

ZU R m ,i,p , which is the ratio of two independent nonidentical Rice distributed random variables, is (t,k )

FU R m ,i,p (z) = Q(c, d) − (σa2 c2 /s2b z 2 ) exp (−(c2 + d2 )/2)I0 (cd)

(10.42)

for z ∈ R+ , where c = (s2b z 2 /(σb2 z 2 + σa2 ))1/2 and d = (s2a /(σb2 z 2 + σa2 ))1/2 . Thus, when combining (10.41) and the constraint C1 in (10.18), we can solve for (t,k ) rD L m ,i,p , which yields ⎛= ⎞ > (t,k ) (t,k ) > η m ,i m ,i,p (t,k ) ⎠=ε FU R m ,i,p ⎝? (t,k ) (t,k ) ( m ,i − ηm ,i,p ) (t,k ) (t,k ) −1(t,k ) Pm ,i,p m ,i (FU R m ,i,p (ε))2 1 (t,k ) ⇒ rD L m ,i,p = log2 1 + . (10.43) (t,k ) −1(t,k ) 2 2( m ,i + (FU R m ,i,p (ε))2 ) −1(t,k )

The inverse CDF FU R m ,i,p (ε) can be implemented as a look-up table or by using the bisection method for practical implementation.

Asymptotic analysis Here, we first show the asymptotic order growth of Rician and Rayleigh random variables, before we obtain the asymptotic order growth of the average system goodput for the PF scheduler. The order of growth of Rician fading coefficients with perfect CSIT and Rayleigh fading coefficients with imperfect CSIT can be derived by using Lemma 10.1. Suppose {h1 , h2 , . . . , hM } are M i.i.d. Rician random variables with Rician factor κ. Let a = κ/(1 + κ), v = 1/(κ + 1), and xi = |hi |2 . Then the set {x1 , x2 , . . . , xM } of the magnitude squared of the Rician

295

Appendix

random variables with PDF f (·) and CDF F (·) is twice differentiable for all x. Therefore, the limit of the reciprocal hazard function is given by [31] lim g(x) = lim

x→∞

x→∞

1 1 − F (x) ≈ f (x) v

(10.44)

which satisfies the sufficient condition in Lemma 10.1 and therefore xmax − lM converges to a Gumbel distribution in the limiting case of M → ∞. Then, solving F (lM ) = 1 − 1/M for lM , we obtain √ 2 v log M + a + O(log log M ). (10.45) lM = Therefore, the growth of xmax is given by O((log M )/(κ + 1)) for sufficiently −1(t,k ) large M . On the other hand, we consider FU R m ,i (ε), k ∈ {1, 2, . . . , KN } for nondelay-sensitive users as defined in Section 10.5.1. By adopting a framework similar to that in and applying Lemma 10.1, it can be shown that for CSIT −1(t,k ) error σe2 (t) ∈ [0, 1), the growth of max1≤k ≤K N FU R m ,i (ε) is given by variance O (1 − σe2 (t)) log KN for sufficiently large KN and the term (1 − σe2 (t)) acts as a penalty on the multiuser diversity gain due to imperfect CSIT for σe2 (t) ∈ [0, 1). Remark 10.1 Since we are interested in the asymptotic performance of the PF scheduler with long-term fairness, the selection of the relay-to-user links will be based on the i.i.d. small-scale fading coefficients only [29], and thus, the extreme value theory for i.i.d. random variables is applicable. Therefore, by considering only the first order growing terms, the asymptotic order growth of the average weighted system goodput is given by Ugoodput (P, R, S)

=

nF nF ,k ) M F w (k ) s(t m ,i,p 2Fn F m = 1 k ∈N t = 1 i = 1 p = 1 m

⎧ ⎛ ⎛ ⎞⎞ (t , k ) (t , k ) (t , k ) (t ) ⎨ Pm , i , p (1 − αm , i )lU R m (1 − σe2 (t))(log KN )lB R m (log M/(κ + 1)) ⎠⎠ × O⎝log2 ⎝ (t , k ) (t ) (t , k ) (t , k ) ⎩ 2 (1 + αm , i )lB R m (log M/(κ + 1)) + (1 − αm , i )lU R m (1 − σe2 (t)) log KN ⎛ ⎛ ⎞⎞⎫ (t , k ) (t , k ) (t ) (t , k ) ⎬ Pm , i , p αm , i lB R m (log M/(κ + 1))lU R m (1 − σe2 (t)) log KN ⎠⎠ +O ⎝log2 ⎝ (t , k ) (t ) (t , k ) (t , k ) ⎭ 2 α l (log M/(κ + 1)) + (2 − α )l (1 − σ 2 (t)) log K m ,i

B Rm

m ,i

U Rm

e

N

(10.46)

where Nm = Um ∩ N is the intersection of sets Um and N . We are now ready to derive the results of Case I and Case II. Case I (Asymptotic system goodput for a large number of non-delay-sensitive users KN and a growing number of relays M ) In this case, we assume that the number of non-delay-sensitive users KN is always larger than the number of relays M and KN grows with M such that limK N ,M →∞ KN /M → ∞. By only considering the first order growing terms, the growth of the average system

296


goodput is given by Ugoodput (P, R, S) (a)

≈

(t,k ) nF nF M F w(k ) sm ,i,p m =1 k ∈Nm t=1 i=1 p=1

(b)

=

log M , O log2 κ+1

2Fn F

× O 2 log2

(t,k ) (t)

Pm ,i,p lB R m (log M/(κ + 1)) 2

(10.47)

where (a) is due to the assumption that limK ,M →∞ K/M → ∞ and (b) is because the channel coefficients of the BS-to-relay links are identical distributed since the distances between the BS and relays are assumed to be same. Case II (Asymptotic system goodput for a large number of relays M and a growing number of non-delay-sensitive users KN ) In this case, we assume that the number of relays M is always larger than the number of users KN and M grows with KN such that limK N ,M →∞ M/KN → ∞. By replacing the channel gain variables with the associated asymptotic growth expression, we obtain the growth of the average system goodput which is given by Ug oodpu t (P, R, S) (c)

≈

(t,k ) nF nF M F w(k ) sm ,i,p m =1 k ∈Nm t=1 i=1 p=1

(d)

≈

2Fn F

× O 2 log2

(t,k ) (t,k )

Pm ,i,p lU R m ((1 − σe2 (t)) log KN ) 2

O log2 (1 − σe2 (F × τ )) log KN ,

(10.48)

where (c) is due to the assumption that limK N ,M →∞ M/KN → ∞ and (d) is due to the fact that the growth of the system goodput is limited by the largest CSIT estimation error variance. It can be observed that in both Case I and Case II, the two-way relay compensates the loss of spectral efficiency due to half-duplexing, i.e., the prelog factor 1 2.

Derivation of feedback condition Let Θth be the threshold representing the global subcarrier usage and replacing (γi + βi ) in (10.30). Furthermore, assume that the SNR is high such (t,k ) (t,k ) (t,k ) (t,k ) that ΛULm ,i,i /(1 + ΛULm ,i,i )+ΛDLm ,i,i /(1 + ΛDLm ,i,p ) ≈ 2 in (10.30). With these (k )

assumptions and sm ,i,j = 1, based on (10.30), we can establish the following (t,k )

upper bound for 0 < αm ,i < 1, which is given by 2 log2

(t,k ) (t,k ) (t,k ) ΛDL m ,i,i ΛUL m ,i,i Pm ,i,p (t,k ) −1(t,k ) (t,k ) lU R m FU R m ,i (ε) − 2 ≥ C˜m ,i,i − − (t,k ) (t,k ) 2 1 + ΛDL m ,i,i 1 + ΛUL m ,i,i ≥

2Θth . (wk + δk )(1 − ε)

(10.49)

References

297

The above upper bound has the same asymptotic order growth as Case II in Theorem 10.2, which suggests that the adopted upper bound is an appropriate choice. Furthermore, the user selection does not depend on the CSI of the BSto-relay link. Therefore, based on (10.49), the proposed user feedback criterion can be obtained as (t,k ) 4Θ th 4Θ th Pm ,i,p (a) 4nF +4 +4 (t,k ) −1(t,k ) ( w k + δ k ) ( 1 −ε ) ( w k + δ k ) ( 1 −ε ) 2 ≈ 2 , lU R m FU R m ,i (ε) ≥ 2 PT (10.50) where (a) is due to the fact that the users do not know the final power allocation before the schedulers perform the resource allocation, and hence equal power allocation is assumed for user selection.

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[12] B. Rankov and A. Wittneben, “Spectral efficient protocols for half-duplex fading relay channels,” IEEE J. Select. Areas in Commun., 25 (2007), 379– 389. [13] T. J. Oechtering, C. Schnurr, I. Bjelakovic, and H. Boche, “Broadcast capacity region of two-phase bidirectional relaying,” IEEE Trans. Inform. Theory, 54 (2008), 454–458. [14] A. S. Avestimehr, A. Sezgin, and D. N. C. Tse, “Approximate capacity of the two-way relay channel: A deterministic approach,” in Proc. of IEEE 46th Annual Allerton Commun., Control, and Computing, 2008, pp. 1582–1589. IEEE, 2008. [15] B. Rankov and A. Wittneben, “Achievable rate regions for the two-way relay channel,” in Proc. of IEEE Int. Symp. on Inform. Theory, 2006, pp. 1668–1672. IEEE, 2006. [16] D. W. K. Ng and R. Schober, “Cross-layer scheduling for OFDMA amplifyand-forward relay networks,” IEEE Trans. Vehi. Technology, to appear. [17] G. D. Yu, Z. Y. Zhang, Y. Chen, S. Chen, and P. L. Qiu, “Power allocation for non-regenerative OFDM relaying channels,” in Proc. of IEEE Int. Conf. on Wireless Commun., Networking and Mobile Computing, 2005, pp. 185– 188. IEEE, 2005. [18] Y. Li, W. Wang, J. Kong, W. Hong, X. Zhang, and M. Peng, “Power allocation and subcarrier pairing in OFDM-based relaying networks,” in Proc. of IEEE Int. Conf. on Commun., 2008, 2602–2606. IEEE, 2008. [19] C. Comaniciu, N. B. Mandayam, and H. V. Poor, Wireless Networks: Multiuser Detection in Cross-Layer Design. 1st ed. Springer, 2005. [20] G. Song and Y. Li, “Cross-layer optimization for OFDM wireless networksPart I: theoretical framework,” IEEE Trans. Wireless Communications, 4 (2005), 614–624. [21] D. P. Palomar and M. Chiang, “A tutorial on decomposition methods for network utility maximization,” IEEE J. Select. Areas in Commun., 24 (2006), 1439–1451. [22] M. Tao, Y. C. Liang, and F. Zhang, “Resource allocation for delay differentiated traffic in multiuser OFDM systems,” IEEE Trans. Wireless Commun., 7 (2008), 2190–2201. [23] G. Caire, G. Taricco, and E. Biglieri, “Optimum power control over fading channels,” IEEE Trans. Inform. Theory, 45 (1999), 1468–1489. [24] R. Narasimhan, “Finite-SNR diversity-multiplexing tradeoff for correlated Rayleigh and Rician MIMO channels,” IEEE Trans. Inform. Theory, 52 (2006), 3965–3979. [25] R. Knopp and P. A. Humblet, “Information capacity and power control in single-cell multiuser communications,” in Proc. of IEEE Int. Conf. on Communications, 1995, pp. 331–335. IEEE, 1995. [26] G. Song and Y. Li, “Asymptotic throughput analysis for channel-aware scheduling,” IEEE Trans. Commun., 54 (2006), 1827–1834.

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[27] M. Sharif and D. Hassibi, “On the capacity of MIMO broadcast channels with partial side information,” IEEE Trans. Inform. Theory, 51 (2005), 506–522. [28] H. A. David Order Statistics. 1st ed. Wiley, 1970. [29] G. Caire, R. R. Muller, and R. Knopp, “Hard fairness versus proportional fairness in wireless communications: The single-cell case,” IEEE Trans. Inform. Theory, 53 (2007), 1366–1385. [30] IEEE 802.16m System Description Document [Draft]; 2009. Available: http://wirelessman.org/tgm/docs/80216m-08 003r9a.doc.zip [31] P. Viswanath, D. N. C. Tse, and R. Laroia, “Opportunistic beamforming using dumb antennas,” IEEE Trans. Inform. Theory, 48 (2002), 1277–1294. [32] K. Jitvanichphaibool, R. Zhang, and Y. C. Liang, “Optimal resource allocation for two-way relay-assisted OFDMA,” IEEE Trans. Vehi. Technology, 58 (2009), 3311–3321. [33] C. K. Ho, R. Zhang, and Y. C. Liang, “Two-way relaying over OFDM: Optimized tone permutation and power allocation,” in Proc. of IEEE Int. Conf. on Commun., 2008, pp. 3908–3912. IEEE, 2008. [34] S. Sanayei and A. Nosratinia, “Opportunistic downlink transmission with limited feedback,” IEEE Trans. Inform. Theory, 53 (2007), 4363–4372. [35] X. J. Zhang and Y. Gong, “Adaptive power allocation in two-way amplifyand-forward relay networks,” in Proc. of IEEE Int. Conf. on Commun., 2009. IEEE, 2009. [36] M. Chen and A. Yener, “Power allocation for multi-access two-way relaying,” in Proc. of IEEE Int. Conf. on Commun., 2009. IEEE, 2009. [37] H. A. Suraweera, R. H. Y. Louie, Y. Li, G. K. Karagiannidis, and B. Vucetic, “Two hop amplify-and-forward transmission in mixed Rayleigh and Rician fading channels,” IEEE Commun. Letters, 13 (2009), 227– 229. [38] J. G. Proakis, Digital Communications. 4th ed. McGraw Hill Higher Education, 2000. [39] G. Song and Y. Li, “Cross-layer optimization for OFDM wireless networkspart II: Algorithm development,” IEEE Trans. Wireless Commun., 4 (2005), 625–634. [40] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge University Press, 2004. [41] S. Boyd, L. Xiao, and A. Mutapcic, Subgradient Methods. Notes for EE392o Stanford University Autumn. 2003–2004. [42] Spatial Channel Model for Multiple-Input Multiple-Output (MIMO) Simulations. 3GPP TR 25.996 V7.0.0 (2007–06).

11 Green communications in cellular networks with fixed relay nodes Peter Rost and Gerhard Fettweis

11.1

Introduction Mobile communication systems have to provide exponentially increasing data rates for an increasing number of subscribers using ubiquitous data services. As the capacity per cell is limited by the available bandwidth, the same time– frequency resources must be spatially reused. Hence, the more the user density increases, the higher the spatial reuse must be to satisfy the demand for high data rate services. This chapter discusses relaying as a candidate technology to increase the spatial reuse and therefore to provide the required data rates while reducing energy consumption in mobile communication systems.

11.1.1

Two motivating examples A challenging property as well as an opportunity for exploiting the wireless channel is nonlinear signal attenuation (path-loss), which offers the possibility to concentrate power at certain points in the network and spatially reuse resources within a mobile communication network. Consider an additive white Gaussian noise (AWGN) channel with a path-loss exponent α = 4, receiver noise power N , and transmission power P . Given these qualities and assuming a downlink transmission where a terminal can use the received signals from each radio access point (RAP), the observed signal-to-noise ratio (SNR) at a normalized distance d is given by ρ(d) = i P/N · |di − d|−α , where di is the position of the ith RAP. Figure 11.1 compares the received SNR in two different configurations of a one-dimensional wireless network: A: RAPs are deployed PA such that PA /N B: RAPs are deployed PB such that PB /N

at di = [0, 3, 6, . . . , i · 3] and each transmits with power = 10 at di = [0, 2, 4, . . . , i · 2] and each transmits with power = 2.

Configuration B increases the RAP density by a factor of 1.5 compared to configuration A but its RAPs transmit with only one-fifth the power PA . Therefore, Cooperative Cellular Wireless Networks, eds. Ekram Hossain, Dong In Kim, and Vijay K. Bhargava. Published by Cambridge University Press. C Cambridge University Press, 2011.

11.1 Introduction

10

0 (a)

20

ρ(d) (dB)

ρ(d) (dB)

20

301

0

2 4 6 8 10 (b) Normalized distance d

10

0

0

2 4 6 8 Normalized distance d

10

Figure 11.1. Spatial power distribution for two different deployment scenarios: (a) configuration A; (b) configuration B.

the total energy consumption in configuration B is less than half of the energy consumption in configuration A, but both achieve the same minimum SNR. In addition to the lower energy consumption, configuration B provides a higher density of RAPs and therefore also a higher spatial reuse, which potentially increases the overall system throughput. Consider a similar setup with two RAPs, which are placed at distance d from each other, and one user terminal (UT), which is placed at distance ∆d, ∆ < 0.5, from its serving RAP. The signal-to-interference-and-noise ratio (SINR) experienced at the UT is given by ρA =

P (∆d)−α . N + P ((1 − ∆)d)−α

(11.1)

Let configuration B again use a higher RAP density, i. e., dA > dB , and let the sum power spent in both configurations be normalized, i. e., the transmission power per node in configuration B is given by P · dB /dA . The ratio of the SINR received at the user terminal in the configurations is given by 1−α dA + P /N ((1 − ∆)dA )−α ρA dB = < 1. (11.2) ρB 1 + P /N ((1 − ∆)dA )−α The probability that a UT experiences a certain ∆ is the same for both scenarios, which implies that even though we move RAPs closer to each other and only exploit the signal received from the assigned RAP, we increase the SINR (in this linear model). In next generation cellular systems not only will the distance between two RAPs decrease but also the carrier frequency will increase. Therefore, in the interference-limited regime (P N ) let dA = dB and αA < αB in

302


order to account for the higher path-loss at higher carrier frequencies: ρA = ρB

∆ 1−∆

α B −α A < 1.

(11.3)

Hence, if we use a higher carrier frequency and move RAPs closer to each other we are able to improve the observed SINR and the spatial reuse of resources.

11.1.2

Scope and key problems These examples illustrate that densely deployed networks potentially provide higher data rates while requiring less transmission energy. In addition, future networks face the challenge of connecting RAPs through a backhaul using outof-band resources in order to exploit interfering signals. Backhaul requirements such as the availability of a high-speed wired connection or microwave links to a central server diminish the deployment flexibility and raise necessary expenditures. Hence, deployment and transmission strategies in next generation networks should be able to mitigate intercell interference and increased deployment costs due to the higher RAP density. In this chapter, we investigate relaying as an opportunity to increase the RAP density in a next generation mobile communication system operating at a carrier frequency of about 4 GHz. Future wireless networks are likely to use multicell multiple-input multiple-output (MIMO) where multiple RAPs cooperatively serve UTs. More specifically, techniques introduced in the context of the MIMO broadcast channel (BC) [1, 2] and MIMO multiple access channel (MAC) [3, 4] are applied to an array of physically separated antennas. Multicell MIMO is able to (partly) cancel interference and to provide an additional array gain. However, in addition to high-quality channel state information (CSI), it requires the exchange of user data over a high-performance backhaul link. In this chapter different aspects of a mobile communication system, which uses both multicell MIMO for interference cancelation and relaying in order to improve the spatial resource reuse, are analyzed and discussed. Studies have shown that the energy consumption in cellular networks already represents a major cost driver, which emphasizes that decreasing the systemwide energy consumption is not only of ecological but also economical interest. In a mobile communication system, we distinguish between the energy consumed by the RF frontend (transmission power) and the energy required for signal processing as well as encoding and decoding (computation power). It does not suffice to solely reduce the transmission power by using (almost) capacity-achieving codes and decoding algorithms, which imply that the additional computation power required outweighs the reduced transmission power [5]. Our goal is to employ low-complexity approaches, which provide a higher throughput while reducing the overall energy spent in the system. The scope of this chapter is the analysis of the cost–benefit tradeoff in relay networks as well

11.2 System model

303

as the tradeoff between computation power, transmission power, and the system performance.

11.1.3

Outline and contributions We explore system architectures based upon the transmission schemes introduced in [6] and apply these techniques to two major scenarios: the wide-area scenario and the Manhattan-area scenario. While previous work considered either downlink or uplink performance, we analyze both jointly. As previously mentioned, the key to green communication is to use low-complexity algorithms as well as to reduce the overall consumed transmission energy. In order to show how conventional and relay-based systems perform with less complex encoding and decoding algorithms, we provide results for different SNR gaps [7, p. 66]. The SNR-gap approximation applies a constant SNR scaling under the assumption that for the considered SNRs the difference between the employed encoding/decoding scheme and the maximum achievable rate is only an SNR shift. Furthermore, we compare femto-cells with high data-rate infrastructure connection and relaying where only in-band connections are available. Each additional relay node (RN) implies additional costs for the deployed system but also provides a performance gain for its users. This relation is examined using a cost– benefit tradeoff analysis, which compares the system performance under a cost constraint. In Section 11.2, we introduce the considered system model and we review the most important parameters of the physical layer. In Section 11.3 we discuss the system and protocol design, and summarize the approaches for the considered mobile communication system. The main part is the discussion of numerical results in Section 11.4. Section 11.5 concludes the chapter.

11.2

System model

11.2.1

Propagation scenarios Our analysis in Section 11.4 is based on two propagation scenarios, which were defined by the European research project WINNER: a macrocellular deployment (referred to as wide-area) and a microcellular deployment (referred to as Manhattan-area) [8]1 . Figure 11.2(a) illustrates the wide-area scenario with uniformly deployed sites at an intersite distance dis,r ef = 1000 m. At each site three base stations (each indicated by “BS”) serve three adjacent sectors, each supported by two fixed RNs (indicated by triangles). Each BS uses a directed antenna (main lobe directions are indicated by arrows) with a downtilt of 5 degrees and an antenna attenuation at an enclosed angle of ϕ given 1

All the WINNER documents referred to are publicly available on http://www.ist-winner.org.

304


BS BS BS

BS BS

BS BS BS

BS BS BS

BS

BS

BS BS BS

BS

BS BS BS

BS BS

30 m

BS BS BS

BS BS

BS

BS BS

BS BS BS

BS

(a)

BS

200 m

BS

(b)

Figure 11.2. The two reference scenarios considered in this chapter: (a) widearea scenario with one tier of interfering sites. Triangles indicate relay nodes and arrows the main lobe direction in each cell; (b) Manhattan-area scenario as defined in [9]. Triangles indicate outdoor relays and squares indoor relays.

by 12 (ϕ/70)2 dB. Throughout our analysis, we consider only the performance results for the central site, which is surrounded by 18 interfering sites. We randomly place users according to a uniform distribution and an average density of 90 users per square kilometer [10]. Users are assigned to RAPs based on their path-loss to the respective base station (BS) or RN. Due to the path-loss-based cell assignment, the actual instantaneous cell layout may differ from the regular layout in Figure 11.2(a). Figure 11.2(b) illustrates the second scenario and its regular street grid as originally defined by the UMTS 30.03 recommendation [9]. In contrast to the widearea scenario where BSs employ directed antennas, omni-directional antennas are used in the Manhattan scenario. Each BS is supported by four RNs of which two are placed indoors (indicated by a square) and two are placed outdoors (indicated by a triangle). Both outdoor and indoor RNs are able to increase a user’s line-of-sight (LoS) probability with its assigned RAP and therefore promise, in particular, to improve data rates indoors, which has been previously demonstrated using field trial results in [11]. The numerical results in Section 11.4 only include the inner three BSs, which are surrounded by 44 interfering cells. User terminals are again randomly placed on streets and within buildings according to a uniform distribution with an average density of 250 users per square kilometer [10]. For each different link between user terminals and RAPs, an LoS probability, a path-loss model, and a power delay profile are defined in [12] for the small-scale

11.2 System model

305

Table 11.1. Used channel models, which are defined in [12] Link BS to RN BS to indoor UT BS to outdoor UT RN to indoor UT RN to outdoor UT Indoor RN to indoor UT

Manhattan-area

Wide-area

B5c B4 B1 B4 B1 A1

B5a C2 C2

fading process, where each tap is assumed to be Gaussian distributed. Table 11.1 lists the channel models, which are used for the numerical evaluation.

11.2.2

Air interface and scheduling Both the wide-area and the Manhattan-area scenario use orthogonal frequencydivision multiple access (OFDMA) [13, 14] at a carrier frequency fc = 3.95 GHz. The system resources are divided in resource blocks of 15 OFDM symbols and 8 subcarriers. Uplink and downlink operate in time-division duplex (TDD) such that the whole bandwidth is alternately occupied by either uplink or downlink (which are separated by a duplex guard of 8.4 µs). Two consecutive resource blocks are assumed to be time-invariant, i.e., we model no Doppler spread resulting from user mobility. Therefore, both uplink and downlink experience the same channel realizations but use a separate radio resource management (RRM). All individual channel models for each link are listed in Table 11.2 and are described in detail in [8]. In order to use the relevant capacity expressions defined in [6], we assume throughout our analysis Gaussian alphabets, perfect rate adaptation, and very large blocklengths. Nonetheless, in order to achieve realistic results we consider a rate clipping at 8 bits per channel use (bpcu) or (bits/symbol) enforced by a corresponding SNR clipping at 28 − 1. We assume that CSI is perfectly available at the receiver as well as at the BS in the downlink. Furthermore, the system is perfectly synchronized. Each transmitter is assumed to have a full queue, which implies that each node transmits at the maximum rate and exploits all available resources. Both scenarios deploy half-duplex RNs, which are connected to their assigned BS using an in-band feederlink operating on the same time–frequency resources as UTs. Furthermore, it might happen that in the downlink an unexpected high throughput between the RN and UTs cannot be supported due to insufficiently filled relay buffers (and similarly in the uplink between the RN and BS). Hence, relay buffer management is an important part of the system in order to guarantee

306


Table 11.2. Parameters of the underlying WINNER system used for the numerical evaluation User density Average no. users/cell Channel models Number of antennas BS/RN/UT BS transmit power RN transmit power RN transmit power UT noise figure Noise power spectral density FFT size Carrier frequency System bandwidth OFDM symbol duration Superframe duration Guard interval Used subcarriers Channel state information

90 per km2 in wide-area, 250 per km2 in Manhattan-area 26 in wide/Manhattan-area As defined in 4/1/1 46 dBm 37 dBm 24 dBm 7 dB −174 dBm/Hz 2048 3.95 GHz 100 MHz 20.48 µs 5.89 ms 2.00 µs [−920; 920] \ {0} Assumed to be perfectly known at transmitter and receiver

that all resources are exploited while keeping the latency as low as possible. Due to the assumption of perfect rate adaptation in our system, we do not consider any automatic repeat-request (ARQ) protocols.

11.3

System and protocol design Assume that two BSs are connected by a high-performance backhaul that does not limit the data exchange between them. Both BSs can be regarded as one virtual antenna array, which realizes an interpath cooperation based on the same approaches as introduced in the context of the BC. Since RNs are not connected to the backhaul, they implement interpath coordination approaches as introduced in the context of the interference channel (IC) [15, 16]. The relay-interference channel combines both models and has been used in [6] to derive and evaluate strategies for a relay-assisted cellular system. In this chapter, we briefly discuss these strategies and apply them to the presented scenarios. However, we do not

11.3 System and protocol design

307

consider intersubsystem cooperation where signals transmitted from the BS and the RN are combined, i.e., cooperative relaying [17].

11.3.1

Non-relaying protocols Conventional mobile communication systems such as GSM and UMTS do not provide the possibility of interpath cooperation but solely coordinate their resources. However, the spatial resource reuse can be improved if all BSs use the same resources to serve UTs experiencing a high SINR (cell-center users) while all other UTs are served using orthogonal resources (cell-edge users) [18]. The actual assignment of users to the individual groups is based upon the expected longterm downlink SINR, which is assumed to be perfectly known. In our analysis, all users with an SINR below 10 dB [19] are assigned to the cell-edge group and all other users are regarded as cell-center users. Such a protocol requires intercell coordination because a change of the resource assignment at one BS directly affects the SINR experienced at UTs assigned to other BSs. As the density of nodes increases, this resource coordination becomes even more complicated using the described conventional protocol. One way to improve the SINR for users suffering from high intercell interference is to employ multicell MIMO transmission approaches [20, 21], which improve the performance by investing in computation power instead of transmission power. The idea of multicell MIMO transmission is that multiple BSs can build one virtual antenna array and exploit interference using coherent transmission. It was shown in [1, 2] that dirty paper coding (DPC) [22] is the capacity approaching strategy for the downlink scenario. In the uplink, multicell MIMO can be regarded as a MIMO-MAC between UTs in different cells and the assigned BSs. For this scenario, the capacity is known [3, 4] and is achieved by successive interference cancelation (SIC), which assumes perfect rate adaptation in order to cancel interference. Furthermore, the application of SIC based on the (quantized) received signal of other BSs again requires a high data-rate backhaul. If the channel is changing quickly, the CSI feedback delay causes a significant performance loss [23] for downlink multicell MIMO transmission. Furthermore, using multicell MIMO requires a very-high-performance backhaul for both uplink and downlink to exchange parts or complete user data in addition to the CSI [21, 24]. In our analysis, we assume that all BSs are connected by an unconstrained backhaul link, which provides the means to exchange user data, unquantized received signals, and perfect channel state information at the transmitter (CSIT). However, we show how the performance is affected in a scenario without intercell backhaul links where only BSs at the same site cooperate.

11.3.2

Relay-only protocol One key problem of nonrelaying protocols is a strongly nonuniform power distribution. A more uniform power distribution is the requirement to lower the

308


system-wide spent transmission energy. Multicell MIMO improves the power distribution by exploiting interfering signals, which otherwise worsen the SINR particularly at the cell edge. An alternative is to increase the RAP density while still keeping the computational overhead reasonably low, for instance using RNs, which aggregate data of multiple users and forward the data to the BSs. If RNs employ low-complex algorithms, not only the transmission power but also the computation power can be decreased. Otherwise, the saved transmission power is traded for computation power, which is then spatially distributed among the RNs. Our analysis considers a protocol in which all users are served by RNs, which employ Han–Kobayashi (HK) coding [25] on the RN-to-UT links. In a halfduplex relay-based system, the in-band feederlink 2 represents the bottleneck, as it reduces the amount of available resources for the R−D links. Based on the results in [6, 26], we assume that RNs are served using multicell MIMO. In comparison to multicell MIMO between BSs and UTs, the signaling overhead is reduced as relays are stationary and can be placed such that they experience a strong LoS towards the base station. This implies a higher coherence bandwidth and coherence time, which allow less complex algorithms. Furthermore, the introduction of RNs might allow a lower density of BSs, which reduces the backhaul requirements, initial deployment costs, and the system-wide spent computation energy.

11.3.3

An integrated approach Users in the cell center of their assigned BS are likely to experience an LoS link towards the BS without strong multipath fading. Hence, for those users the feedback overhead can be reduced by serving them without multicell MIMO or using multicell MIMO involving only BSs at one site. Our analysis considers a simple protocol supporting both multicell MIMO and relaying in order to exploit the benefits of both protocols and to reduce the signaling overhead for multicell MIMO. We constrain the system such that either multicell MIMO or relaying is used on the same time–frequency resource within one cell and the resource assignment to the individual protocols is done adaptively using a fair scheduler. Such an approach is scalable as it exploits relaying for coverage extension and supports multicell MIMO if only intercell interference cancelation is capable of providing the required data rates. Furthermore, since RNs can provide the same wireless interface as BSs, UTs need not implement relaying-specific functions, which reduces the required complexity at UTs and improves the legacy ability.

2

Note that we differentiate between the backhaul connecting multiple sites and in-band feederlinks, which connect BSs and RNs.

11.4 Numerical analysis

11.3.4

309

Simplifications In [2], it has been shown that DPC is the capacity achieving approach for the MIMO BC. However, it requires time-sharing of multiple-user orderings in which user streams are encoded and it also requires the optimization of the precoding matrix. In the case of per-antenna power constraints this is an extensive optimization with nondeterministic complexity [27, 28], which might not be realizable in a real-time system. In this work, we apply zero-forcing DPC (ZF-DPC) [29], which uses the LQ decomposition of the channel matrix. By precoding with the Hermitian of Q, the channel becomes a triangular matrix. Afterwards, DPC is applied such that individual interference-free links result and the power assignment is determined such that the antenna constraints are satisfied [30]. Similarly, at the BS the decoding process in the uplink is based on the QR decomposition. By multiplying the received signal with the Hermitian of Q, the resulting channel matrix is again a triangular matrix. Then, beginning with the first interference-free user stream, the decoder applies SIC in order to obtain interference-free links, which requires perfect rate adaptation in order to avoid error propagation. HK coding requires time-sharing of multiple power assignments, which are difficult to determine in real time. Therefore, we apply Etkin–Tse–Wang (ETW) coding [31], which provides a rule for determining the power levels of common and private messages, and guarantees rates within 1 bpcu of capacity. Applying ETW coding based on the fast-fading information requires a recomputation of the power levels in every frame as well as a significant signaling overhead. Hence, instead of using the fast-fading information, we use the long-term SINR statistics to determine the common and private message power level.

11.4

Numerical analysis The previous sections introduced different approaches for the integration of multicell MIMO transmission and relaying in a next generation mobile network (NGMN). This section presents numerical results for the wide-area and Manhattan-area scenarios in order to demonstrate how both approaches affect the system performance. In particular, we discuss first the ability to counteract inter-cell and intracell interference and how the indoor service quality is affected by relaying. We further evaluate the energy performance and cost–benefit tradeoff of a relay-assisted system, where the provided performance gains are compared based on normalized energy consumption and normalized expenditures.

11.4.1

Simulation methodology The previously presented protocols are analyzed using a snapshot-based systemlevel simulation. Instead of explicitly modeling the user mobility, it models the

310


Table 11.3. Numerical results for the wide-area scenario using in-band feederlinks and full inter-site cooperation Scenario/protocol

θ (MBit/s)

σ (MBit/s)

θ5% (MBit/s)

Downlink

Conventional Multi-cell MIMO 2 Relays, relay-only 2 Relays, mixed

1.3 2.4 3.4 4.9

2.4 3.0 3.1 3.9

2.3 · 10−2 0.2 5.9 · 10−2 0.7

Uplink

Conventional Multi-cell MIMO 2 Relays, relay-only 2 Relays, mixed

0.1 0.2 2.1 3.0

0.5 0.6 2.5 3.0

4.3 · 10−4 3.7 · 10−3 1.8 · 10−2 0.1

effects of user mobility on the experienced channel. For each placement of a group of users and for each frame consisting of 16 OFDM symbols we randomly generate an independent channel realization and perform the resource assignment as well as user scheduling. Block-fading models the situation in which users experience slowly varying channels but the connection spans multiple blocks with independent channel realizations. Due to the fact that we do not explicitly consider user mobility, we also do not have a continuous user context to which the scheduling can be applied. Hence, we partition the overall area into rectangles of equal size, i. e., in the wide-area scenario they are of size 30 m × 30 m and in the Manhattan-area scenario they are of size 10 m × 10 m. For each snapshot consisting of 16 frames, i. e., 256 OFDM symbols, users are randomly placed according to a uniform distribution. Then, for each individual user the corresponding spatial block (x, y) is determined. In order to obtain sufficient statistics, we keep track of all results for all users, such as the average throughput θ(x, y) = Et {θ(x, y, t)}, which is used by a fair scheduler to determine the number of resources of a user placed in spatial block (x, y). More −1 specifically, the number of resources is proportional to θ (x, y). Alternatively, we could use the 5% quantile of throughput θ5% , with Pr {θ(x, y, t) ≤ θ5% } ≤ 5%. In this case, a user with a highly varying performance would receive even more resources at the expense of other users’ performance.

11.4.2

Throughput performance in the wide-area scenario We analyze the ability of relaying and multi-cell MIMO to mitigate and cancel intercell interference in the macrocellular wide-area scenario. Consider Figure 11.3, which shows the cumulative distribution function (CDF) of θ(x, y, t) over all analyzed user snapshots. In addition, Table 11.3 lists the average

311

+

+ 10-1

+

+

Pr {θ(·, ·) ≤ θ}

+

+

100

+


10-2 10-2

10-1

(a)

Conventional Virtual MIMO 2 Relays, relay-only 2 Relays, mixed

100 101 Throughput θ in MBit/s

+ 10-2 10-3

(b)

10-2

+

+

10-1

+

Pr {θ(·, ·) ≤ θ}

+

+

+ + + +

100

102

Conventional Virtual MIMO 2 Relays, relay-only 2 Relays, mixed

10-1 100 Throughput θ in MBit/s

101

Figure 11.3. Marginal throughput for the wide-area scenario using in-band feederlinks and full intersite cooperation: (a) downlink; (b) uplink.

throughput θ, the 5% quantile throughput θ5% , and the standard deviation σ = Var{θ(x, y, t)} for both uplink and downlink. Multicell MIMO doubles the average throughput and improves the 5% quantile throughput by a factor of approximately 6. Due to the improved spatial reuse the cell throughput is increased (average throughput), and in addition due to the additional intercell interference cancelation as well as the array gain using coherent transmission the worst-user performance (5% quantile throughput) is significantly higher. Using the relay-only approach, the average throughput is further improved (by a factor

312


+ + + +

+

+

10-1

+

+

+

Pr {θ(·, ·) ≤ θ}

+

+

+

+ + + + + + +

100

10-2 10-5

10-4

10-3

10-2

10-1

Conventional Multicell MIMO Relay-only, 2 RNs Mixed, 2 RNs Relay-only, 4 RNs Mixed, 4 RNs

100

101

102

Throughput θ in MBit/s Figure 11.4. Marginal uplink throughput for the Manhattan-area scenario using in-band feederlinks. of 3 in the uplink) but the 5% quantile throughput does not improve alike (it even decreases in the downlink). Relay nodes only improve the path-loss and LoS conditions for cell-edge users and users close to a relay node. Users that are closer to the BS now suffer from a high path-loss, which causes a worse service quality for those users. By contrast, the mixed approach significantly improves both average and 5% quantile throughput and outperforms all other protocols. Users near a BS are directly served using multicell MIMO and users at the cell edge or close to a RN are served by relay nodes. The improved spatial reuse of resources using concurrently transmitting relays and the interference mitigation are able to outweigh the loss due to the half-duplex constraint. In this chapter we consider downlink and uplink separately using the marginal CDF of both although both directly affect each other. A joint uplink–downlink analysis taking into account how the net and the gross rate of uplink and downlink influence each other was given in [32].

11.4.3

Throughput performance in the Manhattan-area scenario The previous analysis showed that relaying improves both average throughput and worst-user throughput, in particular for those users at the cell edge. In a microcellular scenario such as the Manhattan-area scenario, we face the problem of providing high data rates for indoor users. Consider Figure 11.4 and Table 11.4, which show the uplink performance for the Manhattan-area scenario (the


313

Table 11.4. Numerical results for the Manhattan-area scenario using in-band feederlinks and full inter-site cooperation Scenario/protocol

θ (MBit/s)

σ (MBit/s)

θ5% (MBit/s)

Downlink

Conventional Multi-cell MIMO Relay-only, 2 RNs Relay-only, 4 RNs Mixed, 2 RNs Mixed, 4 RNs

0.8 0.6 0.5 5.4 1.2 5.8

2.1 1.1 1.0 10.6 2.5 13.0

1.6 × 10−4 1.3 × 10−3 4.0 × 10−4 0.2 2.1 × 10−3 0.2

Uplink

Conventional Multi-cell MIMO Relay-only, 2 RNs Relay-only, 4 RNs Mixed, 2 RNs Mixed, 4 RNs

0.2 0.2 0.4 5.3 0.9 5.7

0.8 0.8 1.0 10.4 2.5 12.0

4.4 × 10−6 3.0 × 10−5 2.0 × 10−5 0.1 7.4 × 10−5 0.2

downlink shows different quantitative but the same qualitative results as the uplink). Both conventional and multicell MIMO transmission are unable to provide fair and sufficient throughput results, particularly for users that are indoors. In contrast, relaying is able to significantly improve the worst-user performance and to deliver a sufficient service quality to indoor and outdoor users. Table 11.4 further highlights that the required performance is only provided by four RNs per cell of which two are indoors and two are outdoors. More specifically, the average rate is improved by a factor of 10 and the 5% quantile throughput by a factor of approximately 103 in the downlink and 104 in the uplink compared with the deployment without indoor relays. There is no significant difference between the performance of the relay-only and mixed approaches, which implies that the system could use only relays in a microcellular scenario and apply multicell MIMO exclusively to the links between BSs and RNs. Since four relays consume less transmission power than one BS (a difference of 3 dB in our setup), the average downlink transmission power is reduced in the relayonly setup. Moreover, the improved performance offers the possibility to use less complex algorithms, which require less computation power.

11.4.4

Femto-cells vs. relaying Femto-cells [33] have attracted significant attention as they provide an efficient way of improving coverage and high data rates for indoor users. Femto-cells are home-deployed by users and exploit the available wired network as the backhaul

314


Table 11.5. Numerical results for the Manhattan-area scenario and using femto-cells instead of in-band feederlinks Scenario/protocol

θ (MBit/s)

σ (MBit/s)

θ5% (MBit/s)

Downlink

Conventional Multi-cell MIMO Femto-only, 2 RNs Femto-only, 4 RNs Mixed, 2 RNs Mixed, 4 RNs

0.8 0.5 0.5 13.4 1.3 13.7

2.4 1.0 1.0 27.5 2.4 31.1

1.2 × 10−4 1.2 × 10−3 5.0 × 10−4 0.7 2.3 × 10−3 0.7

Uplink

Conventional Multi-cell MIMO Femto-only, 2 RNs Femto-only, 4 RNs Mixed, 2 RNs Mixed, 4 RNs

0.2 0.2 0.3 12.1 0.7 12.6

1.3 0.7 0.7 25.3 2.0 29.0

3.3 × 10−6 1.9 × 10−5 2.4 × 10−5 0.7 6.9 × 10−5 0.6

connection. Table 11.5 lists the numerical results for femto-cells using the same parameters as for the previous relay setup except for a perfectly operating backhaul that provides very high data rates to each RN and a perfectly operating relay buffer. The average throughput for the case of four RNs improves by a factor of approximately 2 due to the increased UT resources and the perfectly operating relay buffer. Furthermore, the 5% quantile throughput improves by a factor of 3–5 as a major part of the additional resources are employed for indoor users. The similar uplink and downlink performances suggest that a majority of the SINR values are cut at 8 bpcu. Hence, the higher transmission power in the downlink does not necessarily provide higher data rates, which implies that the relay-assisted network allows a lower RAP transmission power. Femto-cells do not improve the performance if only two outdoor RNs are deployed, which underlines that the major bottleneck is the high path-loss from outdoor BSs to indoor UTs. This supports the field trial results presented in [11], which show significant performance gains for a relay-based communication system in an LTE environment. Femto-cells provide major performance improvements but the necessity to connect indoor RAPs to the data network makes the deployment less flexible. Furthermore, the deployment of femto-cells is more expensive and it is not clear whether the backhaul resources require less computation and transmission power than a direct link between BS and RN. Nonetheless, the results prove the flexibility of the relaying concept as indoor relays could be equipped with both

315


101 Uncoded QAM [7] 0

10

Turbo Codes [7]

+ -2

10

0

2

+

8

10

+

0

+

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+

10-1

+

100

10-3 (b)

4 6 SNR-Gap Γ

101

+

Average throughput in MBit/s

(a)

Virtual MIMO Conventional 2 Relays, relay-only 2 Relays, mixed

+

10-3

+

+

+

10-1

+

+

+

Average throughput in MBit/s

Trellis Codes + THP [35]

4 6 SNR-Gap Γ

8

10

Virtual MIMO Conventional 2 Relays, relay-only 2 Relays, mixed 2

Figure 11.5. Average uplink throughput performance for varying SNR-gap values: (a) Wide-area scenario; (b) Manhattan-area scenario. a wireless interface to connect them directly to the BS and an interface to the wired broadband network.

11.4.5

Computation-transmission-power tradeoff An energy-efficient mobile communication system must consider the tradeoff between computation and transmission power, which differently affect the achieved performance. One way to examine this tradeoff is the SNR gap approximation [7, pp. 66]. This approximation defines an SNR gap Γ ≥ 1 between

316


practically possible modulation and coding schemes (MCS) and the theoretically possible capacity [35, 36]. More formally, given an SNR gap Γ we apply the modified capacity expression SINR . (11.4) CMCS = log2 1 + Γ Hence, the less efficient the MCS, the higher the SNR gap Γ. In particular, it is a useful means of approximating the effects of channel estimation errors, finite blocklengths, and dirty RF effects. In Figure 11.5, we see the average uplink throughput for both scenarios and varying SNR-gaps. It further shows that for uncoded QAM Γg ap = 8.8 dB for an error probability of 10−6 . More complex MCS such as turbo codes [37] achieve smaller SNR gaps of about Γg ap = 1 dB [7]. In [34], the authors showed that the SNR gap for trellis coding and Tomlinson–Harashima precoding [38, 39], which is a practical implementation of DPC, achieve Γg ap = 1.5 dB and up to about Γg ap = 5 dB. Furthermore, in [40] Kannan derived the SNR gaps for different blocklengths and MIMO algorithms such as D-BLAST. The performance drop in Γ for both relaying approaches in the wide-area scenario has a slightly smaller slope than conventional and multicell MIMO transmission. The reason for this behavior is the very high SINR values in a relay-based system and the resulting rate cut at 8 bpcu. For the same reason the slope in the Manhattan-area scenario is smaller than in the wide-area scenario. In order to achieve the same SINR after applying a practical MCS with SNR gap Γ, we had to spend at least additional transmission power Γ. If most SINR values exceed 28 − 1, which occurred for both relaying approaches in the Manhattan-area scenario, we do not need to increase the transmission power by Γ. Hence, the overall system-wide spent computation energy is reduced while providing almost the same performance. However, the optimal operating point is still difficult to determine as the computation power for a specific approach can only be approximated. Nonetheless, this analysis gives an indication that relaying is able to cope with less powerful MCS while still providing significant performance gains over conventional nonrelaying-based approaches using more powerful and more complex MCS. For instance, based on Figure 11.5, relaying with uncoded QAM provides higher data rates than conventional and multicell MIMO transmission without an SNR gap.

11.4.6

Reduced backhaul requirements In the relay-based system, multicell MIMO is particularly important for the area between two cells served at the same site while the cell-edge area between two different sites is covered by RNs. Due to the low intercell interference, the cell-center area in the main lobe direction of the BS could be served using conventional transmission. Since RAPs are uniformly distributed, the main interferers for the BS-to-RN links are located at the same site instead of different sites. This


317

Table 11.6. Numerical results for the wide-area scenario using in-band feederlinks and limited inter-site cooperation. Full cooperation uses virtually infinite backhaul between multiple sites and limited cooperation only uses cooperation at the same site Scenario/protocol

θ (MBit/s)

σ (MBit/s)

θ5% (MBit/s)

Downlink

Conventional Multi-cell, full Multi-cell, limited Mixed, full Mixed, limited

1.3 2.4 1.9 4.9 4.9

2.4 3.0 2.7 3.9 3.9

2.3 × 10−2 0.2 8.6 · 10−2 0.7 0.7

Uplink

Conventional Multi-cell, full Multi-cell, limited Mixed, full Mixed, limited

0.1 2.39 1.92 4.95 4.94

0.5 3.03 2.71 3.91 3.94

4.3 × 10−4 0.16 0.09 0.66 0.65

motivates the investigation of a system where only BSs at the same site cooperate. Such a system uses the same hardware for all BSs at one site and therefore does not increase the backhaul requirements compared to a conventional system. In this Table 11.6 system is compared with limited cooperation and a system with virtually infinite inter-site backhaul between two physically separated sites (full cooperation). Only multicell MIMO transmission is affected by the limitation of the intersite cooperation. More specifically, the average throughput is decreased by about 20 % and the 5% quantile throughput by approximately 50%. The decrease in the worst-user performance is mainly caused by the cell edge between two sites where full cooperation enables interference cancelation. In a relay-based system, most of the cell-edge users between two sites are served by RNs and therefore full and limited cooperation provide the same performance. Such a system using RNs and limited intersite cooperation is more robust against multicell MIMO synchronization errors, low coherence time/frequency, and the quality of the available CSI. In addition, it requires less resource-intensive backhaul network, which contributes a major part to the energy consumption of a mobile network.

11.4.7

Cost–benefit tradeoff So far we have assumed that the additional performance gains from relaying are provided for free, e. g., the increased costs have not been considered and the possible influence on the computation and transmission power in our network

318


Table 11.7. Example for initial and operating costs for a relay node and site with three base stations Item of expenditure

Relay node

Site (with 3 BS)

Hardware Loan Installation Rental costs Energy costs (at 10 cent per kWh) Life span

10 kEUR 3 years at 8 % 5 kEUR 100 EUR per month

80 kEUR 8 years at 8 % 30 kEUR 1000 EUR per month

438 EUR p.a. (500W)

4.4 kEUR p.a. (5kW)

10a

10a

Cost ratio

αRN,

ref

= CRelay /CSite = 0.1

has not yet been evaluated. In order to provide fair results considering among things the energy costs of RAPs, we have the following options: (1) compare the performance for constant energy consumption per area element; (2) compare the required energy and costs for a constant performance measure; and (3) compare the performance for constant costs (including energy costs). In this chapter, we choose the third option and compare the performance for normalized system costs. Let CS ite denote the capital and operational expenditures of a site (consisting of three BSs) including hardware, site rental, average costs for power and backhaul supply. In addition, let CR elay denote the cost for a relay and αR N = CR elay /CS ite the relative costs of an RN compared to a site. Table 11.7 shows an example of the necessary costs of a BS and RN, which imply a relative costs of αR N = 0.1. If we assume a regular grid of sites as shown in Figure 11.2(a) with NR elay = 6 RNs assigned to each site, the intersite distance dis (αR N ) normalizing the system expenditures is given by (dis,r ef is the intersite distance in a system without relays): dis (αR N ) = dis,r ef 1 + αR N NR elay . (11.5) Figure 11.6 presents the 5% quantile uplink throughput depending on the relative relay costs αR N . The mixed approach provides a significant performance gain for all plotted αR N and the relay-only approach for αR N < 0.2. Downlink and uplink transmission show the same behavior (downlink performance results are not shown in this section) although the performance benefits of the downlink transmission are not as dominant. Our analysis uses in-band feederlinks, which still require significant resources for the BS-to-RN links. In the case of

319


+

+

+

Virtual MIMO Conventional 2 Relays, relay-only 2 Relays, mixed

+

10-2

+

10-1

+

5% quantile in MBit/s

+

100

0.10

0.15

0.20

0.25

αRN, ref

10-3

10-4

0

0.05

RN-to-BS cost ratio αRN Figure 11.6. Cost–benefit tradeoff for uplink transmission and 5% quantile throughput.

femto-cells these resources are used by RNs and the shown performance advantage would be even higher. Our cost–benefit analysis included among other things the energy costs, which represent about 13% of the overall expenditure. However, assume that the target is to normalize the system’s energy consumption and let the energy consumption at the relay be ER N = βR N ES ite . Then, Figure 11.6 illustrates the performance gain for a normalized energy consumption depending on the relative energy consumption βR N . Using the particular setup in Table 11.7, an energy normalization implies for βR N < 0.1 that the costs for the resulting relay-based system are also reduced. For βR N = 0.1 and αR N = 0.1 the system is both cost-normalized and energy-normalized while providing significant performance gains over conventional transmission techniques. A provider of mobile communication services is undoubtedly not exclusively interested in the ecological aspects of green communication but also in the economical aspects. Hence, the cost–benefit tradeoff provides an interesting tool to analyze the tradeoff between the system expenditures, the performance, and the energy consumption of the system. In our example we are able to normalize both costs and energy while providing an improved performance in the relayassisted system. In addition, the computation energy can be reduced due to the higher performance in a relay-based system and the much higher SINR values. In this chapter we have not quantitatively considered the fact that relaying allows more deployment flexibilities, very high data rates in otherwise shadowed areas,

320


and the reduced backhaul requirements. All three of these contribute to the energy consumption of the system and further emphasize the ability of relaying to improve both the energy consumption in the system and to reduce the expenditures.

11.5

Conclusion We have introduced an approach to integrate relaying and multicell MIMO in next generation mobile communications systems. In particular, we have compared the achievable throughput performance, the energy saving potential, and how relaying might reduce deployment costs. Relays provide a flexible way to improve the spatial reuse, are less complex than BSs and therefore cheaper to deploy, and reduce both the computation and transmission power in the system. Hence, relays are an ecological and economic alternative to systems based on direct transmission. These benefits result from the more homogeneous power distribution due to a denser RAP distribution and the interference mitigation at the relay nodes. Furthermore, the flexible and scalable deployment of RNs allows for a reuse of existing 2G and 3G sites, which further reduces deployment costs. In addition, a mixed approach using both relaying and on-site multicell MIMO significantly reduces the backhaul requirements, which otherwise increase the deployment costs and require significant energy resources. The probably most challenging problems in a relay-based mobile communication system are the synchronization of all RAPs, the resource assignment and synchronization of multiple cells, and the handover mechanisms. Furthermore, the optimization of the chosen MCS in order to exploit the available resources appears to be challenging. Practical results such as in [11] suggest that the promising results in this chapter are realizable and allow significant performance improvements particularly for indoor users. Femto-cells already represent a way to implement relaying using an existing infrastructure link, but are less flexible and are not an option for those areas where the mobile communications system is the only choice to provide broadband access.

Acknowledgments Part of this work has been performed in the framework of the IST project IST4-027756 WINNER II, which has been partly funded by the European Union, and the Celtic project CP5-026 WINNER+. The authors would like to acknowledge the contributions of their colleagues in WINNER II and WINNER+, although the views expressed are those of the authors and do not necessarily represent the project.

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12 Network coding in relay-based networks Hong Xu and Baochun Li

12.1

Introduction Since its inception in information theory, network coding has attracted a significant amount of research attention. After theoretical explorations in wired networks, the use of network coding in wireless networks to improve throughput has been widely recognized. In this chapter, we present a survey of advances in relay-based cellular networks with network coding. We begin with an introduction to network coding theory with a focus on wireless networks. We discuss various network coded cooperation schemes that apply network coding on digital bits of packets or channel codes in terms of, for example, outage probability and diversity–multiplexing tradeoff. We also consider physical-layer network coding which operates on the electromagnetic waves and its application in relay-based networks. Then we take a networking perspective, and present in detail some scheduling and resource allocation algorithms to improve throughput using network coding in relay-based networks with a cross-layer perspective. Finally, we conclude the chapter with an outlook into future developments. Network coding was first proposed in [1] for noiseless wireline communication networks to achieve the multicast capacity of the underlying network graph. The essential idea of network coding is to allow coding capability at network nodes (routers, relays, etc.) in exchange for capacity gain, i.e., an alternative tradeoff between computation and communication. This can be understood by considering the classic “butterfly” network example. In Figure 12.1, suppose the source S wants to multicast two bits a and b to two sinks D1 and D2 simultaneously. Each of the links in the network is assumed to have a unit capacity of 1 bit per time slot (bps). With traditional routing, each relay node between S and the two sinks simply forwards a copy of what it receives. It is then impossible to achieve the theoretical multicast capacity of 2 bps for both sinks, since the thick link in the middle can only transmit either a or b at a time. However, with network coding, the intermediate relay node (shaded in the figure) can perform coding, in this case a bitwise exclusive-or (XOR) operation, upon the two information bits and generate a + b to multicast towards its two outgoing links. D1 receives Cooperative Cellular Wireless Networks, eds. Ekram Hossain, Dong In Kim, and Vijay K. Bhargava. Published by Cambridge University Press. C Cambridge University Press, 2011.

12.1 Introduction

S

S

a

b

a

a

b

a

a? b?

b

a b

a

b

D2 (a)

b

a+b a+b

a+b

D1

325

D1

D2 (b)

Figure 12.1. The “butterfly” network example of network coding: (a) with traditional routing, the link in the middle can only transmit either a or b at a time; (b) with network coding, the relay node can mix the bits together and transmit a + b to achieve the multicast capacity of 2 bps.

a and a + b, and recovers b as b = a + (a + b). Similarly, D2 receives b and a + b and can recover a. Both sinks are therefore able to receive at 2 bps, achieving the multicast capacity. In the above example, the network coding operation is bitwise XOR, which can be viewed as linear coding over the finite field GF (2). Following the seminal work of [1], Li et al. [2] showed that a linear coding mechanism suffices to achieve the multicast capacity. Ho et al. [3, 4] further proposed a distributed random linear network coding approach, in which nodes independently and randomly generate linear coefficients from a finite field to apply over input symbols without a priori knowledge of the network topology. They proved that receivers are able to decode with high probability provided that the field size is sufficiently large. These works lay down a solid foundation for the practical use of network coding in a diverse set of applications. After the initial theoretical studies in wire-line networks, the applicability and advantages of network coding in wireless networks were soon identified and investigated extensively [5]. Though the noiseless assumption no longer holds for wireless communications, the wireless medium does provide a unique characteristic conducive to network coding operations – the inherent broadcasting capability. Again this can be best understood by a classic example of the “Alice and Bob” topology as in Figure 12.2. Assume that Alice and Bob want to exchange their information represented by bits a and b, respectively, and each link has a static capacity of 1 bps. It can readily be seen that under the traditional routing paradigm, four time slots are needed to exchange the bits through relay R, which

326


Figure 12.2. The benefits of network coding in wireless networks: (a) four time slots are needed for Alice and Bob to exchange information bits through relay R by plain routing; (b) with network coding, R can XOR the bits and broadcast the coded bit to both parties simultaneously, reducing it to three time slots. sequentially forwards one bit at a time. In contrast, with network coding, R can XOR the two bits together and transmit the coded bit. Because of the broadcast nature of wireless medium, this transmission can be heard by both Alice and Bob. Alice then receives a + b, and recovers Bob’s bit b as b = a + (a + b). Similarly Bob can recover a. Therefore only three time slots are needed in this case, which represents a 25% throughput improvement for both parties. Inspired by the mathematical simplicity and practical potential of network coding, the communications and networking communities have devoted a significant amount of research to utilizing it in a number of wireless applications, ranging from opportunistic routing in mesh networks to distributed storage and link inference in sensor networks. Our focus in this chapter is on relay-based networks, which essentially generalizes the example above in various ways depending on the network model. Here, the relays can refer to dedicated stations solely providing traffic relaying for others’ benefits, or to users relaying one another’s signal, i.e., user cooperation. The purpose of relaying can be merely to extend the coverage of a cellular network when the base station is too distant from the mobile station (multihopping), or to combat fading by providing additional cooperative diversity with more advanced receiver hardware. Our discussion will assume that cooperative diversity is exploited whenever possible, i.e., whenever the receiver receives multiple transmissions that contain the same data, and relaying amounts to mere multihopping only when the receiver obtains one copy of the data.

12.2

Network coded cooperation In both wire-line and wireless networks, network coding usually operates over bits, or symbols. The general use of this conventional form of network coding in

327

12.2 Network coded cooperation

a

b

a

a b

A

R

a+b

B

(a)

A

R

b

B

(b)

Figure 12.3. (a) Plain relaying without network coding; (b) network coded cooperation with one dedicated relay. cooperative diversity is usually termed network coded cooperation in the literature. As was originally invented for wire-line networks, network coding can work at or above the MAC layer over the data bits of packets when applied to relaybased wireless networks, assuming the link layer delivers error-free data. In other words, it serves as an “add-on” component to the existing lower layer techniques. Alternatively, it can also be applied at the link layer, by a more dedicated joint design with channel coding/decoding.

12.2.1

Simple network coded cooperation Consider a simple network model where there are two mobile stations transmitting on the uplink to the base station. The simplest and the most naive way to attain cooperative diversity, shown in Figure. 12.3(a), is to replicate the classic three-terminal model in information theory by assigning a relay to users on orthogonal channels (this can be achieved by time, frequency, or code division). The cooperative transmission progresses in two phases [6]. In the first phase, each mobile station transmits its own data on orthogonal channels while its relay receives and decodes the data. In the second phase the relay forwards the data to the base station, again on orthogonal channels. The base station receives both the original and relayed signals which results in a diversity order of 2 for each user. If time-division is used to orthogonalize channels, a total of four time slots is needed for two mobile stations, 2 for the first phase and 2 for the second phase. Chen et al. [7] were among the first to point out that the same diversity gain can be achieved with less spectrum cost by network coding as shown in Figure 12.3(b), where the relay assists both users at the same time by transmitting the XOR-ed version of information from both users in the second phase. If

328


any two of the three transmissions succeed, the base station can still recover both a and b, therefore the diversity order is 2 for both users. By a probabilistic analysis, it can be shown [7] that the above network coded cooperation also provides a lower system outage probability at high SNR if the total power consumption for the system is fixed, since only three transmissions are required for a complete round of cooperative transmission. The above network coded cooperation scheme allows the relay node to first combine information overheard from multiple sources with linear network coding, and then forward the coded data to the destination. This provides diversity for multiple sources with better spectral efficiency because the relaying bandwidth is suppressed. Though the analysis in [7] is fairly elementary, this key idea demonstrates the relevance of network coding in cooperative diversity, and is largely followed in the community. Now consider the more general model of a cellular network with N ≥ 2 users and M ≥ 1 relays communicating with the base station. Following [7], Peng et al. [8, 9] proposed an extended network coded cooperation for multiuser networks. Although their scheme was designed for multiple unicast sessions with N distinct destinations, it can be readily applied to a multiuser cellular network, as outlined above, with one common destination, the base station. In their scheme, each user still transmits its own data in the first phase on orthogonal channels achieved by time-division. Then in the second phase, a single “best” relay is selected from the M candidates that maximizes the worst instantaneous channel conditions of links from users to the relay and from the relay to the base station, and broadcasts the XOR-ed version of data received from each user to the base station. The idea of using a single best relay instead of all available ones is rooted in opportunistic relaying, first proposed in [10]. Recall the conventional cooperation protocols mandate that a relay transmission must be coupled with each source transmission, no matter whether the relay transmission uses distributed space-time coding across multiple relays or opportunistically utilizes a single best relay [10]. Thus with time-division, a total of 2N time slots is needed with N time slots in the first phase and N time slots in the second phase for N users. In contrast, the network coded cooperation in [9] takes only one time slot in the second phase to broadcast the XOR-ed message for all N users, and only N + 1 time slots are required. Therefore, intuitively, the multiplexing gain of the system can be improved by the proposed scheme. The question is, however: can it also maintain the full diversity gain of M + 1 provided by the M + 1 possible paths to the base station as the conventional schemes? A comprehensive diversity–multiplexing tradeoff analysis of the selectionbased network coded cooperation was offered in [9]. Before we present the results, let us recall the definition of the diversity–multiplexing tradeoff. Definition 12.1 A scheme is said to achieve spatial multiplexing gain Rnorm and diversity gain D if the data rate R satisfies lim R(ρ)/ log ρ = Rnorm

ρ→∞

(12.1)


329

and the average error probability pe satisfies − lim log pe (ρ)/ log ρ = D ρ→∞

(12.2)

where ρ denotes the signal-to-noise ratio (SNR). We can see that essentially it is a fundamental tradeoff between error probability and transmission rate, and has been widely recognized and adopted in the literature. Specifically, the following theorem was proved in [9]. Theorem 12.1 [9] In a single-cell network composed of N users and M relays, the above network coded cooperation scheme achieves a diversity–multiplexing tradeoff given as follows: N +1 N Rnorm , Rnorm ∈ 0, . (12.3) D(Rnorm ) = 2 1 − N N +1 As a comparison, conventional cooperation protocols for multi–user networks (distributed space-time coding or opportunistic relaying) achieve a diversity multiplexing tradeoff of D(Rn or m ) = (M + 1) (1 − 2Rn or m ) for Rn or m ∈ 0, 12 . Therefore, only a diversity gain of 2 can be achieved at high SNR, while the multiplexing gain can indeed be improved from 12 to N/N + 1. In other words, the proposed network coded cooperation scheme achieves a different tradeoff. The reason why XOR network coding does not help in attaining the full diversity gain in this case is that, although the coded message can be potentially helpful for any user, it can only help at most one user provided that all the other N − 1 users’ data are decoded correctly, no matter what the number of relays is. The end-to-end performance of one user is bottlenecked by all the other users, attributing to the diversity order1 of 2. Interestingly, as a special case, when M = 1, i.e., only one relay exists in the network, network coded cooperation achieves the full diversity order of 2 and has a strictly better diversity–multiplexing tradeoff than the conventional scheme 2 (1 − 2Rn or m ) for Rn or m ∈ 0, 12 . It entails less loss in spectral efficiency to achieve the same diversity gain, and offers larger diversity order at the same spectral efficiency in this case. Finally, Figure 12.4 graphically summarizes the above discussion and comparison of the diversity–multiplexing tradeoff for different cooperative diversity schemes. 1

In the case of multiple unicast sessions, it can be shown that this network coded cooperation has a diversity–multiplexing tradeoff of D(R n o r m ) = (M + 1) (1 − N + 1/N R n o r m ) , R n o r m ∈ (0, N/N + 1), assuming that each distinct destination dj can reliably overhear messages from other sources sj , j = i. This assumption, however, implicitly requires enormous power consumption during sj s transmission and is strongly weakened when the network scales. It may not be convincing to demonstrate the superiority of networkcoded cooperation.

330


D(Rnorm) M

M

N N

Rnorm

Figure 12.4. Diversity–multiplexing tradeoff comparison.

Another user cooperation protocol, named adaptive network coded cooperation (ANCC), which essentially achieves the same diversity–multiplexing tradeoff as conventional cooperation protocols in the multiuser setting, was proposed in [11]. It also takes 2N time slots to complete one round of cooperation for N users. The basic idea is that in the second phase, each user, acting now as a relay, takes turns to select (randomly) a subset of messages it correctly overheard, and to transmit the binary checksum of them. From a coding perspective, the network coded cooperation can be viewed as matching network-on-graph, i.e., instantaneous network topologies described in graphs, with the well-known class of code-on-graph, i.e., low-density parity-check (LDPC) codes, on the fly; hence the term adaptive. Analysis of the achievable rate and outage rate coupled with numerical evaluations shows that ANCC outperforms repetition-based cooperation and is on a par with space-time coded cooperation. This scheme, however, does introduce some level of overhead in transmitting a bitmap so the base station knows how the checksums are formed. Further, decoding also requires an adaptive architecture, and may not be practical in reality. From the above discussion, we can see that in a multiuser cellular network, the superiority of network coded cooperation mainly lies in its adaptivity to the lossy nature of the wireless media, and its operational simplicity. The peruser complexity, for both schemes in [9, 11], is invariant as the network grows, compared with space-time coded cooperation, whose complexity and overhead increases linearly with the network size. We also note that, despite the fact that these proposals are available for combining network coding and cooperative relaying and show the benefits of network coding in some scenarios, further research is required to unleash full potential of network coded cooperation and make it practical in more general scenarios.


12.2.2

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Joint network and channel coding/decoding The discussion so far has focused on using network coding on packets produced by channel decoding. Network coding essentially works as an erasure–correction code that operates above the link layer and offers reliable communication through redundant transmission of packets. Channel coding, on the other hand, is an error-correction technique in a wireless environment. It is used in the link layer to recover erroneous bits through appending redundant parity-check bits to a packet. By treating them separately, a certain degree of performance loss is introduced. Erasure–correction decoding cannot utilize the redundant information in those packets that fail the channel decoding, and hence are discarded at the link layer, while error-correction decoding cannot take advantage of the additional redundancy provided in the erasure codes. Indeed, in one early work on network coding [12] it was shown that, in general, capacity can only be achieved by a joint treatment of channel and network coding. A number of research efforts have directed at unifying the two techniques in order to obtain further performance improvement. We survey some important ones in the following.

3 1

x1

x3 3

x2

x1 4

x3

x2 2 (a)

(b)

Figure 12.5. (a) A multiple-access relay channel; (b) a two-way relay channel.

Let us first revisit the example of Figure 12.3 where two users share one relay on the uplink to the base station, which resembles the multiple-access relay channel in coding and information theory as shown in Figure 12.5(a). Hausl et al. [13] first considered joint network-channel decoding in this model, assuming that the relay can reliably decode messages from both users. A distributed regular LDPC code is used for network-channel coding. Unlike in [7] in which the two messages transmitted from the users with the network coded message transmitted from the relay are separately decoded, they proposed to decode the three messages jointly on a single Tanner graph [14] with the iterative message-passing algorithm. More precisely, let ui denote the information bits of user i, i ∈ {1, 2}, xi the network-channel code, and Gij the generator matrix on the link from i to j.

332


Then the network encoder of [14] at the relay produces2 x3 = u1 G31 + u2 G32 .

(12.4)

The encoding operations at the users and the relay can be jointly described as

0 G31 G14 = uG. (12.5) x = [x1 x2 x3 ] = [u1 u2 ] 0 G24 G32 Then the parity-check matrix H of the network-channel code has 2N + NR columns and 2(N − K) + NR rows and has to fulfill GHT = 0, where N and NR denote the channel code length and network code length, respectively and K denotes the length of information bits u1 , u2 . The decoder at the base station decodes the LDPC code with parity-check matrix H on the Tanner graph and exploits the diversity provided by network coding. In [13] the diversity and code length gain of network-channel code was shown by numerically comparing it with two references systems, one where the relay is shared without network coding, and another where no relay is employed. The diversity and code length gain is not difficult to explain intuitively. For the comparison to be fair, the numbers of code bits used in all systems, 2N + NR , have to be equal. Consider the setup with K = 1500 and N = NR = 2000, which corresponds to a channel code rate of 0.75 in the first phase of cooperation. Network-channel code achieves the full diversity order of 2 since x4 contains both u1 and u2 . For the system without network coding, the relay is shared and only transmits 1000 code bits for each user, while there are 1500 information bits. Thus it is impossible to achieve full diversity. Now consider another setup with K = 1500 and N = NR = 4000. Without network coding, the relay transmits 2000 code bits for each user and full diversity order can be achieved, with a channel code rate of 0.75 to the base station in the relaying phase. The networkchannel code, in this case, provides a more robust code rate of 0.375 to the base station for each user. In [13] the LDPC-based network-channel coding was not compared with separate network and channel coding. In [15] the same idea was followed and turbocode-based network-channel coding for the multiple-access relay channel was proposed. Moreover, it was shown that even though full diversity order can be obtained with separate network-channel coding, joint network-channel coding based on turbo codes is able to exploit the additional redundancy in the relay transmission and exhibits strictly better bit error rate (BER) and frame error rate (FER) performance. Hausl further extended joint network-channel coding to a similar model, the two-way relay channel [16] as in Figure 12.5(b). It is essentially an abstraction of the “Alice and Bob” example shown in Figure 12.2. Note that simple network 2

Note that the scheme in [7] does not consider interleaving and produces x 3 = (u 1 + u 2 )G 3 , which is slightly inferior in terms of bit error probability, though a diversity order of 2 is achievable.


333

coded cooperation proposed for the multiple-access relay channel as in [7] works without any change for the two-way relay channel, and full diversity order can be exploited. However, joint network-channel coding does call for a different design. The subtle difference is that in the two-way relay channel, each user exchanges information through a relay in the middle and decodes the other’s message, whereas in the multiple-access relay channel a common destination decodes both messages from each user. An example of the two-way relay channel is the uplink and downlink transmissions between a mobile station and a base station with a relay. Thus the joint network-channel decoder at the mobile station takes as inputs the channel code from the base station and the network-channel code from the relay, and jointly decodes them to obtain the data from the base station. Its own data are utilized during the decoding process, since the network-channel encoder at the relay is a convolutional encoder coding the interleaved bits from both the mobile station and the base station together. The network-channel decoder at the base station works in a similar way. Again, joint network-channel decoding is able to obtain the full diversity order of 2 here with better BER performance. The proposals in [13, 15, 16] rely on the key assumption that the relay is able to reliably decode the messages from both ends, and utilize the simplest XOR network coding. Yang and Koelter [17] and Kang et al. [18] broke this assumption and designed iterative network and channel decoding when the relay cannot perfectly recover packets. Guo et al. [19] took one step further and proposed a practical scheme, called nonbinary joint network-channel decoding, which couples non-binary LDPC channel coding and random linear network coding in a highorder Galois field. A joint network-channel coding scheme was also proposed in [20] for user cooperation that endows users with efficient use of resources by transmitting the algebraic superposition of their locally generated information and relayed information that originated at the other user. Finally, we offer an information theoretic perspective regarding joint networkchannel coding on the two-way relay channel in Figure 12.5(b) before we end the discussion. The second phase of transmission involves the relay broadcasting to two receivers at each end, and can be seen as the well-studied broadcast channel. Joint network-channel coding, as we discussed above, performs network coding across channel codewords, i.e., x3 = π32 (u1 ) + π31 (u2 ),

(12.6)

where πij (·) denotes the channel encoding function for link ij. In general, the capacity-achieving code rate varies for different links, and by coding channel codewords the capacity of each link involved in the broadcast is achieved as in the single-link transmission.3 The only difference here is that for user i, certain 3

Note that all works we have described, including [13, 15, 17–20] which were not designed for the two-way relay channel, assume that the code rate is the same for all channel codes involved on all links to ease the decoding design. These proposals will work for the more

334


bits in the channel code are flipped with a known pattern π3j (ui ) at the relay as in (12.6), and they are flipped back after demodulation at i. If separate network channel coding is used, x3 = π3 (u1 + u2 ). We can readily see that the rate of π3 has to be confined to the minimum rate of links 31 and 32 for both users to be able to decode, resulting in performance loss in terms of achieving the broadcast channel capacity. This is referred to as the coding to the worst rate problem. It is easy to verify that this problem does not exist in the multiple-access relay channel.

12.3

Physical-layer network coding The main distinguishing characteristic of wireless communications is its broadcast nature. The radio signal transmitted from one node is often overheard by many neighboring nodes, and causes interference to their reception. Conventional wisdom treats interference as a nuisance and strives to avoid it by making the transmissions orthogonal to each other in time, frequency, or by code, which in effects disguises a wireless link as a wired one. In the preceding discussions of network coded cooperation, network coding takes advantage of the broadcast nature without changing this fundamental interference-avoiding structure of wireless transmissions. Opposite to this line of thinking, a novel paradigm that embraces interference as a unique capacity-boosting advantage was developed in [21] and is gaining momentum. The idea is to encourage interference from concurrent transmissions, and by smart physical-layer techniques transform the superposition of the electromagnetic waves as an equivalent network coding operation that mixes the radio signals in the air. An apparatus of network coding is then created at the physical layer, and works on the electromagnetic waves in the air rather than on the digital bits of data packets or channel codes. Therefore, this is termed physical-layer network coding (PNC), or analog network coding, while the term digital network coding refers to its conventional counterpart. More specifically, Figure 12.6(a) illustrates the working and power of PNC, on the familiar two-way relay channel. Using PNC, only two time slots are needed for each user to exchange information, as opposed to three using digital network coding and four using direct transmission. In the first time slot each user concurrently transmits to the relay. For simplicity, assume that BPSK modulation is used, and symbol-level and carrier phase synchronization and channel preequalization are done perfectly, so that the frames from users arrive at relay with the same amplitude and phase. Then the baseband signal received by the

general case where code rate is different, with proper modification, mostly of the decoding algorithm.

12.3 Physical-layer network coding

335

Time

–1 2,–2

Time

Figure 12.6. (a) The intuitive benefits of physical-layer network coding. The top graph shows the transmission schedule using digital network coding, and the bottom graph shows that of physical-layer network coding. (b) BPSK modulation/demodulation mapping for physical-layer network coding. relay is r(t) = S1 (t) + S2 (t) = (a1 + a2 ) cos ωt,

(12.7)

where Si (t) is the baseband signal from user i. The relay does not decode both BPSK signals a1 and a2 from r(t). Instead it tries to decode and transmit the signal a1 + a2 . The original BPSK scheme has only two signals, 1 and −1 corresponding to data bits of 1 and 0, respectively. However r(t) has three signals, −2, 0, and 2. A modulation/demodulation mapping, shown in Figure 12.6(b), was developed for BPSK in [21] so that superposition of the analog signals a1 + a2 can be mapped to arithmetic addition of the digital bits they represent in GF (2). In theory, physical-layer network coding has the potential to improve throughput performance greatly (by 100% compared with direct transmissions and by 33.3% compared with digital network coding as in Figure 12.6(a)). This, however, does come with a nonnegligible price – the loss of diversity gain. Recall that the full diversity order of 2 is achievable in a two-way relay channel for conventional and network-coded cooperation as discussed in Section 12.2.2. Since PNC entails concurrent transmissions in the first time slot, both users only receive one transmission in the second slot when the relay broadcasts,4 whereas they receive a direct transmission and a relay transmission in conventional and network-coded cooperation. Hence, cooperative diversity cannot be exploited and only a diversity order of 1 can be obtained with PNC, and relaying here boils down to simple multihopping. For this reason, to our knowledge almost all subsequent works on the subject compare PNC with multihopping and draw conclusions without considering cooperative diversity, even if it is possible. Hence unless otherwise 4

The standard assumption of half-duplex radio hardware is assumed.

336


specified, our discussion of PNC hereafter inherits this assumption from the literature, the validity and fairness of which, however, remain disputable and left to the judgment of readers. Given its promising potential, the idea of physical-layer network coding has generated a considerable amount of interest. Hao et al. [22] first analyzed the achievable rates of PNC, assuming the additive white Gaussian noise (AWGN) channel model. Through numerical analysis it was shown that PNC outperforms digital network coding and direct transmission significantly, and approaches the capacity limit of the two-way relay channel with appropriate modulation schemes. This is not unexpected as illustrated in the aforementioned example in Figure 12.6(a). Several estimation techniques were developed for PNC to deal with noise in the decoding process in [23]. The rigid and unpractical requirements of perfect synchronization and channel preequalization then became the focal point of critics of PNC, as the detrimental effect of imperfect synchronization can be substantial (6 dB loss as shown in [22]). General PNC schemes that relax the synchronization requirement while preserving the performance superiority are actively being pursued. An amplify-andforward scheme, in which the relay directly amplifies and forwards the interfered signal to both users as opposed to the decode-and-forward strategy in [21], was proposed and studied in several works [22, 24–27]. It was generally found that amplify-and-forward PNC is more robust and offers better performance when synchronization is absent than decode-and-forward PNC [22], whereas when perfect synchronization is provided amplify-and-forward PNC suffers from a loss of optimality in terms of achievable rate [25]. The robustness of amplify-and-forward PNC is more pronounced for general scenarios because no channel preequalization is required. In [26, 27] the case in which there are M relays available for the two-way relay channel was considered. To effectively utilize multiuser diversity offered by relays, a distributed relay selection strategy was proposed with selection criteria specifically designed for amplify-and-forward PNC. Two information theoretic metrics, outage and ergodic capacities, closely related to the diversity and multiplexing gains of the system, were analytically and numerically evaluated to confirm its advantage. Indeed, the following theorem can be proved as in [27]. Theorem 12.2 [27] The amplify-and-forward PNC scheme in [27] achieves a diversity-multiplexing tradeoff of the following: D(Rnorm ) = M (1 − Rnorm ), Rnorm ∈ (0, 1].

(12.8)

Clearly, multiuser diversity is capitalized as the diversity order is M . Moreover, the same multiplexing gain of 1 as direct transmission can also be attained, echoing our remark on the benefit of network coding in suppressing bandwidth for relaying in Section 12.2.1. On the other hand, decode-and-forward PNC is not able to utilize multiuser diversity gain, due to the operational requirement

12.4 Scheduling and resource allocation: cross-layer issues

337

of channel preequalization before decoding in order to make sure both signals are received with equal amplitude. One immediately realizes that, despite the technical difficulty, channel preequalization effectively inverses the fading effect of the channel, and results in loss of diversity gain. Joint network-channel coding/decoding is also explored in the area of PNC. The main objective is to design a good coding/decoding scheme that maximizes the amount of information that can be reliably exchanged through the two-way relay channel. More advanced coding that applies lattice code on the relay was discussed in [28, 29]. We make a few comments about open issues and future directions of physicallayer network coding. First, several theoretic issues remain unsolved or unexplored, as research in this area is still in its nascent stage. Most importantly, only the simplest XOR network coding on GF (2) is realized with signal superposition in the air, while linear network coding can work on a much larger Galois field. Note that in wireless communications, path-loss and channel fading effectively couple to the transmitted signal a complex coefficient, which, to some extent, resembles the multiplication operation in a finite field of complex numbers, while signal superposition resembles the addition operation. It is therefore interesting, but certainly nontrivial, to investigate whether the complex channel coefficient can be “transformed” to an equivalent network coding coefficient to realize an even larger improvement, in performance. In addition, all the developed schemes remain fairly theoretical, and very few researchers have attempted to evaluate the true performance of PNC in a real hardware implementation. To the best of our knowledge, the only work in which the practical coding and decoding algorithms for MSK modulation based on amplify-and-forward PNC is sketched, and the system using software radios implemental is [24]. It is asserted that PNC is indeed practical, and achieves significantly higher throughput than digital network coding. While this conveys an optimistic message, one should realize that physical-layer network coding marks a significant departure from the conventional wisdom, and tremendous efforts have to be made across layers of the protocol stack which are designed to avoid interference before it can be implemented in general scenarios.

12.4

Scheduling and resource allocation: cross-layer issues The discussion so far has largely focused on the lower layers of the protocol stack. From communications and information theory point of view, numerous schemes have been developed based on network coding to utilize a given budget of resources to transmit information as efficiently as possible. In other words, they answer the question of how to transmit in a given scenario for individual nodes. From a networking point of view, provided with the lower-layer transmission protocol, upper-layer protocols have to coordinate the transmissions between nodes in the network, and allocate resources network-wise (such as channels) and

338


Figure 12.7. (a) A cellular network with multiple relays. Solid lines denote direct transmissions while dotted ones denote relay transmissions. All transmissions happen on orthogonal OFDM subchannels. Note that one mobile station (MS) can be paired up with multiple relays (RSs), while one relay could help multiple mobile stations, complicating the scheduling and resource allocation. (b) XORassisted cooperative diversity as adapted from [31]. Here different line types denote different subchannels. (BS – base station).

node-wise (such as power) adequately to these competing sessions so as to optimize some network-wise metrics. In other words, we need to create scenarios amenable for network coding aided relay transmission protocols such that performance is maximized from a network perspective. The use of network coding certainly calls for new designs of cross-layer scheduling and resource allocation protocols on existing cellular network architectures. To this end, there exist only a few publications in the literature. Zhang and Li [30] were arguably the first to venture into this area. They considered the use of simple network coded cooperation on the two-way relay channel, with the base station serving as the relay to XOR the incoming packets and broadcast to two users. They assumed an orthogonal frequency-division multiple-access (OFDMA) based cellular network model, and developed a coding aware dynamic subcarrier assignment heuristic in a frequency-selective multipath fading environment. The idea is that in such an environment, different OFDM subcarriers have independent channel gains to the same mobile station (multichannel diversity), and even the same subcarrier fades differently on different mobile stations (multiuser diversity). By dynamically matching the subcarriers to the best mobile stations for network coded cooperation while taking fairness into account, a substantial throughput improvement was reported in [30]. Another work, that of Xu and Li [31], represents an in-depth investigation in this area, which is discussed in detail here. Consider the more general scenario in Figure 12.7(a). Assume multiple relays are available for the OFDMA-based network, and all transmissions happen on orthogonal OFDM subchannels. An XOR-assisted cooperative diversity scheme, named XOR-CD, is employed by replicating the two-way relay channel using bi-directional traffic of a given mobile

12.4 Scheduling and resource allocation: cross-layer issues

339

station as in Figure 12.7(b). Specifically, it works as follows. In the first phase of cooperation, on the uplink MS sends packet A to the base station and on the downlink base station sends packet B to mobile station, simultaneously on orthogonal subchannels. Transmissions are overheard by the relay. In the second phase, the relay broadcasts A + B using another orthogonal subchannel. We can readily see that cooperative diversity can still be exploited as in conventional schemes, which require four subchannels and more power to complete the same job. Extending to the network scale, while XOR-CD shows promise, it seems prohibitive in terms of cost and complexity to design good scheduling and resource allocation algorithms for the following reasons. First, one mobile station can be paired up with multiple relays and one relay could help multiple mobile station, as can be illustrated in Figure 12.7(a). Second, for one mobile station, direct transmission, conventional cooperative diversity, and XOR-CD can be utilized at the same time on different subchannels, depending on the dynamic channel conditions and resource availability. Third, there is an intricate interplay between three of the problems, namely relay assignment, relay-strategy selection, and subchannel assignment, further aggravating the problem. The contributions of [31] is two-fold. First, a unifying optimization framework is developed that jointly considers relay assignment, relay-strategy selection, and subchannel assignment for both mobile station and relays. Second, the joint optimization problem, referred to as a relay assignment, relay-strategy selection and subchannel assignment (RSS) XOR problem, is shown to be NP-hard, and an efficient approximation algorithm is proposed based on set packing with a provable approximation ratio. Specifically, the following theorem is shown to hold. Theorem 12.3 [31] The RSS-XOR problem is equivalent to a maximum weighted three-set packing problem, and is NP-hard. Proof. Construct a collection C of sets from a base set ζ ∪ ψ as shown in Figure 12.8, where ζ is the set of data subchannels and ψ the set of relay subchannels. As we can see, there are three kinds of sets, representing three possible transmission modes (ci ), ci ∈ ζ, represents the direct transmission with data subchannel ci : (ci , cr ), ci ∈ ζ, cr ∈ ψ; corresponds to the conventional cooperative diversity with data subchannel ci and relay subchannel cr ; finally, (ci , cj , cr ), ci , cj ∈ ζ, cr ∈ ψ, corresponds to XOR-CD with data subchannel pair (ci , cj ) and relay subchannel cr . Sets intersect if they share at least one common channel, and are otherwise said to be disjoint. Each set has a corresponding weight, denoting the maximum marginal utility found across all possible assignments of this set to different combinations of relays and links.5 The utility function is defined such that proportional fairness is taken into account. For (ci , cj , cr ), its weight is found 5

One mobile station has two links, namely the uplink and the downlink.

340


Figure 12.8. Set construction and transformation into an intersection graph with two data subchannels and two relay subchannels. Vertices in GC correspond to sets in C. Edges are added between vertices whose corresponding sets intersect. over all possible assignments of this set to combinations of relays and both links of a MS. The RSS-XOR problem is to find the optimal strategy to choose the transmission mode and assign relays and channels to each link in order to maximize the aggregated throughput. The maximization is done across all links. Equivalently, we can also interpret it as finding the optimal strategy to select disjoint channel combinations, and assign relays and links to them so as to maximize the objective. In this alternative interpretation, the maximization is done over all possible channel sets by matching them to the best possible links and relays, without violating the obvious constraint that each channel can only be used once. The number of elements in a set is at most three; therefore, this problem is essentially a weighted three-set packing problem [32], which is NP-complete. To propose an approximation algorithm, we first construct an intersection graph GC , such that the a vertex in the vertex set VC corresponds to a set in the set system C, and there is an edge between two vertices in GC if the two corresponding sets intersect, as shown in Figure 12.8. Weighted set packing can then be generalized as a weighted independent set problem, the objective of which is to find a maximum weighted subset of mutually nonadjacent vertices in GC [33]. The size of sets is at most three, therefore GC is three-claw free. Here, a d-claw c is an induced subgraph that consists of an independent set Tc of d nodes. The best-known approximation algorithm for the weighted independent set problem in a claw-free graph is proposed in [33] and then acknowledged in [32], which is then adopted in [31] as the solution algorithm with an approximation ratio of 23 as proved in [33]. As a side note, it was also shown in [31] that the joint optimization problem that involves only conventional cooperative diversity and direct transmission can be cast as a weighted bipartite matching problem, which admits polynomial-time algorithms to obtain the optimal solution. This demonstrates the interesting point that, although network coding provides significant performance gains, it may render the scheduling and resource allocation problems even more involved at least in some cases. Moreover, this also reflects the importance of developing

12.5 Conclusion

341

cross-layer protocols to fully realize the benefits of network coding in relay-based networks. While an attempt was made to address these upper-layer issues in [30, 31], the algorithms developed are still impractical for implementation in real-world cellular networks. Full channel state information (CSI) is assumed to be available at the base station, which may not be the case for fast fading environments. The complexity of the algorithms is high for real-time scheduling at the time scale of 5–10 ms, which is the common frame length. Therefore, substantial efforts in design, implementation, and evaluation of practical protocols are imperative to further understand and to conquer the challenges network coding brings to relay-based networks.

12.5

Conclusion Network coding, by allowing network nodes to mix information flows, represents a paradigm shift for communication networks. With the broadcast nature of the wireless medium, it can be naturally applied to wireless communications and brings the promise of performance improvement in relay-based cellular networks. The question is: what is the most efficient way to utilize network coding in relaybased networks, and how practical is it to be adopted in the real world? We have started with network-coded cooperation that applies network coding on digital bits of information, both without and with a joint consideration of channel codes. We have noted the operational simplicity and multiplexing gain of network-coded cooperation, and have shown that in general a joint design of network and channel coding/decoding is required to achieve the information theoretic capacity, at a cost of increased decoding complexity. Then we have extended the discussion to physical-layer network coding, a radical yet interesting idea that treats the signal superposition in the air as the XOR networkcoding operation. By embracing interference, physical-layer network coding has the potential dramatically to improve the throughput performance of relay-based networks. From the communications and information theory perspective, the overall message appears to be very optimistic. From a networking perspective, although network coding is mostly applied in the lower layers of the protocol stack, upper layers have to be coding-aware and perform scheduling and resource allocation accordingly. In other words, cross-layer efforts are needed to realize network coding in a practical network setting. To this end, we have presented some initial cross-layer studies on cellular relay networks. An important lesson is that network coding may render the scheduling and resource allocation more complicated, at least in some cases, because it mixes information flows from different sessions. Despite a significant amount of research, the use of network coding in relaybased cellular networks remains largely theoretical. Substantial efforts on implementation and evaluation of network-coding-aided transmissions in large-scale

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relay networks are imperative at this stage. With the proliferation of wireless technologies and devices, and the ever-growing bandwidth demand from dataintensive mobile applications, we envision that network coding could become a practical and important component in future wireless technologies, and play an important role in the quest of high throughput and ubiquitous connectivity in wireless communications.

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Part IV Game theoretic models for cooperative cellular wireless networks

13 Coalitional games for cooperative cellular wireless networks Walid Saad, Zhu Han, and Are Hjørungnes

13.1

Introduction Cooperation among wireless nodes has attracted significant attention as a novel networking paradigm for future wireless cellular networks. It has been demonstrated that, by using cooperation at different layers (physical layer, multiple access channel (MAC) layer, network layer), the performance of wireless systems such as cellular networks can be significantly improved. In fact, cooperation can yield significant performance improvement in terms of reduced bit error rate (BER), improved throughput, efficient packet forwarding, reduced energy, and so on. In order to reap the benefits of cooperation, efficient and distributed cooperation strategies must be devised in future wireless networks. Designing such cooperation protocols encounters many challenges. On the one hand, any cooperation algorithm must take into account not only the gains but also the costs from cooperation which can both be challenging to model. On the other hand, the wireless network users tend to be selfish in nature and aim at improving their own performance. Therefore, giving incentives for these users to cooperate is another major challenge. Hence, there is a strong need to design cooperative strategies that can be implemented by the wireless nodes, in a distributed manner, while taking into account the selfish goals of each user as well as all the gains and losses from this cooperation. This chapter describes analytical tools from game theory that can be used to model the cooperative behavior in wireless cellular networks. In this context, the key tool that will be explored is the framework of game theory/coalitional game theory. For instance, coalitional game theory is the main branch of game theory/cooperative game theory and it describes the formation of cooperating groups of players, referred to as coalitions [1, 2]. Coalitional games prove to be a very powerful tool for designing fair, robust, practical, and efficient cooperation strategies, which can be used to model cooperative behavior in wireless networks. The main goal in this chapter is to give the reader a good understanding of how cooperative behavior in a wireless system can be modeled through coalitional game theory. In particular, the chapter gives a better understanding Cooperative Cellular Wireless Networks, eds. Ekram Hossain, Dong In Kim, and Vijay K. Bhargava. Published by Cambridge University Press. C Cambridge University Press, 2011.

348

Coalitional games for cooperative cellular wireless networks

of two main applications of coalitional games in wireless networks: (i) distributed cooperation for virtual multiple-input multiple-output (MIMO) formation; and (ii) the impact of cooperative transmission and relaying on network formation in a wireless network. To achieve these goals, the chapter is organized as follows. In Section 13.2, we provide a brief introduction to the main ideas of coalitional game theory. Then, in Section 13.3, we present a coalitional game model that allows single antenna users to benefit from the performance advantage of MIMO systems, through cooperation. Further, in Section 13.4, we discuss how coalitional game theory can be used to study the structure and dynamics of the wireless network architecture in the presence of relay station nodes utilizing cooperative transmission. Finally, a chapter summary is provided in Section 13.5.

13.2

A brief introduction to coalitional game theory In general, coalitional game theory involves a set of players that are seeking to form cooperative entities, i.e., coalitions. Let N denote the set of these players. By forming any coalition S ⊆ N , the players can improve the utility they obtain in the game. Thus, another main concept of coalitional game theory is the value or utility which describes the total benefit that the members of a coalition S can obtain when acting cooperatively. The value of a coalitional game can have different forms: characteristic form, partition form, or graph form. Briefly, a coalitional game is in a characteristic form if the utility of a coalition S depends solely on the members of that coalition, with no dependence on the players in N \ S. In contrast, a game is in partition form if, for any coalition S ⊆ N , the coalitional value depends on both the members of S as well as the coalitions formed by the members in N \ S. In certain coalitional games, the different players are connected to each other through a graph structure. Consequently, for modeling such coalitional games, the value is considered in graph form, i.e., for each graph structure, a different utility can be assigned. Independent of the form of the game, every coalitional game is uniquely defined by the pair (N , v), where N is the players’ set and v is the coalitional value. In any coalitional game, it is always important to distinguish between two entities: the value of a coalition and the payoff received by a player. The value of a coalition represents the amount of utility that a coalition, as a whole, can obtain. In contrast, the payoff for a player represents the amount of utility that a player, the member of a certain coalition, will obtain. For instance, depending on how the value is mapped into payoffs, the coalitional game can be either with transferable utility (TU) or with nontransferable utility (NTU). A TU game implies that the total utility received by any coalition S ⊆ N can be apportioned in any manner between the members of S. A prominent example of TU type games is when the value represents an amount of money, which can be distributed in any way between coalition members. In contrast, in an NTU,

13.2 A brief introduction to coalitional game theory

349

the individual payoff obtained by any player within a coalition S is restricted by some underlying structure of the game. In a TU environment, the utility obtained by a coalition is characterized by a function over the real line, while in an NTU framework, the utility of a coalition S is a set of payoff vectors of size 1 × |S| (|S| represents the cardinality of set S), whereby each element of any vector, represents the payoff that a particular player in S receives. Depending on the metric being used as a utility, the game can be transferable or non-transferable. Consequently, depending on the form, type, and objectives of a coalitional game, three classes of games can be distinguished [3]: canonical coalitional games, coalition formation games, and coalitional graph games. Each class has its own properties, solutions, and challenges. For instance, the canonical coalitional game class can be used to model problems where: (i) the value is in characteristic form (or can be mapped to the characteristic form through some assumptions); (ii) cooperation is always beneficial, i.e., including more players in a coalition does not decrease its value; and (iii) there is a need to study how payoffs can be allocated in a fair manner that stabilizes the grand coalition, i.e., coalition of all players. In wireless networks, such problems are of interest to study the limits and fairness of cooperation, when no cost for forming coalitions exists. For example, using canonical coalitional games, the work in [4] focused on devising a cooperative model for rate improvement through ideal receivers cooperation. Using canonical games, the authors of [4] showed that, for the receiver coalition game in a Gaussian interference channel and synchronous CDMA multiple access channel (MAC), a stable grand coalition of all receivers can be formed if no cost for cooperation is taken into account. In addition, using canonical games, the fair allocation of rate for cooperating users in an interference channel was studied in [5] for the transmitters. Under some assumptions on the users’ behavior, the authors showed that a unique rate allocation exists verifying certain well-defined fairness axioms from canonical coalitional games. In canonical games, there is an implicit assumption that forming a coalition is always beneficial. In contrast, coalition formation games consider cooperation problems in the presence of both gains from and costs of cooperation. This is quite a useful class of games since, in several problems, forming a coalition requires a negotiation process or an information exchange process which can incur a cost, thus reducing the gain from forming the coalition. In general, coalition formation games are of two types: static coalition formation games and dynamic coalition formation games [3]. On the one hand, for static coalition formation games, a coalitional structure is imposed on the game through some external factor (e.g., a network owner), and, hence, the goal of static games is to study the already formed structure. On the other hand, in dynamic coalition formation games, the main objectives are to analyze the formation of a coalitional structure, through players’ interaction, as well as to study the properties of this structure and its adaptability to environmental variations or externalities. As a result, a key question that dynamic coalition formation games seek to answer is “which

350


coalitions will form in a given game?”.1 For instance, in any problem where the benefit–cost tradeoff from cooperation is of interest, coalition formation games constitute a well-suited analytical tool since they provide rules, concepts, and algorithms for characterizing the coalitional structure that can emerge for a given coalitional game. A coalition formation game can be in either characteristic or partition form, as the network structure plays a key role in any solution. In wireless systems, coalition formation games are quite a useful tool for studying various problems such as virtual MIMO formation [6], cognitive radio networks [7, 8], or physical layer security [9, 10]. In both canonical and coalition formation games, the utility or value of a given coalition has no dependence on how the players inside (and outside) the coalition communicate. Nonetheless, in certain scenarios, the underlying communication structure, i.e., the graph that represents the connectivity between the players in a coalitional game can have a major impact on the utility and other characteristics of the game [1, 3]. In such scenarios, coalitional graph games constitute a strong tool for studying the graph structures that can form based on the cooperative incentives of the various players. In coalitional graph games, instead of focusing on forming or studying the properties of coalitions, one is interested in studying the properties of various graph structures. In this regard, coalitional graph games can be used in many wireless and communications applications such as routing, network formation, and vehicular networks. In the remainder of this chapter, we will illustrate, in detail, the use of coalition formation games and coalitional graph games in two main applications in cooperative wireless cellular networks. On the one hand, we will discuss how coalition formation games can be used for distributed virtual MIMO formation. On the other hand, we will formulate a coalitional graph game for studying the network architecture that will form in the uplink next-generation wireless systems when cooperative transmission is used. Finally, we note that, although canonical coalitional games also admit many interesting applications within cooperative wireless cellular networks (notably when cooperation has no costs), their treatment is outside the scope of the present chapter and the interested reader is referred to [3–5].

13.3

A coalition formation game model for distributed cooperation In this section, we investigate the use of coalition formation games for modeling cooperative behavior among the users of a wireless network. In particular, we emphasize the problem of the formation of multiple antenna systems through cooperation among single-antenna transmitters. First, we motivate the problem

1

In the remainder of this chapter, the term “coalition formation game” refers to a dynamic coalition formation game.

13.3 A coalition formation game model for distributed cooperation

351

and provide a suitable system model. Then, we formulate the problem using coalitional game theory, we describe the properties of the resulting game, and we derive an algorithm for coalition formation.

13.3.1

Motivation and basic problem An important application for cooperation in wireless cellular networks is the formation of virtual MIMO systems through cooperation among single-antenna devices. In this context, a number of single-antenna devices can form virtual multiple-antenna transmitters or receivers through cooperation, and consequently, benefit from the advantages of MIMO systems without the extra burden of having multiple antennas physically present on each transmitter or receiver. Thus, the basic idea of virtual MIMO is to rely on cooperation among mobile devices in order to benefit from the widely acclaimed performance gains of MIMO systems. An intensive research effort has been dedicated to information theoretic studies of virtual MIMO systems. For instance, the authors of [11] showed the interesting gains in terms of outage capacity resulting from the cooperation of two singleantenna devices that are transmitting to a far away receiver in a Rayleigh fading channel. Further, the work in [12, 13] considered cooperation among multiple single-antenna transmitters as well as receivers in a broadcast channel. Different cooperative scenarios were thus studied and the results showed the benefits of cooperation from a sum-rate perspective. It is important also to note that virtual MIMO gains are not only limited to rate gains. For example, forming virtual MIMO clusters in sensor networks can yield gains in terms of energy conservation [14]. Implementing distributed cooperation algorithms that allow the wireless network to reap these capacity or energy benefits in a practical wireless network is challenging and desirable. In this regard, using concepts from coalitional game theory to design such distributed algorithms is quite appealing [3]. Thus, consider the single cell of a wireless cellular network having N single-antenna transmitters (e.g., mobile users) sending data in the uplink to their serving base station (BS) which possesses K > 1 receive antennas. Let N = {1 . . . N } denote the set of all N users in the network. For multiple access, we consider a TDMA transmission in the network,2 thus, in a noncooperative manner, the N users require a time scale of N slots to transmit as every user occupies one time slot. In order to improve their system performance, the users can cooperate. For instance, if the users cooperate, each group, i.e., coalition S ⊆ N , of cooperating single-antenna transmitters can be seen as a single-user MIMO device (since the system already has multiple antennas at the receiving end, i.e., the BS). These cooperative

2

Note that the subsequent model and formulation can also be tailored for other multiple access schemes such as OFDMA or CDMA.

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Coalition 2 User 4

User 6

User 5

Coalition 3 Base station with K antennas User 2

Time slot 1

User 1

Time slot 2 Time slot 3 Time slot 4

User 2

User 3

User 4

Time slot 5 Time slot 6

User 5

User 6

User 1 User 3

Time slot 1

Coal. 1

Time slot 2 Time slot 3 Time slot 4

Coal. 1

Coal. 1

Coal. 2

Time slot 5 Time slot 6

Coal. 3

Coal. 2

Coalition 1 Figure 13.1. An illustrative example of a single cell with N = 6 users cooperating for virtual MIMO formation.

coalitions subsequently transmit in a TDMA manner, i.e., one coalition per time slot. Hence, during the time scale N , each coalition is able to transmit within all the time slots previously held by its users. By doing so, there is a cooperative scheme within every cell in a wireless cellular network. An illustrative example of this network model is shown in Figure 13.1 for N = 6. The key issues that need to be tackled in this model are two-fold: (i) What are the benefits and costs from cooperation? (ii) Given the benefit–cost tradeoff which groups of users should cooperate? Given a coalition S ⊆ N with |S| users (| · | represents the cardinality of a set), we consider a block fading K × |S| channel matrix H S with a path-loss model between @ the users in S and the BS with each element of the matrix hi,k = ej Φ i , k κ/dµi,k with µ the path-loss exponent, κ the path-loss constant, Φi,k the phase of the signal from transmitter i to the BS receiver k, and di,k the distance between transmitter i and the base BS’s receiver k. Further, for the considered TDMA system, we define a fixed transmit power constraint per time slot, i.e., a power constraint per coalition P˜ . This average power constraint is applied to all the transmitters that are part of the coalition active in the slot. In the noncooperative scenario, this same power constraint per slot is simply the power constraint per individual user active in the slot. In fact, due to ergodicity, for each time slot, the average long-term power constraint per individual user and the power constraint per slot (i.e., constraining all transmitters of a coalition active in a slot) are the same [12, 13]. Subsequently, each coalition transmits in a slot, hence, perceiving no interference from other coalitions during transmission. As a result, in a slot, the sum-rate capacity of the virtual MIMO formed by a


353

coalition S, under a power constraint PS with Gaussian signaling is given by [15] CS = max I(xS ; y S ) = max(log det(I K + H S · QS · H †S )) QS

QS

subject to: tr[QS ] ≤ PS ,

(13.1)

where xS and y S are, respectively, the transmitted and received signal vectors of coalition S of size |S| × 1 and K × 1, QS = E [xS · x†S ] is the covariance of xS and H S is the channel matrix with H †S its conjugate transpose. The considered channel matrix H S is assumed perfectly known at the transmitter and receiver. Thus, the maximizing input signal covariance is given by QS = V S D S V †S [15], where V S is the unitary matrix given by the singular value decomposition of H S = U S ΣS V †S and D S is an |S| × |S| diagonal matrix given by D S = diag(D1 , . . . , DF , 0, . . . , 0). Here F ≤ min (K, |S|) is the number of positive singular values of the channel H S (eigenmodes) and each Di + is given by Di = (µ − λ−1 by water-filling to satisfy i ) , where µ is determined the coalition power constraint tr[QS ] = tr[D S ] = i Di = PS , and λi is the ith eigenvalue of H †S H S . Using [15], the resulting capacity, in a slot, for a coalition S is CS =

K

(log (µλi ))+ .

(13.2)

i=1

To form the considered virtual MIMO coalitions and benefit from the capacity gains, the users need to exchange their data information and their channel (user-BS) information. For this purpose, we will consider a cost for information exchange in terms of transmit power. This transmit power cost mainly models the data exchange penalty. As we consider block fading channels with a long coherence time, the additional power penalty for exchanging the user-BS channel information can be deemed as negligible relative to the data exchange cost, since the considered channel varies slowly (for example, exchange of the channel information can be done only periodically). Consequently, the cost for information exchange is taken as the sum of the powers required by each user in a coalition S to broadcast to its corresponding farthest user inside S. Due to the broadcast nature of the wireless channel, once a coalition member broadcasts its information to the farthest user, all the other members can also receive this information simultaneously. The power needed for broadcast between a user i ∈ S and its corresponding farthest user î ∈ S is ν0 · σ 2 , P¯i,î = h2i,î

(13.3)

where ν0 is a target@average SNR for information exchange, σ 2 is the noise variance, and hi,î = κ/dµi,î is the channel gain between users i and î with di,î the distance between users i and î. In consequence, the total power cost for a

354


coalition S having |S| users is given by PˆS as follows: PˆS =

|S |

P¯i,î .

(13.4)

i=1

It is interesting to note that the defined cost depends on the location of the users and the size of the coalition; hence, a higher power cost is incurred whenever the distance between the users increases or the coalition size increases. Thus, the actual power constraint PS per coalition S with cost is PS = (P˜ − PˆS )+ ,

(13.5)

where P˜ is the average power constraint per coalition (per slot), PˆS is the cooperation power cost given in (13.4), and a+ max (a, 0). In order to achieve the capacity in (13.2), within a slot, each user of a coalition S adjusts its power value based on the water-filling solution, taking into account the available power constraint PS . Note that, since the power constraint P˜ applied over a coalition is the same as the maximum power constraint per individual user in the coalition, the water-filling solution always yields a power value per user that does not violate the user’s available power after deducing the cost for cooperation in (13.3) from its individual long-term power constraint. The considered power cost does not take into account the interference during exchange of information between users and can be considered as a lower bound of the penalty incurred by cooperation. In addition to this power cost, a fraction of time may be required for the data exchange between the users prior to cooperation. However, due to the fact that the power cost given in (13.4) depends on distance and coalition size, the formed coalitions will typically consist of small clusters of nearby users, and thus the users can exchange information at high rates rendering the time for data exchange negligible relative to the transmission time slot (typically, the distance between the users of a coalition and the BS is larger than the distance between the coalition users themselves). Furthermore, in practice, cooperating to form a virtual MIMO formation can require a synchronization at the carrier frequency between the nodes, yielding some costs for practical implementation. In this chapter, we will not account for these carrier synchronization costs; however, this could constitute quite an interesting future direction. The coalition formation results derived in this chapter could also be applied for other cost functions without loss of generality. For example, the cost of power can be replaced by the cost of bandwidth where one could quantify the use of an additional band for information exchange, orthogonal to the band of transmission. Given this benefit–cost tradeoff, the following subsections mainly deal with: (i) formulating a coalitional game among the users by defining an appropriate value function, and (ii) classifying and studying the properties of the game.


13.3.2

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Distributed virtual MIMO coalition formation game Coalition formation game formulation By investigating the illustrative example in Figure 13.1, one can easily see that to form a virtual MIMO system a coalitional game can be defined with the players set being the set N of all users. The next step is to define an appropriate value for the game. For instance, based on the capacity benefit and power cost defined, respectively, in (13.2) and (13.5), over the TDMA time scale of N , for every coalition S ⊆ N , the utility (value) function in characteristic form is defined as |S| · CS , if PS > 0, (13.6) v(S) = 0, otherwise, where PS is given by (13.5), CS is given by (13.2), and |S| is the number of users in S. This utility represents the total capacity achieved by coalition S during the time scale N while accounting for the cost through the power constraint. A coalition of |S| users will transmit with capacity CS during |S| time slots, thus achieving a total sum-rate of v(S) during the time scale N (e.g., in Figure 13.1, during N = 6 coalition 2 consisting of two users achieves C2 in slot 4 and C2 in slot 6; thus a total of 2 · C2 during N = 6 slots). The second case in (13.6) implies that if the power for information exchange is larger than (or equal to) the available power constraint the coalition cannot be formed due to a utility of 0. By a close inspection of (13.6), one can immediately make the following remark. Remark 13.1 The virtual MIMO formation game can be formulated as an (N , v) coalitional game in characteristic form with transferable utility (TU). For instance, it is easily seen that the value function in (13.6) depends only on the users inside S and, thus, the game is in characteristic form. Moreover, the utility in (13.6) represents the sum-rate achieved by coalition S, therefore, this sum-rate can be divided in any manner between the coalition members in order to obtain the individual user payoff achieved. This individual user payoff, denoted φvi , represents the total rate achieved by user i during the transmission time scale N . Due to the TU property of the game, the payoff φvi of each user i in a coalition S can be computed by a fair division of the utility v(S) through various criteria such as proportional fair division, Shapley value (SV) division, egalitarian fair division, or max–min fair division using the nucleolus. In this chapter, we restrict ourselves to the proportional fair and SV divisions defined below (interested readers can see [6] for information on the other rules). Proportional fairness In practice, a network user experiencing a good channel might not be willing to cooperate with a user with bad channel conditions unless the payoff it receives

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takes into account its contribution to the coalition. To account for the channel differences, one can use the proportional fairness criterion, in which the extra benefit from forming a coalition is divided in weights according to the users’ noncooperative utilities. Thus, ⎛ ⎞ v({j})⎠ + v({i}), (13.7) φvi = wi ⎝v(S) − j ∈S

where i∈S wi = 1 and within the coalition wi /wj = v({i})/v({j}). Thus, within the coalition for proportional fair division, the users with good channel conditions deserve more extra benefits than the users with bad channel conditions. Shapley value (SV) fairness Another measure of fairness for payoff division can be done using the SV [1], defined as follows. Definition 13.1 An SV φv is a function that assigns to each possible characteristic function v a vector of real numbers, i.e., φv = (φv1 , φv2 , . . . , φvN ), where φvi represents the worth or value of user i in the game (N , v). There are four Shapley axioms that φv must satisfy: (1) efficiency axiom: i∈N φvi = v(N ); (2) symmetry axiom: if user i and user j are subject to v(S ∪ {i}) = v(S ∪ {j}) for every coalition S not containing user i and user j, then φvi = φvj ; (3) dummy axiom: if user i is subject to v(S) = v(S ∪ {i}) for every coalition S not containing i, then φvi = 0; (4) additivity axiom: if u and v are characteristic functions, then φu + v = φv + u = φu + φv . It is shown [1] that there exists a unique function φv satisfying the Shapley axioms given by (|S|)!(N − |S| − 1)! [v(S ∪ {i}) − v(S)]. (13.8) φvi = N! S ⊆N −{i}

The SV provides a fair division which takes into account the randomly ordered joining of the users in the coalition. Under the assumption of randomly ordered joining, the Shapley function of each user is its expected marginal contribution when it joins the coalition [1]. In general, the SV is used in games where the grand coalition, i.e., the coalition of all users, will form (such as in canonical games). However, whenever independent coalitions can form in the network such as in the virtual MIMO game (as will be seen later in this section), given any coalition S, one can consider the payoff division by SV by applying (13.8) on each restricted game (S, v) in the network. In fact, it is shown in [16] that, in a game where a coalitional structure is


357

present (not just a single grand coalition), the SV of the whole game (N , v) is found by using the SV on the game restricted to each coalition S in the structure. Given the formulated (N , v) TU coalitional game for virtual MIMO formation, we investigate some of the properties of this game in order to map it into a suitable class of coalitional game theory. First, we investigate the property of superadditivity defined as follows: Definition 13.2 A coalitional game (N , v) with transferable utility is said to be superadditive if for any two disjoint coalitions S1 , S2 ⊂ N , v(S1 ∪ S2 ) ≥ v(S1 ) + v(S2 ). Theorem 13.1 The virtual MIMO formation (N ,v) coalitional game is nonsuperadditive. The proof of this theorem can be found in [6]. Theorem 13.1 implies that, for the virtual MIMO formation game, due to the cost for cooperation implies, whenever the coalition grows, the total utility, i.e., sum-rate, that it generates may decrease (depending on the users’ channels). For instance, the cost for information exchange grows with the size of the coalition as well as the distance between these users. Further, we define the following concepts of coalitional game theory [1]. Definition 13.3 A payoff vector φv = (φv1 , . . . , φvN ) for dividing the value v of v a coalition is said to be group rational or efficient if N i=1 φi = v(N ). A payoff vector φv is said to be individually rational if the player can obtain a benefit no less than acting alone, i.e., φvi ≥ v({i}), ∀ i. An imputation is a payoff vector satisfying the above two conditions. Definition 13.4 An imputation φv is said to be unstable through a coalition S if v(S)> i∈S φvi , i.e., the players have an incentive to form coalition S and reject the proposed φv . The set C of stable imputations is called the core, i.e., 4 v v v C= φ : φi = v(N ) and φi ≥ v(S) ∀ S ⊆ N . (13.9) i∈N

i∈S

A nonempty core means that the players have an incentive to form the grand coalition. Remark 13.2 In general, the core of the (N ,v) virtual MIMO formation game is empty. In the discussed model, the costs of cooperation for a coalition S increase as the number of users in a coalition increases as well as when the distances between the users increase, hence affecting the topology. In particular, consider the grand coalition N of all N users in the network. This coalition consists of

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a large number of users who are randomly located at different distances. Hence, the grand coalition will often have a value of v(N ) = 0 due to the cooperation costs and several coalitions S ⊂ N have an incentive to deviate from this grand coalition and form independent disjoint coalitions. Consequently, an imputation that lies in the core cannot be found, and, due to cost, the core of the virtual MIMO formation (N ,v) game is generally empty. Hence, as seen in Figure 13.1 and corroborated by the nonsuperadditivy of the game and the emptiness of the core, in general, due to the cost for coalition formation, the grand coalition will not form. Instead, independent and disjoint coalitions appear in the network as a result of the virtual MIMO formation process. In this regard, the game is classified as a coalition formation game [3], and the objective is to find the coalitional structure that will form in the network, instead of finding only a solution concept, such as the core. Further, note that one implication of the nonsuperadditivity of the game is that the SV might not be individually rational, hence, any coalition formation algorithm that will be constructed must handle this property with an appropriate coalition formation decision. In the next section, we will devise an algorithm for coalition formation that can take into account all these properties of the virtual MIMO coalition formation game and that allows to characterize the network structure in the presence of the users’ cooperative behavior.

Coalition formation algorithm Coalition formation has been a topic of great interest in game theory [2, 3, 17, 18]. By using mathematical tools from coalition formation games, one can build algorithms to form coalitions dynamically among a group of players, and, thus these algorithms can be applied in a distributed manner, notably in a wireless scenario. To devise a suitable algorithm for virtual MIMO formation, several concepts from coalition formation games need to be defined as follows. Definition 13.5 A collection of coalitions, denoted by S, is defined as the set S = {S1 , . . . , Sl } of mutually disjoint coalitions Si ⊂ N . In other words, a collection is any arbitrary group of disjoint coalitions Si of N , not necessarily spanning A all players of N . If the collection spans all the players of N ; i.e., lj =1 Sj = N , the collection is a partition of N . Definition 13.6 A preference operator or comparison relation is an order defined for comparing two collections R = {R1 , . . . , Rl } and S = {S1 , . . . , Sp } that are partitions of the same subset A ⊆ N (i.e., same players in R and S). Therefore, R S implies that the way R partitions A is preferred to the way S partitions A. Various well-known orders can be used as comparison relations in different scenarios [3]. For the virtual MIMO coalition formation game, we define the following order.


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Definition 13.7 Consider two collections R = {R1 , . . . , Rl } and S = {S1 , . . . , Sm } that are partitions of the same subset A ⊆ N (same players in R and S). For a collection R = {R1 , . . . , Rl }, let the utility of a player j in a coalition Rj ∈ R be denoted by φvj (R). Then R is preferred over S by Pareto order, written as R S, iff R S ⇐⇒ {φvj (R) ≥ φvj (S) ∀ j ∈ R, S} with at least one strict inequality (>) for a player k.

(13.10)

In other words, a collection is preferred by the players over another collection, if at least one player is able to improve its payoff without hurting the other players. Subsequently, to perform autonomous coalition formation between the users in the wireless network, we construct a distributed algorithm based on two simple rules denoted as “merge” and “split” [17] defined as follows. Definition 13.8 Merge rule Merge any set of coalitions {S1 , . . . , Sl } whenever the merged form is preferred by the players, i.e., where {

l 3

Sj } {S1 , . . . , Sl }.

j =1

A Therefore, {S1 , . . . , Sl } → { lj =1 Sj }. Definition 13.9 Split rule Split any coalition is preferred by the players, i.e., where {S1 , . . . , Sl } {

l 3

Al j =1

Sj whenever a split form

Sj }.

j =1

Al

Thus, {

j =1

Sj } → {S1 , . . . , Sl }.

In brief, multiple coalitions will merge (split) if merging (splitting) yields a preferred collection based on the Pareto order. Thus, coalitions will merge only if at least one user can enhance its individual payoff through this merge without decreasing the other users’ payoffs. Similarly, a coalition will split only if at least one user in that coalition is able to strictly improve its individual payoff through the split without hurting other users. A decision to merge or split is thus tied to the fact that all users must benefit from the merge or split, therefore any merged (or split) form is reached only if it allows all involved users to maintain their payoffs with at least one user improving. In summary, using merge and split one can devise a coalition formation algorithm with partially reversible agreements [2], where the users sign a binding agreement to form a coalition through the merge operation (if all users are able to improve their individual payoffs from the previous state) and they can only split this coalition if splitting does not decrease the payoff of any coalition member (partial reversibility).

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For the virtual MIMO formation game, the coalition formation algorithm consists of two phases: adaptive coalition formation and transmission. In the adaptive coalition formation phase, an iteration of sequential merge-and-split rules is performed until a final network partition composed of independent disjoint coalitions is obtained. In the transmission phase, the formed coalitions transmit in their corresponding slots in a TDMA manner. The transmission phase may occur several times prior to the repetition of the coalition formation phase, notably in a low-mobility environment where changes in the coalition structure due to mobility seldomly occur. Although any arbitrary merge process can be used, we consider a distributed cost-based merge procedure allowing the coalitions (users) to perform a local search for partners. Consequently, the decision to merge with neighboring coalitions is taken based on the Pareto order proceeding from the partner that provides the lowest cost. In order for coalition S1 to merge with another coalition S2 , the utility of the formed coalition through merge must be positive; i.e., v(S1 ∪ S2 ) > 0 otherwise no benefits exist for the merge. Thus, based on the defined power cost (13.4) and utility (13.6), coalitions can only merge when the cost for cooperation is less than P˜ . Otherwise, when the cost is greater than or equal P˜ , through (13.6) the utility of the merged coalition will be 0 and there is no mutual benefit. Thus, using (13.4) the merge is possible (nonzero utility) for |S 1 ∪S 2 | ¯ Pi,î < P˜ , which, by (13.3), yields S1 with S2 if PˆS 1 ∪S 2 < P˜ , i.e., i=1 |S 1 ∪S 2 |

i=1

P˜ 1 . µ < di,î ν0 · σ 2 · κ

(13.11)

Thus, a coalition will only attempt to merge with other coalitions where (13.11) can be verified. Each stage of the coalition formation algorithm starts from an initial network partition T = {T1 , . . . , Tl } of N . In this partition, any random coalition (user) can start with the merge process. For implementation purposes, assume that the coalition Ti ∈ T which has the highest utility in the initial partition T starts the merge by attempting to cooperate with the coalition yielding the lowest cost. On one hand, if merging occurs, a new coalition T˜i is formed and, in its turn, coalition T˜i will attempt to merge with the lowest-cost partner. On the other hand, if Ti were unable to merge with the lowest-cost coalition, it would try the next lowest-cost partner, proceeding sequentially through the coalitions verifying (13.11). The search ends with a final merged coalition Tifinal composed of Ti and one or more of the coalitions in its vicinity (or just Ti , if no merge occurred). The algorithm is repeated for the remaining Ti ∈ T until all the coalitions have made their local merge decisions, resulting in a final partition W. The coalitions in the resulting partition W are next subject to split operations, if any are possible. An iteration consisting of multiple successive merge-and-split operations is repeated. As shown in [17], any arbitrary sequence of merge-and-split rules will terminate, and, thus, the convergence of the first phase of the algorithm is


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Table 13.1. One stage of the merge-and-split coalition formation algorithm Initial state The network is partitioned by T = {T1 , . . . , Tk } (at the beginning of all time T = N = {1, . . . , N } with non-cooperative users). Coalition formation algorithm Phase I Adaptive coalition formation: Coalition formation using merge-and-split occurs. repeat (a) Coalitions begin the local search merge operation: W = Merge(T ). (b) Coalitions in W decide to split based on the Pareto order. T = Split(W). until merge-and-split iteration terminates. Phase II Virtual MIMO transmission: The coalitions transmit during the time scale N with 1 coalition per slot with each coalition occupying all the time slots previously held by its members. The algorithm is repeated periodically, enabling the users to autonomously self-organize and adapt the topology to environmental changes such as mobility.

always guaranteed. Table 13.1 shows a summary of one round of the coalition formation algorithm. For networks where the environment is changing, e.g., due to mobility, the algorithm in Table 13.1 can be repeated periodically in order to adapt the network structure to the environmental changes. The result of the algorithm in Table 13.1 is a network partition composed of disjoint independent coalitions. First and foremost, one would note that, in the final network structure, due to convergence, no coalition has an incentive to pursue any further merge or split procedure. Thus, the resulting network structure is merge-and-split stable in the sense that no coalition has an incentive to deviate from this structure through merge or split rules. This stability of the resulting network partition can be further investigated with respect to the concept of a defection function D [17]. Definition 13.10 A defection function D is a function which associates with each partition T of N a family (group) of collections in N . A partition T = {T1 , . . . , Tl } of N is D-stable if no group of players is interested in leaving T when the players who wish to leave can only form the collections allowed by D.

362


The most important defection function is the Dc (T ) function (denoted Dc ) which associates with each partition T of N the family of all collections in N . This function allows any group of players to leave the partition T of N through any operation and create an arbitrary collection in N . From the Dc function one can define a strong stability concept. Definition 13.11 A partition T of the players’ set N is said to be Dc -stable, if no players in T are interested in leaving T to form other collections in N . For instance, whenever a Dc -stable partition exists for a given coalitional game, this partition possesses the following properties: (1) If it exists, a Dc -stable partition is the unique outcome of any arbitrary iteration of merge and split. (2) A Dc -stable partition T is a unique -maximal partition, i.e., for all partitions T = T of N , T T . In the case where represents the Pareto order, this implies that the Dc -stable partition T is the partition that presents a Pareto optimal payoff distribution for all the players. Clearly, a Dc -stable partition is an optimal partition that the wireless network can seek as it provides a payoff distribution that is Pareto optimal for all users with respect to any other network partition. In addition, this partition is a unique outcome of any arbitrary iteration of merge-and-split rules. However, the existence of a Dc -stable partition is not always guaranteed [17]. The Dc -stable partition T = {T1 , . . . , Tl } of the whole space N exists if a partition of N verifies two necessary and sufficient conditions [17]: (1) For each i ∈ {1, . . . , l} and each pair of disjoint coalitions A and B such that {A ∪ B} ⊆ Ti we have {A ∪ B} {A, B} (referred to as cond. (A) hereafter). (2) For the partition T = {T1 , . . . , Tl } a coalition S ⊂ N formed of players belonging to different Ti ∈ T is T -incompatible if for no i ∈ {1, . . . , l} we have S ⊂ Ti . Dc -stability requires that for all T -incompatible coalitions {S}[T ] {S}, where {S}[T ] = {S ∩ Ti ∀ i ∈ {1, . . . , l}} is the projection of coalition S in partition T (referred to as cond. (B) hereafter). If no partition of N can satisfy these conditions, then no Dc -stable partition of N exists. Since the Dc -stable partition is a unique outcome of any arbitrary merge-and-split iteration, we have Lemma 13.1 For the (N , v) virtual MIMO coalition formation game, the mergeand-split algorithm of Table 13.1 converges to the optimal Dc -stable partition, if such a partition exists. Otherwise, the algorithm yields a final network partition that is merge-and-split proof.


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In the transmitter cooperation game, the existence of a Dc -stable partition depends on various factors. For instance, cond. (A) states that, for a Dc -stable partition T , every coalition Ti ∈ T must verify the Pareto order not only at the level of the whole coalition Ti but also at the level of all disjoint coalitions subsets of Ti . Verifying the Pareto order requires that the utility of every union of any two disjoint coalitions subsets of a coalition Ti must yield an extra utility over the disjoint case; i.e., v(A ∪ B) > v(A) + v(B) ∀ A, B ⊂ Ti . In an ideal case with no cost, as the number of transmit antennas is increased for a fixed power constraint, the overall system diversity increases as the data pass through different channel values allowing, with adequate coding, the symbols to be recovered without error at a higher rate [19]. In such a case, since A ∪ B has a larger number of antennas than A and B, ∀ A, B ⊂ Ti and for each Ti we have CA ∪B > max (CA , CB ) and thus |A ∪ B| ·CA ∪B >|A| · max (CA , CB ) + |B| · max (CA , CB ), |A ∪ B| · CA ∪B >|A| · CA+|B| · CB ⇔ v(A ∪ B)>v(A)+v(B),

(13.12)

which is sufficient to verify cond. (A) for Dc -stability when adequate payoff divisions are done. However, due to the cost CA ∪B , CA and CB can have different power constraints and (13.12) may not be guaranteed ∀A, B ⊂ Ti . Guaranteeing this condition is directly dependent on the cooperation cost within the coalitions in T and, thus, on the users’ location. In practical networks, verifying cond. (A) for Dc -stability depends on the users’ random locations. Cond. (B) for the existence of a Dc -stable partition T is that players formed from different Ti ∈ T have no incentive to form a coalition S outside of T . In the transmitter cooperation game, cond. (B) is also dependent on the location of the coalitions Ti ∈ T ; specifically on the distance between the users in different coalitions Ti ∈ T . Thus, cond. (B) is verified whenever two users belonging to different coalitions in a partition T are separated by a large distance. A sufficient condition for verifying this second requirement can be derived. Theorem 13.2 For a network partition T = {T1 , . . . , Tl } resulting from the coalition formation algorithm, if the distance di,j between any two users i ∈ Ti µ1 and j ∈ Tj with Ti = Tj verifies di,j > κ · P˜ /2 · ν0 · σ 2 = dˆ0 , then the second condition for Dc stability, cond. (B), is verified. Proof. Since a Dc -stable partition is a unique outcome of any merge-and-split iteration, we will consider the partition T = {T1 , . . . , Tl } resulting from any merge-and-split iteration in order to show when cond. (B) can be satisfied. A T -incompatible coalition is a coalition formed from users belonging to different Ti ∈ T . Consider the T -incompatible coalition {i, j} that can potentially form between two users i ∈ Ti and j ∈ Tj with Ti = Tj . The total power cost for {i, j} is given by (13.3) as Pˆ{i,j } = P¯i,j + P¯j,i = 2 · P¯i,j . In the case where the total power cost is larger than the constraint, we have Pˆ{i,j } ≥ P˜

364


and thus P¯i,j ≥ P˜ /2 which yields the required condition on distance di,j ≥ 1 (κ · P˜ /2 · ν0 · σ 2 ) µ = dˆ0 . We have by (13.6) v({i, j}) = 0, and, thus, φvi ({i, j}) = φvj ({i, j}) = 0. Or we have that {i, j}[T ] = {{i, j} ∩ Tk ∀ k ∈ {1, . . . , l}} = {{i}, {j}}, and, thus, φvi ({i, j}[T ]) = v({i}) > φvi ({i, j}) = 0 and φvj ({i, j}[T ]) = v({j}) > φvj ({i, j}) = 0. Consequently, {i, j}[T ] {i, j} and cond. (B) is verified for any T -incompatible coalition formed of two users. Moreover, when any two users i ∈ Ti and j ∈ Tj with Ti = Tj are separated by dˆ0 , T -incompatible coalitions S with |S| > 2 have a cost PˆS > Pˆ{i,j } ≥ P˜ and thus v(S) = 0; yielding S[T ] S for all T -incompatible coalitions S. Hence, when any two users in the network partition T resulting from merge and split are separated by a distance larger than dˆ0 , then cond. (B) for Dc stability existence is verified. In summary, the existence of the Dc -stable partition is closely tied to the users’ location, which is a random parameter in practical networks. However, when such a partition does exist, the network resulting from the coalition formation algorithm will converge to that Dc -stable partition as per Lemma 13.1. The algorithm in Table 13.1 can be implemented in a distributed way. As the user can detect the strength of other users’ uplink signals (through techniques similar to those used in the ad-hoc routing discovery), nearby coalitions can be discovered and the local merge algorithm performed. Each coalition surveys neighboring coalitions satisfying (13.11) and attempts to merge based on the Pareto order. The users in a coalition need only to know the maximum distances with respect to the users in neighboring coalitions. Moreover, each formed coalition internally decides to split if its members find a split form by Pareto order. By using a control channel, the distributed users can exchange some channel information and then cooperate using our model (exchange data information if needed, form a coalition then transmit). Signaling for this handshaking can be minimal.

Numerical results To assess the performance of coalition formation for distributed virtual MIMO, we set up a single-cell composed of a single BS with K = 3 equally spaced antennas located at the center of a square of 4 km× 4 km. Without loss of generality, at the receiver, we consider antennas that are separated enough while3 Φi,k = 0 ∀i, k. The propagation loss is set to µ = 3 and the path-loss constant κ = 1. The power constraint per slot is P˜ = 10 mW, the cost SNR target for information exchange is ν0 = 10 dB, and noise level is −90 dBm. First, we set up a network with N = 10 users where the users are located in a way that a Dc -stable partition exists. Figure 13.2 shows that the coalition 3

This choice provides a lower bound on the performance gain of the coalition formation algorithm (i.e., the gains mainly stemming from the transmitters cooperation which is the main objective of this section); considering different phases certainly yields an additional multiplexing gain and it does not affect the analysis or the results hereafter.


365

Figure 13.2. Convergence of the algorithm to a final Dc -stable partition. formation algorithm converges to the final Dc -stable network partition T = {T1 , . . . , T5 } (valid for both proportional fair and SV fairness criteria). Cond. (A) for Dc -stability is easily verified for coalitions consisting of at most two users since such coalitions do not form unless the Pareto order is internally verified (definition of the merge rule). For the three-users coalition T2 = {7, 9, 10} Table 13.2 shows the payoffs of the different subcoalitions for both fairness types. Table 13.2 shows that the Pareto order is internally verified for T2 , that is ∀A, B ⊂ T2 ; {A ∪ B} {A, B} for all fairness cases. In addition, by inspecting Figure 13.2 it is clear that any two users belonging to T -incompatible coalitions are separated by a distance larger than the maximum distance, which is dˆ0 = 0.793 km, computed using Theorem 13.2 for the simulation parameters. Thus, Theorem 13.2 is satisfied and cond. (B) is verified. For example, for the T -incompatible coalition S = {4, 7} equation (13.6) yields v(S) = 0 and thus φv4 (S) = φv7 (S) = 0 due to the distance between users 4 and 7. The projection of S in T is S[T ] = {{4, 7} ∩ T1 , {4, 7} ∩ T2 , {4, 7} ∩ T3 , {4, 7} ∩ T4 , {4, 7} ∩ T5 , {4, 7} ∩ T6 } = {{4}, {7}}. In S[T ], the payoffs of users 4 and 7 are respectively φv4 (S[T ]) = v({4}) = 7.6069 and φv7 (S[T ]) = v({7}) = 3.1077, by Pareto order φv4 (S[T ]) > φv4 (S) and φv7 (S[T ]) > φv7 (S), thus, S[T ] S. In Figure 13.3, we show the average total individual user payoff (rate) improvement achieved during the whole transmission time scale as a function of the network size. This result is averaged over the random locations of the users. We compare the performance of the coalition formation algorithm to that of

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Table 13.2. Payoffs for coalition T2 = {7, 9, 10} of Figure 13.2 and its sub-coalitions Proportional fair User 7 {7} {9} {10} {7, 9} {7, 10} {9, 10}

3.1077

T2 = {7, 9, 10}

4.6431

User 9

User 10

Shapley User 7

User 9

3.1077 2.7173

2.7173 2.7345

4.0416 4.0648

User 10

3.5338 3.6206

3.5779 3.5967

4.0869

4.0598

2.7345 3.9829 4.7863 4.5210

3.5925 3.5996

4.4406 3.6177

4.1558

4.1131

Figure 13.3. Cooperation gains in terms of the average individual user payoff achieved by the merge-and-split scheme during the whole transmission duration compared with the noncooperative case and the centralized optimal solution for different network sizes and different fairness criteria. the noncooperative case as well as the optimal partition found by a centralized entity through exhaustive search. For the cooperative case, the average user’s payoff increases with the number of users N since the possibility of finding cooperating partners increases. In contrast, the noncooperative approach presents an


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fair SV

Figure 13.4. Frequency of merge-and-split operations per minute for different speeds in a mobile network of Mt = 50 users. almost constant performance with different network sizes. Cooperation presents a significant advantage over the noncooperative case in terms of average individual utility for all fairness types, and this advantage increases with the network size. The proportional fair division presents the best performance, as it allows an improvement of up to 40.42% over the noncooperative case at N = 100. This result also highlights the tradeoff between fairness and cooperation gains. For instance, while the proportional fairness presents an advantage in terms of payoff gain, since it allows larger coalitions to form (due to it being less strict in fairness than the SV), the SV presents lower gains but more fairness in allocating payoffs. Furthermore, compared to the optimal solution, the merge-and-split algorithm achieves a highly comparable performance with a performance loss not exceeding 1% at N = 20 users. This clearly shows that, by using the distributed merge-and-split algorithm, the network can achieve a performance that is very close to optimal. Note that, for more than 20 users, finding the optimal partition by exhaustive search is mathematically and computationally intractable. To show how the coalition formation algorithm can handle mobility, we deploy a network of N = 50 mobile users (random walk mobility model) for a period of 5 minutes. For N = 50, each TDMA transmission requires 50 × θ seconds with θ the slot duration (we let θ = 10 ms). The results in terms of frequency of mergeand-split operations per minute are shown in Figure 13.4 for various speeds. As the speed increases, for both fairness types, the number of merge-and-split operations increases due to the changes in the network structure incurred by mobility. Fairness types that potentially yield large coalitions, such as proportional

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fair, incur a higher frequency of merge and split since such coalitions require additional merge operations and are more prone to splitting due to mobility. In contrast, strict fairness criteria, such as the SV, yield relatively lower frequency of merge and split. In a nutshell, Figure 13.4 demonstrates that, by periodic runs of the coalition formation algorithm and through adequate merge-and-split decisions, the users can self-organize and adapt to the changes in the environment.

13.4

Coalitional graph game among relay stations In this section the challenges of deploying relay stations in next generation wireless systems are studied. For this purpose, we examine the use of coalitional graph games for modeling the interactions among the relay stations seeking to send data in the uplink of a wireless system. First, we motivate the problem and provide a suitable system model. Then, we formulate a network formation game among the relay stations, investigate the resulting graph structure, and study their properties.

13.4.1

Motivation and basic problem In order to mitigate the fading effects of the wireless channel, several nodes or relays can cooperate with a given source node in the transmission of its data to a far away destination, thereby, providing spatial diversity gains for the source node. By doing so, one can significantly improve the performance of the source node. This class of cooperation is commonly referred to as cooperative communications [20]. It has been shown that by using one or more relays [19–21] a significant improvement can be obtained in terms of BER, throughput, or other quality of service (QoS) parameters. Moreover, different aspects of cooperative transmission have been discussed in the literature such as performance analysis and resource allocation [19–21]. Due to this proven advantage of cooperative communications, a key feature in next generation wireless systems, such as 3GPP’s long-term evolution advanced (LTE-Advanced) [22], or the forthcoming IEEE 802.16j WiMAX standard [23], is the introduction of the relay station (RS) nodes which can enable relaying in the network. Deploying RSs in a wireless system faces several challenging issues. For instance, as they are deployed in the network, the RSs need to route, among them, different packets received from external mobile stations using advanced techniques such as cooperative transmission. Due to the presence of RSs, the architecture of next generation wireless networks is governed by a multihop network structure formed between the RSs and their serving BS. Consequently, one prominent challenge is the design and study of the network multihop architecture that will connect the BS to the RSs in its coverage area given the cooperative strategies of the RSs and the existing network traffic. Thus, consider the uplink of a wireless system with M RSs (fixed, mobile, or nomadic) under the coverage area of a single BS. The RSs transmit their

13.4 Coalitional graph game among relay stations

369

data in the uplink to the BS through multihop links, and, therefore, a tree architecture needs to form, in the uplink, between the RSs and their serving BS. Once the uplink tree is formed, mobile stations (MSs) can hook up to the network by selecting a serving RS (or directly connecting to the BS). Each MS is assigned to the closest RS. We consider that the MSs deposit their packets to their serving RSs using direct transmission. In their turn, the serving RSs act as source nodes transmitting the received MS packets to the BS through one or more hops in the formed tree, using cooperative transmission. This assumption of direct transmission between MS and RS allows the provision of a tree formation algorithm that can be easily incorporated in a new or existing wireless network without relying on external entities such as the MSs. For cooperative transmission between the RSs and the BS, the decoded relaying multihop diversity channel of [21] is considered whereby each intermediate node on the path between a transmitting RS and the BS combines, encodes, and reencodes the received signal from all preceding terminals before relaying (decode-and-forward relaying). Formally, each MS k in the network is considered as a source of traffic following a Poisson distribution with an average arrival rate λk . With such Poisson streams at the entry points of the network (the MSs), we assume that for every RS incoming packets are stored and transmitted in a first-in first-out (FIFO) fashion and that we have Kleinrock’s independence approximation [24, Chap. 3] with each RS being an M/D/1 queueing system. With this approximation, the generation of the total traffic that RS i receives from the MS that it is serving is a Poisson process with an average arrival rate i λl , where Li is the number of MSs served by RS i. Moreover, RS i of Λi = Ll=1 also receives packets from RSs that are connected to it with a total average rate ∆i . For these ∆i packets, the sole role of RS i is to relay them to the next hop. In addition, any RS i that has no assigned MSs (Li = 0, Λi = 0, and ∆i = 0), transmits “HELLO” packets, generated with a Poisson arrival rate of η0 in order to keep its link to the BS active during periods of no actual MS traffic. An illustrative example of this model is shown in Figure 13.5. The main objective in this section is to provide a distributed algorithm that allows the RSs in a wireless system to autonomously form the uplink tree structure such as in Figure 13.5, adapting it to environmental changes as the network evolves. Further, another key goal is to model the gains in terms of cooperative transmission, while accounting for the costs in terms of the buffering and transmission delay incurred by the multihop transmission. In this context, the remainder of this section is dedicated to providing an accurate model for the uplink tree formation problem.

13.4.2

A network formation game among relay stations Game formulation To model the interactions among the RSs seeking to form the uplink network structure, we refer to coalitional graph games [3] which is a class of coalitional

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Figure 13.5. A prototype of the uplink tree model that governs the network architecture of next generation wireless systems. game theory that deals with the formation of network graphs among a number of nodes seeking to cooperate. In particular, for the RSs game, we utilize a subclass of coalitional graph games known as network formation games. For instance, network formation games are a hybrid class of games that combine concepts from both cooperative and noncooperative game theory [3, 18, 25]. In such games, several independent decision makers (players) interact in order to form a network graph among them. Depending on the goals of each player, a final network graph G, resulting from individual players’ decisions, forms. We model the uplink tree formation problem among the RSs as a network formation game with the RSs being the players. The result of the interactions among the RSs is a directed graph G(V, E) with V = {1, . . . , M + 1} denoting the set of all vertices (M RSs and the BS) and E denoting the set of all edges (links) between pairs of RSs. Each link between two RSs i and j, denoted (i, j) ∈ E, corresponds to an uplink traffic flow between RS i and RS j. First and foremost, we define the notion of a path: Definition 13.12 A path between two nodes i and j in the graph G is defined as a sequence of nodes i1 , . . . , iK such that i1 = i, iK = j and each directed link (ik , ik +1 ) ∈ G for each k ∈ {1, . . . , K − 1}. This section considers solely multihop tree (or forest, if some parts of the graph are disconnected) architectures, since such architectures are ubiquitous in next


371

generation networks [22, 23]. In this regard, throughout the remainder of this section we adopt the following convention. Remark 13.3 Each RS i is connected to the BS through at most one path, and, thus, we denote by qi the path between any RS i and the BS whenever this path exists. Further, we delineate the possible actions or strategies that each RS can take in the network formation game. The strategy space of each RS i consists of the RSs (or the BS) to which i wants to connect. Consequently, the strategy of RS i is to select the link that it wants to form from the available strategy space. We note that RS i cannot connect to RS j, which is already connected to i, in the sense that if (j, i) ∈ G, then (i, j) ∈ / G. Formally, for a current network graph G, let Ai = {j ∈ V \ {i}|(j, i) ∈ G} be the set of RSs from which RS i accepted a A link (j, i), and Si = {(i, j)|j ∈ V \ ({i} Ai )} as the set of links corresponding to the nodes (RSs or the BS) with whom i wants to connect (note that i cannot connect to RSs that are already connected to it, i.e., RSs in Ai .). Consequently, the strategy of RS i is to select the link si ∈ Si that it wants to form, i.e., choose the RS to which it will connect. Based on Remark 13.3, an RS can be connected to at most one other node in our game so choosing to form a link si implicitly implies that RS i will replace its previously connected link (if any) with the new link si . Having modeled the tree formation problem as a network formation game, we introduce a utility function that takes into account the QoS in terms of the packet success rate (PSR) as well as the delay incurred by multihop transmission. Consider an actual network tree graph G where each RS extracts a positive utility from the packets successfully transmitted to the BS out of the packets received from the MSs. Each transmitted packet is subject to a BER due to the transmission over the wireless channel using one or more hops. For example, for a transmission between RS V1 ∈ V and destination Vn +1 (the destinaton is always the BS) going through n − 1 intermediate relays {V2 , . . . , Vn } ⊂ V , let Nr be the set of all receiving terminals, i.e., Nr = {V2 . . . Vn +1 } and Nr (i) be the set of terminals that transmit a signal received by a node Vi . Hence, for a relay Vi on the path from the source V1 to the destination Vn +1 , we have Nr (i) = {V1 , . . . , Vi−1 }. Given this notation, the BER between a source RS V1 ∈ V and the destination Vn +1 = BS is computed along the path qV 1 = {V1 , . . . , BS} using the tight upper bound given in [21, Eq. (10)] for the decoded relaying multihop diversity channel with BPSK modulation and Rayleigh fading as follows: ⎛ ⎤⎞ ⎡ 1⎜ ⎢ ⎥⎟ γk ,i γk ,i ⎜ ⎥⎟ . ⎢ × 1 − PqeV ≤ ⎝ ⎣ 1 2 γk ,i − γj,i γk ,i + 2 ⎦⎠ N i ∈Nr

N k ∈Nr ( i )

N j ∈Nr ( i ) N j = N k

(13.13)

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Here, γi,j = Pi · gi,j /σ 2 is the average received SNR at node j from node i, where Pi is the transmit power of node i, σ 2 the noise variance, and gi,j = 1/dµi,j is the path-loss with di,j the distance between i and j and µ the path-loss exponent. Without loss of generality, we assume that all the RSs transmit with equal power Pi = P˜ , ∀i. Finally, for RS i which is connected to the BS through a direct transmission path qid ∈ Qi with no intermediate hops, the BER is given 1 e by Pq d = 2 1 − γi,B S /(1 + γi,B S ) [21], where γi,B S is the SNR at the BS i for transmission from RS i. Using the BER expression in (13.13) and with no channel coding, the PSR ρi,q i perceived by RS i over a path qi is defined as follows: ρi,q i (G) = (1 − Pqei )B ,

(13.14)

where B is the number of bits per packet. The PSR is a function of the network graph G as the path qi varies depending on how RS i is connected to the BS in the formed network tree structure. Transmitting over multihop links incurs a significant delay due to buffering and multiple transmissions. For this purpose, we consider the average delay τi,q i along the path qi = {i1 , . . . , ik } from RS i1 = i to the BS. A measure of the average delay over qi in a network with Poisson arrivals at the entry points and considering the Kleinrock approximation as in the previous section (each RS is an M/D/1 queueing system) is given by [24, Chap. 3, eqs. (3.42), (3.45), and (3.93)] τi,q i (G) =

(i k ,i k + 1 )∈q i

Ψi k ,i k + 1 1 + 2µi k ,i k + 1 (µi k ,i k + 1 − Ψi k ,i k + 1 ) µi k ,i k + 1

,

(13.15)

where Ψi k ,i k + 1 = Λi k + ∆i k is the total traffic (packets/s) originating from MSs (Λi k ) and from RSs (∆i k ) traversing link (ik , ik +1 ) ∈ qi between RS ik and RS ik +1 . The ratio 1/µi k ,i k + 1 represents the average transmission time (service time) on link (ik , ik +1 ) ∈ qi with µi k ,i k + 1 being the service rate on link (ik , ik +1 ). This service rate is given by µi k ,i k + 1 = Ci k ,i k + 1 /B where Ci k ,i k + 1 = W log (1 + νi k ,i k + 1 )

(13.16)

is the capacity of the direct transmission between RS ik and RS ik +1 , νi k ,i k + 1 = P˜ gi k ,i k + 1 /σ 2 is the received SNR from RS ik at RS ik +1 , and W is the bandwidth available for RS ik which is assumed the same for all RSs in the set of vertices V, without loss of generality. Similarly to the PSR, the delay depends on the paths from the RSs to the BS, hence is a function of the network graph G. For VoIP services, given the delay and the PSR, an appropriate utility function can be defined through the concept of the R-factor [26]. The R-factor is an expression that links the delay and packet loss to the voice quality as


373

follows [26]: Ui (G) = Ωa − 1 τi,q i (G) − 2 (τi,q i (G) − 3 )H − υ1 −υ2 ln (1 + 100υ3 (1 − ρi,q i (G))),

(13.17)

where τi,q i is the delay given by (13.15) expressed in milliseconds, 100(1 − ρi,q i ) represents the packet-loss percentage (we consider only the packet loss due to errors through ρi,q i in (13.14), ignoring packet loss due to overloaded links). The remaining parameters are constants defined as follows: Ωa = 94.2, 1 = 0.024, 2 = 0.11, 3 = 177.3, H = 0 if τi,q i < 3 , H = 1 otherwise. The parameters υ1 , υ2 , and υ3 depend on the voice speech codec. The relationship between the R-factor and the VoIP service quality is such that as the R-factor increases, the voice quality improves. For different voice codecs, different R-factor ranges provide an indication of the voice quality varying through poor, low, medium, high to best as the R-factor increases [26]. For example, for certain speech codecs as the R-factor increases in steps of 10 from 50 to 100, the voice quality is poor, low, medium, high and best, respectively [26]. Although the RSs are the players of the game, in the final results the performance of the MSs must be assessed in terms of the R-factor achieved (considered as MS utility). To compute the R-factor of the MSs, the PSR, and the delay for the whole transmission from MS to BS must be considered. For instance, the PSR perceived by each MS i served by RS j is given by ζi,j (G) = ρi,ij · ρj,q j (G),

(13.18)

where ρi,ij is the PSR on the direct transmission between MS i and RS j (independent of network graph G) and ρj,q j (G) is the PSR from RS j to the BS along path qj given by (13.14) (which can be either a multihop transmission or a direct transmission depending on how RS j is connected in the tree graph G). Moreover, the delay perceived by an MS i served by RS j is given by (13.15) by taking into account, in addition to the delay on the path qj , the traffic on the link (i, j) between the MS and the RS, i.e., the buffering and transmission delay at the MS level. Having the PSR given by (13.18) and the delay, the utilities of the MSs can be computed for performance assessment.

Network formation algorithm Having formulated a network formation game between the RSs, the next step is to define an algorithm of interaction between the RSs in order to form the desired network graph. For the RSs game, prior to providing a network formation algorithm, we first highlight that any such algorithm will result in a connected tree structure, as follows: Proposition 13.1 Any network graph G resulting from a network formation algorithm applied to the RSs network formation game is a connected directed tree structure rooted at the BS.

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The proof of this property can be found in [27]. Briefly, due to the high disconnection cost, if an RS is unable to find any partner suitable for forming a link, it will connect to the BS through direct transmission. Thus, the network initially starts with all the RSs connected to the BS (star topology), before engaging in the network formation game. Let Gs i ,s−i denote the graph G formed when RS i plays a strategy si ∈ Si while all other RSs maintain their vector of strategies s−i = [s1 , . . . , si−1 , si+1 , . . . , sM ]. We define the best response for an RS as follows [25]. Definition 13.13 A strategy s∗i ∈ Si is a best response for RS i ∈ V if Ui (Gs ∗i ,s−i ) ≥ Ui (Gs i ,s−i ), ∀si ∈ Si . Thus, the best response for RS i is to make the selection of the link that maximizes its utility given that the other RSs maintain their vector of strategies. By using the different properties of the RS network formation game, one can build a best response-based algorithm that allows a distributed formation of the network graph. In this algorithm, the RSs are assumed to be myopic in the sense that the RSs aim at improving their payoff considering only the current state of the network without taking into account the future evolution of the network. Finding an optimal network formation algorithm is a very complex problem, and no strict rules exist for doing so in the literature [18, 25]. Therefore, for each network formation game model, different operations must be applied suited to the model considered. Network formation literature encompasses several myopic dynamics for various game models with directed and undirected graphs [18, 25]. Inspired by [18] and [25], an algorithm composed of several rounds is constructed. In this algorithm, each round consists mainly of two phases: a fair prioritization phase and a myopic network formation phase. In the fair prioritization phase, we consider a priority function that assigns a priority to each RS. In the myopic network formation phase, by increasing priority, the RSs are allowed to interact. Therefore, each round of the network formation algorithm begins with the fair prioritization phase where each RS is assigned a priority depending on its actual perceived BER: RSs with a higher BER are assigned a higher priority. The motivation behind this procedure is to allow RSs that are perceiving a bad channel fairly to possess an advantage in selecting their partners for the purpose of improving their BER. Thus, the RSs experiencing a high BER can select their partners out of a larger space of strategies during the dynamics phase. Other priority functions can also be used, and in a general case, a random priority function can be defined. Following prioritization, the RSs start selecting their strategies sequentially in order of priority. During its turn, each RS i chooses to play its best response s∗i ∈ Si in order to maximize its utility at each round given the current network graph resulting from the strategies of the other RSs. The best response of each RS can be seen as a replace operation, whereby the RS will replace its current link to the BS with another link that maximizes its utility (if such a link is available).


375

Table 13.3. One round of the RSs network formation algorithm Initial state All the RSs start by directly connecting to the BS in a star topology. Two phases in each round of network formation Phase 1 Fair prioritization: Prioritize the RSs from the highest to the lowest current BER. Phase 2 Myopic network formation: The RSs take action sequentially by priority. Each RS i plays its best response s∗i , maximizing its utility (R-factor). The best response s∗i of each RS is a replace link operation through which a RS i splits from its current parent RS and replaces it with a new RS that maximizes its utility. Multiple rounds are run until convergence to the final Nash tree G† after which no RS can improve its utility by a unilateral change of strategy.

Multiple rounds consisting of the above two phases are run until convergence to the final tree structure G† after which the RSs can no longer improve their utility through best responses. A summary of this algorithm is shown in Table 13.3. The stability of the final graph G† is given using the concept of Nash equilibrium applied to network formation games [25]. Definition 13.14 A network graph G in which no node i can improve its utility by a unilateral change in its strategy si ∈ Si is a Nash network. Therefore, a Nash network is a network where the links chosen by each node are the best responses. Hence, in such a network, the nodes are in a Nash equilibrium with no node able to improve its utility by unilaterally changing its current strategy. When our dynamics converge, and as an immediate consequence of playing a best response dynamics, we have: Lemma 13.2 The final tree structure G† resulting from the RSs network formation algorithm is a Nash network.

Numerical results In order to highlight the properties and performance of the network formation game among the RSs, we consider a square area of 4 km × 4 km with the BS at the center. We deploy the RSs and the MSs within this area. Further, we set the

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Figure 13.6. Snapshot of a tree topology formed using the RSs network formation algorithm with 10 RSs before (solid line) and after (dashed line) the random deployment of 50 MSs (MS positions not shown for clarity).

transmit power to P˜ = 50 mW (RSs and MSs), the noise level to −110 dBm, and the bandwidth per RS to W = 100 kHz. For path-loss, we set the propagation loss to µ = 3. For the VoIP traffic, we consider a traffic of 64 kbps, divided into packets of length B = 200 bits with an arrival rate of 320 packets/s. For the HELLO packets we set η0 = 1 packet/s with the same packet length of B = 200 bits. For voice, we select the G.729 codec, hence υ1 = 12, υ2 = 15 and υ3 = 0.6 [26]. In Figure 13.6 we randomly deploy M = 10 RSs within the BS area. The network formation game starts with the star topology where all RSs are connected directly to the BS. Prior to the presence of the MSs in the network (only HELLO packets present), the RSs interact and converge to a final Nash tree structure shown by the solid lines in the figure. This figure clearly shows how the RSs connect to their nearby partners, forming the tree structure. Furthermore, we randomly deploy 50 MSs in the area, and show how the RSs autonomously adapt the topology to this incoming traffic. The resulting network structure upon deployment of MSs is shown in Figure 13.6 in dashed lines. The RSs autonomously self-organize and adapt to the deployed traffic. For instance, RS 3 can no longer accommodate the traffic generated by RS 2 as it drastically decreases its utility. As a result, RS 2 takes the decision to disconnect from RS 3 and improve its Rfactor by directly connecting to the BS. Similarly, RS 7 disconnects from RS 10 and connects directly to the BS. Moreover, RS 9 finds it beneficial to replace its link with RS 5 with a link with the less loaded RS 6.


377

Figure 13.7. Self-adaptation of the network’s tree topology to mobility shown through the variation of the utility of RS 5 as it moves upwards on the y-axis prior to any MS presence. Furthermore, we assess the effect of mobility on the network structure. We consider the network of Figure 13.6 prior to the deployment of the MSs and we assume that RS 5 is moving upwards on the positive y-axis while the other RSs remain fixed. The changes in utility of the concerned RSs during the movement of RS 5 are shown in Figure 13.7. As RS 5 moves upwards, its utility starts by dropping since the distance to its serving RS (RS 6) increases. Upon moving 0.3 km, RS 5 finds it beneficial to replace its link with RS 6 with a direct link to the BS, adapting the topology. Meanwhile, RS 9 decides to remain connected to RS 5 since it cannot improve its utility elsewhere. However, when RS 5 has moved 0.4 km, RS 9 decides to disconnect from RS 5 and connect directly to RS 6 improving its utility. This decreases the traffic on RS 5 which is now closer to RS 3 and can maximize its utility by connecting to RS 3. As RS 5 moves closer to RS 3, its utility continues to improve. After moving 1.2 km, RS 5 approaches RS 8 which finds it beneficial to disconnect its link with RS 3 and connect to RS 5. At this point the utility of RS 5 drops due to the newly accepted traffic; moreover, this utility drops further as RS 5 distances itself from its serving RS (RS 3). Meanwhile, the utility of RS 8 continues to improve as RS 5 moves closer to it. Through these results, we clearly illustrate how the RSs can autonomously self-organize adapting the topology to mobility. Similar results can be shown when new RSs enter the network or RSs leave the network with or without the presence of MSs. In Figure 13.8, we show the average achieved utility per MS as the number of RSs, M , in the network increases. The results are averaged over random positions

378


Figure 13.8. Performance assessment of the distributed tree formation algorithm for a network with 40 MSs shown through the average achieved MS utility vs. number of RSs M in the network (average over random positions of MSs and RSs). of the MSs and the RSs in a network having 40 MSs. We compare the performance of the network formation algorithm with the star topology whereby each RS is directly connected to the BS as well as the scenario where there are no RSs in the network. In this figure, we clearly see that as the number of RSs in the network increases the performance of the network formation algorithm as well as of the star topology improves. However, for the star topology the slope of increase is much lower than that of the network formation algorithm. In addition, the network formation algorithm presents a clear performance advantage, increasing with the number of the RSs, and reaching 40.3% and 42.75% (at M = 25 RSs) relative to the star topology and the no RSs case, respectively.

13.5

Conclusion Coalitional game theory presents a rich framework that can be used to model various aspects of cooperative behavior in wireless cellular networks. On the one hand, for ideal cooperation, one can utilize the various solution concepts of canonical coalitional games to study the stability and fairness of allocating utilities when all the users in the network cooperate. Although in this chapter canonical games have not been explored, their applications are numerous and they provide useful analytical tools for studying the limits of cooperation and the

13.5 Conclusion

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feasibility of providing incentives for the wireless users to maintain a cooperative behavior, when cooperation is ideal. On the other hand, whenever there is a benefit–cost tradeoff for cooperation, one can revert to a class of coalitional games, known as coalition formation games, to derive models and algorithms that can help in analyzing the cooperating groups that will emerge in a given wireless network. For example, using simple concepts from coalition formation game theory such as the merge-and-split rules, single-antenna users can cooperate to form virtual MIMO coalitions and, thus, benefit from the advantages of multiple-antenna systems. Using merge and split for cooperation is not limited to the single cell of a wireless cellular system nor to the virtual MIMO application. In fact, cooperative approaches based on coalition formation games can extend to multicell systems and can model a variety of scenarios. For example, in a wireless cellular network, one can adopt a merge-and-split algorithm for cooperation among the BSs in order to benefit from receive diversity, receive or transmit beamforming, interference cancelation, and other advanced communication techniques. In brief, the coalition formation game class constitutes an appropriate framework for modeling the cooperative behavior in wireless systems, and, thus, it will admit numerous applications in the future. Further, for analyzing routing problems, network structure formation, and graph interconnection, coalitional graph games provide several algorithms and solutions, notably through the framework of network formation games. As demonstrated in this chapter, network formation games are quite useful for modeling the interactions among the relay stations that are bound to be deployed in next generation cooperative wireless systems. In this context, one can design efficient and robust strategies for forming the network structure that will govern the architecture of wireless systems. The application of network formation games is not limited to the RSs problem studied in this chapter. In fact, this framework admits numerous uses in wireless systems such as modeling the downlink transmission path in multihop systems, studying network routing in cooperative wireless cellular systems, identifying the hierarchy that can govern the architecture of wireless systems, modeling wireless peer-to-peer interaction. Also, an interesting aspect of network formation is to study the cooperative behavior of the nodes whenever they are far sighted, i.e., they make decisions based on future rewards. In a nutshell, using coalitional game theory one can design efficient, robust, and fair models for cooperative wireless cellular networks. Consequently, the use of these games and models is bound to be prevalent in the design and analysis of cooperative behavior in future wireless communication networks.

Acknowledgments This research is supported by the Research Council of Norway through projects 183311/510, 176773/510, 18778/VII.

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14 Modeling malicious behavior in cooperative cellular wireless networks Ninoslav Marina, Walid Saad, Zhu Han, and Are Hjørungnes 14.1

Introduction Future communication systems will be decentralized and ad-hoc, hence allowing various types of network mobile terminals to join and leave. This makes the whole system vulnerable and susceptible to attacks. Anyone within communication range can listen to and possibly extract information. While these days we have numerous cryptographic methods to ensure high-level security, there is no system with perfect security on the physical layer. Therefore, the physical layer security is attracting renewed attention. Of special interest is so-called information-theoretic security since it concerns the ability of the physical layer to provide perfect secrecy of the transmitted data. In this chapter, we present different scenarios of a decentralized system that protects the broadcasted data on the physical layer and makes it impossible for the eavesdropper to receive the packets no matter how computationally powerful the eavesdropper is. In approaches where information-theoretic security is applied, the main objective is to maximize the rate of reliable information from the source to the intended destination, while all malicious nodes are kept ignorant of that information. This maximum reliable rate under which a perfectly secret communication is possible is known as the secrecy capacity. This line of work was pioneered by Aaron Wyner, who defined the wiretap channel and established the possibility of secure communication links without relying on private (secret) keys [1]. Wyner showed that when the eavesdropper channel is a degraded version of the main channel, the source and the destination can exchange perfectly secure messages at a nonzero rate. The main idea proposed by him is to exploit the additive noise impairing the eavesdropper by using a stochastic encoder that maps each message to many codewords according to an appropriate probability distribution. With this scheme, a maximal equivocation (i.e., uncertainty) is induced at the eavesdropper. In other words, a maximal level of secrecy is obtained. By ensuring that the equivocation rate is arbitrarily close to the message rate, one can achieve perfect secrecy in the sense that the eavesdropper is limited to learning almost nothing about Cooperative Cellular Wireless Networks, eds. Ekram Hossain, Dong In Kim, and Vijay K. Bhargava. Published by Cambridge University Press. C Cambridge University Press, 2011.

14.1 Introduction

C

S

383

D

Cm E Figure 14.1. The eavesdropper channel.

the source–destination messages from its observations. Follow-up work by LeungYan-Cheong and Hellman characterized the secrecy capacity of the additive white Gaussian noise (AWGN) wiretap channel [2]. In their landmark paper, Csisz´ ar and K¨ orner generalized Wyner’s approach by considering the transmission of confidential messages over broadcast channels [3]. There have been considerable efforts to generalize these studies to the wireless channel and multiuser scenarios ([2, 4–11]). The basic scenario, called the eavesdropper channel, is shown in Figure 14.1. There is a source S that is transmitting a message to a destination D, while an eavesdropper E is trying to listen to the communication between S and D. In the following text we shall also use the term malicious node for the eavesdropper. A perfect information-theoretically secret system is a system with positive secrecy capacity. In addition to the secrecy capacity being positive it is beneficial for the source to have it as large as possible to enable higher-rate secret communication. For the class of channels of interest here, the secrecy capacity is defined as Cs

=

max(C − Cm , 0),

(14.1)

where C is the capacity of the direct point-to-point channel between the source and the destination and Cm is the capacity of the channel between the source and the eavesdropper. Having a positive secrecy capacity guarantees perfect secrecy. Note that it is in the interest of the system designer to make Cs as large as possible. To increase Cs , it is obvious from (14.1) that one has to either increase C or decrease Cm or both. In the rest of this chapter we describe three different scenarios for how the secrecy capacity could be changed by cooperation. First in Section 14.2 we describe how cooperation with some friendly jamming nodes can decrease Cm , which results in increasing Cs . In order to study what the incentive is for the friendly jammer to help the source, we analyze the system by using the Stockholder game. In Section 14.3 we study how the cooperating nodes can help the source by relaying the useful information to the destination while at the same time jamming the eavesdropper. Here we realize that for such a model

384


there is an area that the eavesdropper must not be allowed to enter in order to ensure a positive secrecy capacity. We call this region the vulnerability region and we study its size as the number of cooperative relaying nodes increases. Finally, in Section 14.4 we warn that as well as the “good guys”, the eavesdroppers can also organize themselves, making the secrecy capacity lower. We study a scenario in which eavesdroppers form coalitions, thereby decreasing the secrecy capacity acted much more than if the eavesdroppers act individually. The cooperative behavior of the eavesdroppers is studied by using coalition games.

14.2

Cooperating jammers In this section, we investigate the interaction between the source and friendly jammers, who help the source by jamming the eavesdropper. Although the friendly jammers help the source by reducing the data rate that is “leaking” from the source to the malicious node, at the same time they also reduce the useful data rate from the source to the destination. Using well-chosen amounts of power from the friendly jammers, the secrecy capacity can be maximized. In the game that we define here, the source pays jammers to interfere with the malicious eavesdropper and therefore to increase the secrecy capacity. The jammers charge the source a certain price for jamming the eavesdropper. It can be seen that there is a tradeoff when deciding the price: If the price of a certain jammer is too low, its profit is also low; if its price is too high, the source will buy from another jammer. In modeling the outcome of the above games our analysis uses the Stockholder type of game. Initially, the existence of equilibrium will be studied. Then, a distributed algorithm will be proposed and its convergence will be investigated. The outcome of the distributed algorithm will be compared with the centralized genie-aided solution. Some implementation concerns are also discussed. From the simulation results, we can see the efficiency of friendly jamming and the tradeoff for setting the price; the source prefers buying service from only one jammer, and the centralized scheme and the proposed game scheme have similar performances. Jamming [12–14] has been studied for a long time to analyze the hostile behaviors of malicious nodes. Jamming has been employed as a physical layer security method to reduce the eavesdropper’s ability to decode the source’s information [15]. In other words, the jamming is friendly in this context. Moreover, the friendly helper can assist the secrecy by sending codewords, and bring further gains relative to unstructured Gaussian noise [15–17]. Game theory [18] is a formal framework with a set of mathematical tools to study some complex interactions among interdependent rational players. There has been a surge in research activity that employs game theory to model and analyze modern distributed communication systems. Most of this

14.2 Cooperating jammers

C

S

D

Cm

385

S – Source D – Destination M – Malicious node (Eavesdropper) J1,…,JJ – J Friendly jammers

J1 M

Useful data Interference Payment

J2 JJ

Figure 14.2. System model for the proposed information-theoretic security game.

research [19–22] concentrated on the distributed resource allocation for wireless networks.

14.2.1

System model We consider a network with a source, a destination, a malicious eavesdropper node, and J friendly jammer nodes as shown in Figure 14.2. The malicious node tries to eavesdrop the transmitted data coming from the source node. When the eavesdropper channel from the source to the malicious node is a degraded version of the main source–destination channel, the source and destination can exchange perfectly secure messages at a nonzero rate. By transmitting a message at a rate higher than the rate of the malicious node, the malicious node can learn almost nothing about the messages from its observations. The maximum rate of secrecy information from the source to its intended destination is defined by the term secrecy capacity. Suppose the source transmits with power P0 . The channel gains from the source to the destination and from the source to the malicious node are Gsd and Gsm , respectively. Each friendly jammer i, i = 1, . . . , J, transmits with power Pi and the channel gains from it to the destination and the malicious node are Gid and Gim , respectively. We denote by J the set of indices {1, 2, . . . , J}. If the path-loss model is used, the channel gain is given by the distance to the negative power of the path-loss coefficient. The thermal noise for each channel is σ 2 and the bandwidth is W . The channel capacity for the source to the destination is P0 Gsd . (14.2) C = W log2 1 + 2 σ + i∈J Pi Gid

386


The channel capacity from the source to the malicious node is P0 Gsm . Cm = W log2 1 + 2 σ + i∈J Pi Gim

(14.3)

As we know from (14.1), the secrecy capacity is Cs = max(C − Cm , 0). Both C and Cm are decreasing and convex functions of the jamming powers Pi . However, Cs = C − Cm is not a monotonous and convex function. This is because the jamming power might decrease C faster than Cm . As a result, Cs might increase for some values of Pi . So, the questions to be considered are whether or not Cs can be increased, and how the jamming power can be controlled in a distributed manner. We will solve the problems in the following text using a game theoretical approach.

14.2.2

The game Next we describe how game theory can be used to analyze information-theoretic security in a cooperative network. First, we define the game between the source and the friendly jammers. We optimize the source side and the jammer side, respectively. Then, we prove some properties of the proposed game. Furthermore, a comparison is made with the centralized scheme. Finally, we discuss some implementation concerns. The source can be modeled as a buyer who wants to optimize its secrecy capacity minus cost by modifying the “service” (jamming power Pi ) from the friendly jammer, i.e., source’s game: max Us = max(aCs − M ), subject to : Pi ≤ Pm ax ,

(14.4)

where a is the gain per unit capacity, Pm ax is the maximal power that a jammer can provide, and M is the cost to pay for the other friendly jamming nodes. Here pi P i , (14.5) M= i∈J

where pi is the price per unit power for the friendly jammer, Pi is the friendly jammer’s power, and J is the set of friendly jammers. From (14.4) we note that the source will not participate in the game if C < Cm , or, in other words, the secrecy capacity is zero. For each jammer, Ui (pi , Pi (pi )), is the utility function of the price and power bought by the source. For the jammer’s (seller’s) utility, we define the following utility Ui = pi Pic i ,

(14.6)

where ci ≥ 1 is a constant to balance the payment pi Pi from the source and the transmission cost Pi . Notice that Pi is also a function of the vector of prices (p1 , . . . pN ), since the power that the source will buy also depends on the price that the friendly jammers ask. Hence, for each friendly jammer, the optimization

387


problem is friendly jammer’s game: max Ui .

(14.7)

pi

In the following text, we analyze the optimal strategies for the source and friendly jammers to maximize their own utilities. Introducing A = P0 Gsd /σ 2 , B = P0 Gsm /σ 2 , ui = Gid /σ 2 , and vi = Gim /σ 2 , i ∈ J , we have ⎛ ⎛ ⎞ ⎞⎞+ ⎛ ⎜ ⎜ ⎜ Us = aW ⎜ ⎝log ⎝1 +

1+

A

u j Pj

⎟ ⎜ ⎟ − log ⎜1 + ⎠ ⎝

1+

j ∈J

B

vj P j

⎟⎟ ⎟⎟ − pj P j . ⎠⎠ j ∈J

j ∈J

(14.8) For the source (buyer) side, we analyze the case C > Cm . By differentiating (14.4), we have ∂Us ∂Pi

= − +

(1 + A +

aW Aui / ln 2 j ∈J uj Pj )(1 + j ∈J uj Pj )

(1 + B +

aW Bvi / ln 2 − pi = 0. j ∈J vj Pj )(1 + j ∈J vj Pj )

(14.9)

Rearranging the above equation, we have Pi4 + Fi,3 Pi3 + Fi,2 (pi )Pi2 + Fi,1 (pi )Pi + Fi,0 (pi ) = 0,

(14.10)

where Fi,3 = (2 + 2αi + A)2 + (2 + 2βi + B)2 , B (2 + 2αi + A)(2 + 2βi + B) Li Ki aW A , + 2 + 2 − − Fi,2 (pi ) = u i vi vi ui p i u i vi vi ui Li Ci + Ki Di aW (ADi − BCi ) Fi,1 (pi ) = + , (14.11) u2i vi2 pi u2i vi2 Ki Li aW (Aui Li − Bvi Ki ) Fi,0 (pi ) = 2 2 + , ui vi pi u2i vi2 and αi =

Gj d Pj ,

βi =

j = i

Gj m Pj ,

(14.12)

j = i

Ki = (1 + αi )(1 + αi + A),

(14.13)

Li = (1 + βi )(1 + βi + B),

(14.14)

Ci = ui (2 + 2αi + A),

(14.15)

Di = vi (2 + 2βi + B).

(14.16)

The solutions of the quartic equation (14.10) can be expressed in a closed form but this is not the primary goal here. It is important that the solution we are

388


interested in is given by the following function: Pi∗ = Pi∗ (pi , A, B, {uj }, {vj }, {Pj }j = i ).

(14.17)

Note that 0 ≤ Pi ≤ Pm ax . Since Pi satisfies the polynomial function, we can have the optimal strategy as Pi∗ = min[max(Pi , 0), Pm ax ].

(14.18)

Because of the complexity of the closed-form solution of the quartic equation in (14.18), we also consider two special cases: the low interference case and the high interference case. (a) Interference at the destination is much smaller than the noise (low interference case) Remember the definitions: A = P0 Gsd /σ 2 , B = P0 Gsm /σ 2 , ui = Gid /σ 2 , and vi = Gim /σ 2 . Imagine a situation in which all jammers are close to the malicious node and far from the destination node. In that case the interference from the jammer to the destination is very small in comparison with the additive noise and therefore Us ≈ aW

log (1 + A) − log 1 +

1+

+

B

j ∈J

vj P j

−

pj Pj .(14.19)

j ∈J

Then aW Bvi / ln 2 ∂Us − pi = 0. = ∂Pi (1 + B + j ∈J vj Pj )(1 + j ∈J vj Pj )

(14.20)

Rearranging we get Pi2 +

2 + 2βi + B (1 + βi )(1 + B + βi ) aW B = 0. Pi + − vi vi2 pi vi ln 2

(14.21)

Solving the above equation we obtain a closed-form solution 7 2 + 2β (1 + βi )(1 + B + βi ) aW B + B (2 + 2βi + B)2 i Pi∗ = − + − + 2vi 4vi2 vi2 pi vi ln 2 zi = qi + wi + , (14.22) pi where 2 + 2βi + B , 2vi (2 + 2βi + B)2 (1 + βi )(1 + B + βi ) − , 4vi2 vi2 aW B . vi ln 2

qi

= −

(14.23)

wi

=

(14.24)

zi

=

(14.25)


389

Finally, by comparing Pi∗ with the power under the boundary conditions (Pi = 0, Pi = Pm ax , and Cs = 0), the optimal Pi∗ in the low-SNR region can be obtained. (b) One jammer with interference that is much higher than the noise but much smaller than the received power at the destination and the malicious node In this case the interference from the jammer is much higher than the additive noise but much smaller than the power of the received signal at the destination and the malicious node. In other words, 1 1, ηI(p) ≥ I(ηp). In [24], it has been proved that the price will converge to the fixed point (i.e., the Stockholder equilibrium in our case) from any feasible initial price vector. The positivity is very easy to prove. If the price pi goes up, the source will buy less from the ith friendly jammer. As a result, ∂Pi∗ /∂pi in (14.27) is negative, and we prove positivity pi = Ii (p) > 0. We prove the monotonicity and scalability only for the low-interference case. In this case, from (14.22) it is obvious that 2 wi p2i + zi pi (qi pi + wi p2i + zi pi ) (Pi∗ ) Ii (p) = − = , (14.39) ∂P ∗ ci zi ci i ∂pi which is monotonically increasing in pi . For scalability, we have wi p2i + zi pi /η(qi pi + wi p2i + zi pi /η) Ii (ηp) = 1.

(14.40)

392


For more general cases, the analysis is not tractable. In our simulations, we employ general simulation setups. The simulation results show that the proposed scheme can converge and outperform the no-jammer case. Traditionally, the centralized scheme is employed assuming all channel information is known. The objective is to optimize the secrecy capacity under the constraints of maximal jamming power: ⎡ ⎛ ⎞ ⎤ ⎢ ⎜ max Cs = max ⎢ W log2 ⎜ ⎣ ⎝ Pi

1+ 1+

σ2 +

σ2 +

P0 Gs d i ∈J P i G i d

P G 0 sm i∈J Pi Gim

⎟ ⎥ ⎟ , 0⎥ ⎠ ⎦

subject to 0 ≤ Pi ≤ Pm ax , ∀i.

(14.41)

The centralized solution is found by maximizing the secrecy capacity only. If we do not consider the constraint, we have ∂Cs ∂Pi

=

−AW ui (1 + αi + ui Pi )(1 + A + αi + ui Pi ) BW vi = 0. + (1 + βi + ui Pi )(1 + B + βi + ui Pi )

(14.42)

Rearranging we get Au2i (2 + B + 2βi ) − Bvi2 (2 + A + 2αi ) Pi Au3i − Bvi3 Aui (1 + βi )(1 + B + βi ) − Bvi (1 + αi )(1 + A + αi ) + = 0. (14.43) Au3i − Bvi3

Pi2 +

Using the Karush–Kuhn–Tucker (KKT) condition [25], the final solution would be obtained by comparing the boundary conditions (i.e., Pi = 0, Pi = Pm ax , and Cs = 0). Notice that our proposed algorithm is distributive, in the sense that only the pricing information needs to be exchanged. In the simulation results, we compare the proposed game-theoretical approach with this centralized scheme. There are several implementation concerns for the proposed scheme. First, the channel information from the source to the malicious eavesdropper might not be accurately known. Under this condition, the secrecy capacity formula should be rewritten considering the uncertainty. If the direction of arrival is known, multiple antenna techniques can be employed such as in [11]. Second, the proposed scheme needs to update the price and power information iteratively. A natural question arises if the distributed scheme has less signalling than the centralized scheme. The comparison is similar to distributed and centralized power control in the literature [23, 24]. Since the channel condition is continuously changing, the distributed solution only needs to update the difference of the parameters such as power and price to be adaptive, while the centralized scheme requires


393

1 Jammer location (50,75) Jammer location (10,75)

0.9 0.8

Secrecy capacity Cs

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

0.005

0.01 Jamming power

0.015

0.02

Figure 14.3. Secrecy capacity vs. the power of the single jammer.

all channel information in each time period. As a result, the distributed solution has a clear advantage and dominates current and future wireless network design. For example, in the power control for cellular networks, the open-loop power control is done only once during the link initialization, while the closedloop power control (distributed power allocation such as [24]) is performed 1500 times for UMTS and 800 times for CDMA2000. Finally, for the multisource multidestination case, there are two possible choices to solve the problem. First, we can use a clustering method to divide the network into subnetworks, and then employ the single-source–destination pair and multiple-friendly-jammers solution proposed in this section. If we believe that the jamming power can be useful for multiple eavesdroppers, techniques such as double auction could be investigated.

14.2.3

Simulation results The simulation was set up as follows. The source and friendly jammers have power of 0.02, the bandwidth is 1, the noise level is 10−8 , the propagation loss factor is 3, and an additive white Gaussian noise (AWGN) channel is assumed. The source, destination, and eavesdropper are located at the coordinates (0,0), (100,0), and (50,50), respectively. Here we select a = 2 for the friendly jammer’s utility in (14.6). For the single-friendly-jammer case, we show the simulation with the friendly jammer at a location of (50,75) and (10,75). In Figure 14.3, we show the secrecy


0.016 Jammer location (50,75) Jammer location (10,75)

0.014 0.012 Amount of power bought

394

0.01 0.008 0.006 0.004 0.002 0

0

50

100 Jammer price

150

200

Figure 14.4. How much power the source buys as a function of the price.

capacity as a function of the jamming power. We can see that with the increase of the jamming power, the secrecy capacity first increases and then decreases. This is because the jamming power has different effects on C and Cm . There is an optimal point for the jamming power. Also the optimal point depends on the location of the friendly jammer, and a friendly jammer close to the eavesdropper is more effective in improving the secrecy capacity. Moreover, notice that the curve is neither convex nor concave. Figure 14.4 shows how the amount of the power bought by the source from the jammer depends on the requested price. We can see that the power is reduced if the price is high. At some point, the source would stop buying the power. So there is a tradeoff for setting the price, i.e., if the price is too high, the source will buy less power or even stop buying it. For the two-jammer case, we set up the following simulations. The malicious node is located at (50,90), the first friendly jammer is located at (50,50), and the second friendly jammer is located at (50,75). Figures 14.5, 14.6, and 14.7 show, respectively, the source’s utility Us , the first jammer’s utility U1 , and the second jammer’s utility U2 as a function of both users’ price. We can see that the source will buy service from only one of the friendly jammer. If the friendly jammer asks too low a price, the jammer’s utility is very low. On the other hand, if the jammer asks too high a price, it risks the situation in which the source will buy the service from another friendly jammer. There is an optimal price for each friendly jammer to ask, and the source will always select the one that can provide the best performance improvement. Next, we set up a simulation of mobility. The first friendly jammer is fixed at (50,50), while the second friendly jammer moves from (−50,75) to (100,75).


395

1

Source Us

0.8

0.6

0.4

0.2 0 100 User 1 Price p 2

0 50

200 100 150 300

User 2 Price p 1

Figure 14.5. Us vs. the prices of both users. (Source (0,0), destination (100,0) malicious node (50,90), user 1(50,50), user 2(50,75).)

'

Figure 14.6. U1 vs. the prices of both users. (source (0,0), destination (100,0) malicious node (50,90), user 1(50,50), user 2(50,75).)

In Figure 14.8, we show the source utilities for the centralized scheme and the proposed game. The centralized scheme serves as a performance upper bound. We observe that the game result is not far away from the upper bound, while the game solution can be implemented in a distributed manner. The performance difference is insignificant when friendly jammer 2 is close to the malicious eavesdropper (e.g., the friendly jammer is at locations from (20, 75) to (70, 75)). In

396


Figure 14.7. U2 vs. the prices of both users. (Source (0,0), destination (100,0) malicious node (50,90), user 1(50,50), user 2(50,75).)

Figure 14.8. Us vs. the location of the second jammer.

Figure 14.9, we show the jammer power as a function of the location of jammer 2. We can see that depending on the jammers’ locations, the source switches between the two jammers for the best performance. Moreover, the source also buys the optimal amount of jamming power: when the jammer is close to the malicious eavesdropper, the source buys less power since the jammer is more


397

Figure 14.9. Power vs. the location of the second jammer.

utility

utility utility

location

Figure 14.10. Utility vs. the location of the second jammer. effective at improving the secrecy capacity. In Figure 14.10, we show the corresponding friendly jammers’ utilities of the proposed game. Finally, we show the effect of parameter a on the friendly jammer’s utility in (14.6). When a is large, the friendly jammer’s utility reduces quickly if the source does not buy the service. As a result, the friendly jammer would not ask an arbitrary price, and the performance gap to the optimal solution is small. In

398


1 Optimal solution Game result

0.95

Secrecy capacity

0.9 0.85 0.8 0.75 0.7 0.65

2

2.5

3

3.5 Factor a

4

4.5

5

Figure 14.11. Effect of the parameter a on the game.

Figure 14.11, we show the secrecy capacity as a function of a when the second jammer is located at (0,75). We can see that the performance gap shrinks when a increases. To summarize, if the source pays friendly jammers to interfere with the malicious eavesdropper, the secrecy capacity, and therefore the security of the network is increased. The friendly jammers charge the source a price for the jamming. To analyze the game outcome, we investigated the Stockholder game and constructed a distributed algorithm. Some properties such as equilibrium and convergence were analyzed. From the simulation results, we conclude the following. First, there is a tradeoff for the price: if the price is too low, the profit is low; and if the price is too high, the source will not buy or buy from another jammer. Second, for the multiple-jammer case, the source will buy service from only one jammer. Third, the centralized scheme and distributed scheme have similar performances, especially when a is sufficiently large. Overall, the proposed game theoretical scheme can achieve a comparable performance with distributed implementation.

14.3

Cooperating relays In this section, we observe how node cooperation improves the informationtheoretic security of a simple wireless network by reducing the surface of the geographical area in which the malicious nodes can listen to the data transmitted from the source to the destination. Our analysis and simulation

14.3 Cooperating relays

399

Relay 1

Relay 2

Source node

Destination node

Relay 3

Relay M

Figure 14.12. Cooperative network with a source, a destination, M cooperative relays, and a malicious node. results show a dramatic improvement even for cooperation with only one relay node. Adding more cooperating nodes gives greater improvement. We also observe that when cooperating nodes are closer to the line that connects the source and the destination node, the region in which the malicious node can profit from the eavesdropping is smaller.

14.3.1

System model We analyze the Gaussian parallel multiple-relay network. Although the capacity of this network is not known, we use its upper and lower bounds, with a hope that our results will initiate further thought in this interesting and important research area. Observe the network in Figure 14.12. There is a source node that transmits data to a destination node, while a malicious node “listens” to the transmitted information. There are several relay nodes that help the source by relaying the transmitted data. We consider the additive complex white Gaussian noise model. A message at the source node is encoded into a codeword {X[j]}nj=1 of length n. The components X[j] are complex numbers that satisfy the power constraint n−1

n

E[|X[j]|2 ] ≤ P.

(14.44)

j =1

At time j each of the M relays observes an attenuated and noisy version of the input, i.e., Yi [j] = hi,s X[j] + Zi [j],

i = 1, 2, . . . , M,

400


where Zi [j] is an independent and identically distributed (i.i.d.) circularly symmetric complex Gaussian random variable of zero mean and (without loss of generality) variance σ 2 . Moreover, Zi and Z are independent for i = . The coefficients hi,s , i = 1, 2, . . . , M , are fixed real-valued constants, assumed to be known throughout the network. For that reason we may assume that all noise processes Zi are of same variance σ 2 without loss of generality. Observing {Yi [j]}nj=1 at each relay i produces a sequence {Xi [j]}nj=1 that must be causal, i.e., Xi [j] = fi,j (Yi [j − 1], Yi [j − 2], . . . , Yi [1]), and satisfies the individual power constraint n−1

n

E[|Xi [j]|2 ] ≤ Pi .

(14.45)

j =1

The received signal at the destination node is Y [j] = hd,s X[j] +

M

hd,i Xi [j] + Zd [j],

i=1

where Zd [j] is a sequence of i.i.d. zero-mean circularly symmetric complex Gaussian random variables of variance σ 2 . The coefficients hd,s and hd,i , where i = 1, 2, . . . , M , are fixed and assumed to be known throughout the network. We assume that the coefficient ha,b between two nodes a and b is −β /2

ha,b = da,b ,

(14.46)

where β is the path-loss exponent and da,b is the distance between the nodes a and b. In this case, the distance between the source and the destination is denoted by dd,s , that between the source and relay i, by di,s , i = 1, 2, . . . , M , and that between relay i and the destination, by dd,i , where i = 1, 2, . . . , M .

14.3.2

Secrecy capacity Here we develop expressions for the secrecy capacity of the cooperative system described in Figure 14.12. It is assumed that the malicious node may eavesdrop on the source as well as on the cooperating relay nodes. Note, however, that in order to get full use of the signals transmitted from the source and the relay nodes, the source must be fully synchronized with all of them. To capture the effect of synchronization, we model the received signal at the malicious node as follows: √ hm ,i ki Xi [j] + Zm [j], Ym [j] = hm ,s qX[j] + M

i=1


Zm ∼ CN

0, σ + (1 − 2

q)P d−β m ,s

+

M

401

(1 −

ki )Pi d−β m ,i

,

(14.47)

i=1

where Zm [j] is a sequence of i.i.d. circularly symmetric complex Gaussian ran√ dom variables of zero mean and variance σ 2 + (1 − q)P + M i=1 hm ,i 1 − ki Pi , −β /2 −β /2 hm ,s = dm ,s , and hm ,i = dm ,i , i = 1, 2, . . . , M . How well the malicious node is synchronized with the source is modeled by q ∈ [0, 1], while how well it is synchronized with the relay node i is modeled by ki ∈ [0, 1] for i = 1, 2, . . . , M . More precisely, q is the fraction of the source transmitting power that will be received by the malicious node as useful signal for itself, while (1 − q) is the fraction of the source power that makes interference at the malicious node. If q = 1, then the malicious node is perfectly synchronized with the source node, while if q = 0 there is no synchronization and the malicious node receives only noise from the source. Similarly, ki is the fraction of the transmitting power of relay node i that will be received by the malicious node as useful signal for itself, while (1 − ki ) is the fraction of the power of relay node i that makes interference at the malicious node. The same explanation is valid for the parameters ki . That means, an omnipotent eavesdropper will have q = ki = 1 for all i = 1, 2, . . . , M and a “dummy” eavesdropper will have q = ki = 0 for all i = 1, 2, . . . , M . In the former case, the vulnerability region will be maximal, while in the latter, it vanishes, i.e., we have a perfect secrecy system. In order to make the eavesdropper capabilities closer to reality, we introduce two models to describe the synchronization parameters as a function of the distance between the eavesdropper and the eavesdropped node. Model 1 is the exponential model, defined as q

= e−d m , s ,

ki

= e−d m , i .

(14.48)

Model 2 is the squared exponential model (Gaussian model), defined as q

= e−d m , s ,

ki

= e−d m , i .

2

(14.49)

2

For notational convenience, we use definitions similar to those in, i.e., aM = d−β d,s +

M

d−β i,s ,

i=1

bM =

M 2 d−β i,s P + σ i=1

dβi,s d−β d,i

dM = d−β d,s +

M i=1

,

d−β d,i .

402


With all these assumptions we will be able to determine the bounds on the secrecy capacity, since the capacity of a general nondegraded relay channel is not known in general. First, the capacity of the main channel (the parallel relay channel between the source and the destination) is upper bounded by min{aM P, (P + M i=1 Pi )dM } . (14.50) C ≤ log2 1 + σ2 The lower bound of the capacity of the main channel is given by ⎞ ⎛ @ −β M ⎟ ⎜ (aM − d−β ⎜ i=1 Pi ⎟ d,s ) + 2 bM dd,s / ⎟. P C ≥ log2 ⎜ 1 + ⎟ ⎜ P + σ2 ) bM (d−β ⎠ ⎝ d,s 2 σ + −β M (aM − dd,s ) i=1 Pi

(14.51)

The capacity of the eavesdropper channel (the maximum rate that can be achieved by the malicious node) is given by ⎛ ⎞ M ki Pi qP + ⎜ ⎟ β ⎜ ⎟ dβm ,s i=1 dm ,i ⎟ Cm = log2 ⎜ 1 + (14.52) ⎜ ⎟ M ⎝ (1 − q)P (1 − ki )Pi 2⎠ + +σ dβm ,s dβm ,i i=1 where Pi is the transmit power of relay i. Note that it might be obtained after some allocation process since we have the total power constraint applied to all relays, given by (14.45). The secrecy capacity is then defined as [2] Cs = max{C − Cm , 0}.

(14.53)

In other words, the secrecy capacity is positive only if C > Cm . In order to analyze how cooperation improves the secrecy, we introduce the following two definitions. Definition 14.3 The geometrical area (region) in which the secrecy capacity is positive is called the secrecy region. Definition 14.4 The geometrical area (region) in which the secrecy capacity vanishes is called the vulnerability region. Obviously, we want to keep all malicious nodes away from the vulnerability region. In other words, the system is more secure if its vulnerability region is minimized, or, equivalently, if its secrecy region is maximized. Note that if there are no cooperating relay nodes (M = 0), it can be shown that the vulnerability region is a circle (disk) since in that case the capacity of the main channel is the capacity of the point-to-point Gaussian channel between the source and the


destination. More precisely the region is determined from P d−β d,s C = log2 1 + σ2 qP d−β m ,s < log2 1 + = Cm . 2 (1 − q)P d−β m ,s + σ

403

(14.54)

Solving (14.54), we get that the vulnerability region is a disk centered at the source with radius d∗m ,s

= dd,s (max {0, q(1 + γ) − γ})1/β ,

2 where γ = P d−β d,s /σ . In other words, ⎧ ⎨0, d∗m ,s = ⎩dd,s (q(1 + γ) − γ)1/β ,

(14.55)

γ for 0 ≤ q ≤ , 1+γ γ ≤ q ≤ 1. for 1+γ

This means that for a high SNR, it is easier to get a perfectly secure system if q ≤ γ/(1 + γ). If q = 1, d∗s,m

= dd,s ,

while for 0 ≤ q ≤ γ/(1 + γ) the vulnerability region vanishes, which is a desired situation. In order to compare the vulnerability region to some reference region we introduce the normalized vulnerability region. Definition 14.5 The normalized vulnerability region is the ratio of the vulnerability region to the surface of the disk with radius dd,s . The definition tells us that if the normalized vulnerability region of a cooperative system is less than 1, we get a smaller vulnerability region than for a noncooperative system, or in other words, cooperation increases network security. In our numerical analysis we observe the following bounds on the secrecy capacity: CsU B

=

max(C U B − Cm , 0),

CsL B

=

max(C L B − Cm , 0).

In a cooperative system, where M ≥ 1, we can determine numerically the lower and the upper bound of the normalized vulnerability region. It is natural that they depend heavily on the position of the cooperating relays, and that the lower bound of the vulnerability region is determined by the upper bound of the capacity of the main channel (14.50), while the upper bound of the vulnerability region is determined by the lower bound on the capacity of the main channel (14.51).

404


LB

UB

LB

UB

LB

UB

Figure 14.13. Examples of the lower bound (LB) and upper bound (UB) on the shape of a typical vulnerability region for M = 1 (upper), M = 3 (middle), and M = 5 (lower).

14.3.3

Simulation results In this subsection, we show several examples of the shape of the secrecy region in a cooperative system. We also observe how the average surface depends on the number of relays. We fix the parameters as follows: σ 2 = 1, P = Pi = 1, i = 1, 2, . . . , M , and β = 2. For these parameters, typical vulnerability regions are described in Figure 14.13 for M = 1, M = 3, and M = 5, using model 2. The source node is represented by a centrally positioned star, the destination node by a square positioned to the right of the source, and the randomly placed relay nodes by diamonds. When the malicious node is positioned in a dark area, perfectly secure communication is possible (i.e., the secrecy capacity is positive). The white areas (islands) represent the vulnerability regions. It is easily noticeable that an increased number of cooperating relays reduces the vulnerability region, hence, increasing the system secrecy.


405

0.6

0.5

Bounds

0.4

0.3

UB

0.2

0.1 LB

(a)

0 1

2

3

4

5

6

4

5

6

M 0.6

0.5

Bounds

0.4

UB

0.3

0.2 LB 0.1

0

(b)

1

2

3 M

Figure 14.14. Lower bound (LB) and upper bound (UB) of the normalized vulnerability region for β = 2 and (a) correlation model 1 and (b) correlation model 2 as a function of the number of cooperating relays M . In order to understand the importance of the cooperation in increasing the secrecy capacity or, equivalently, the secrecy region of a certain network, we characterize the surface of the vulnerability region. To that end, we analyze how the normalized vulnerability region depends on the number of cooperative relays. The dependence of the lower and upper bounds of the normalized vulnerability region on the number of relay nodes, for β = 2, for both correlation models is shown in Figure 14.14. Our simulations indicate that choosing cooperation relays that are closer to the line that connects the source and the destination, minimizes the vulnerability region. In Figure 14.15 we observe the dependence of the normalized vulnerability region bounds on the number of relay nodes, for β = 2, for both correlation models (model 1 and model 2) when the relays are placed on the line connecting the source and the destination. Note that for both models the secrecy region is smaller in this case. This indicates that the source should choose relays that are closer to the line in order to minimize the secrecy region. This is not surprising


0.4 0.35 0.3

Bounds

0.25 0.2 0.15 0.1

UB

0.05 LB 0

(a)

1

2

3

4

5

6

4

5

6

M 0.4 0.35 0.3 0.25

Bounds

406

UB 0.2 0.15 0.1 LB 0.05 0

(b)

1

2

3 M

Figure 14.15. Lower bound (LB) and upper bound (UB) of the normalized vulnerability region for β = 2 and (a) correlation model 1 and (b) correlation model 2 as a function of the number of cooperating relays M that are placed on the line between the source and the destination.

since the relaying is the most efficient when the relay node lies on the line between the source and the destination. For M = 1, we notice in Figure 14.16 a minimum of the lower and upper bounds on the normalized vulnerability region if the relay is placed between the source and the destination. The minimum depends on β, P, Pi as well as on the model chosen. It is very intuitive that choosing a larger transmit power for either the source or the relays makes the system more vulnerable, and, hence, the secrecy region larger. Finally, we would like to comment that correlation model 2 is worse than correlation model 1. This comes from the properties of the exponential and the Gaussian function and how they affect the secrecy capacity. We have demonstrated that the information-theoretic security of a network can be increased by cooperation. Depending on the capabilities of the malicious node, one could improve the security a great deal, by minimizing the vulnerability region. As we include more and more relays, the increase in the improvement

14.4 Eavesdroppers’ cooperative model

407

0.7

0.6

Bounds

0.5

0.4 UB

0.3

0.2 LB 0.1

0

0

0.2

0.4

0.6

0.8

1

d1,s

Figure 14.16. Lower (LB) and upper bound (UB) of the normalized vulnerability region for β = 2 and correlation model 1 as a function of the distance between relay 1 in the cooperative system with one relay (M = 1) which is placed along the line between the source and the destination. is less and less. The most dramatic improvement is obtained by cooperation with one relay and for each additional relay the improvement that is obtained decreases. From the simulation results, we see that depending on the correlation model of the eavesdropper, we have a different size vulnerability region. In addition, the source should choose relays that stay close to the line that connects the source and the destination in order to minimize the secrecy region. Depending on the system parameters there is a distance between the source and the relay node that results in the region being minimal. By a simple analysis we have shown that cooperation can dramatically improve the information-theoretic security in a given wireless network. One has to be aware, however, that the security improvement is not simply because of the reduction of the transmission range between the hops in a multihop communication setting. It actually comes from the fact that cooperation increases the capacity of the main channel for more than the eavesdropper channel can benefit from eavesdropping on the sources plus multiple relay nodes.

14.4

Eavesdroppers cooperative model While there has been increased attention paid to physical layer security, a significant amount of the research has been devoted to studying methods and techniques for improving the secrecy rate of wireless nodes in the presence of eavesdroppers. However, in order to understand better the defense mechanisms that wireless users can adopt protect their transmission from eavesdroppers it is necessary to understand how the eavesdroppers themselves operate in the network. In this context, it is of interest to study how the malicious nodes, i.e., the

408


eavesdroppers, can use different strategies to increase the amount of damage they can cause on the network’s nodes. For instance, with the emergence of cooperation as a new communication paradigm, the eavesdroppers in a wireless network can benefit from various cooperative techniques for improving their reception of the signal that they are interested in tapping. Hence, while most literature is focused mainly on the users’ side in physical layer security problems, this section aims to provide cooperation models for the eavesdroppers. In this regard, the main objectives of this section are to propose: (i) a cooperation protocol that allows a network of eavesdroppers to interact to improve their eavesdropping performance; (ii) an adequate utility function for the eavesdroppers that accounts for the cooperation gains and cost; and (iii) a coalitional game-based model for forming cooperative groups among the eavesdroppers. Using the proposed coalitional game model, the eavesdroppers can take distributed decisions to form or break up a cooperative group depending on their gains from and costs of cooperation. Consequently, by allowing the eavesdroppers to cooperate, independent disjoint eavesdroppers’ coalitions will be formed in the network. Consider a network having K single-antenna eavesdroppers (static or mobile) that intend to tap into the transmissions of N wireless transmitters which are communicating with a central base station (BS). Let us denote by K and N the sets of eavesdroppers and users, respectively. In a noncooperative approach, consider a time-slotted system whereby during a single slot of duration θslot all K eavesdroppers, each acting on its own (noncooperatively), are interested in tapping into the transmission of one of the N users in the network.1 The eavesdroppers can attack the users in any arbitrary manner over the slots but, for convenience (and due to the ergodicity of the attacks over time), in slot 1, it is assumed that all eavesdroppers are noncooperatively attacking user 1, in slot 2, all eavesdroppers are non-cooperatively attacking user 2, and so on until all N users have been attacked once by the eavesdroppers. Consequently, a total of N slots is required to complete one round of eavesdropping on all N users. Every block of N slots will be referred to as the eavesdropping cycle and the eavesdroppers engage in multiple eavesdropping cycles over time. During a single eavesdropping cycle (N slots), the objective of every eavesdropper is to maximize the damage caused on the users, which translates into minimizing the secrecy capacities of all N users (during one cycle). Thus, the total damage that an eavesdropper k ∈ K can cause to the transmitters through a single eavesdropping cycle is given by overall reduction of the secrecy capacities that k yielded, as follows: + Cid − Cke ,i , (14.56) u(k) = − i∈N

1

This model is selected for simplicity; however, the case where each eavesdropper may select a different user to tap into within a slot can also be treated using the proposed coalitional game model.


409

2 where Cid = W · log2 (1 + gi,BS · P˜ /σ 2 ) is the capacity of user i ∈ N achieved at the BS with gi,B S being the channel gain between i and the BS, W being the available bandwidth, P˜ being the transmit power of user i (assumed to be the same for all users in N ), and σ 2 the variance of the Gaussian noise. 2 · P˜ /σ 2 ) is the capacity of the point-to-point Further, Cke ,i = W · log2 (1 + gi,k channel between user i and eavesdropper k. A quasi-static channel model is considered whereby the channel gain gi,j between any two nodes (users–BS, eavesdropper–user, or eavesdropper–eavesdropper) is given by

gi,j = ai,j ·

@

d−µ i,j ,

(14.57)

where di,j is the distance between nodes i and j, µ is the path-loss exponent, and ai,j is a Rayleigh distributed fading amplitude with variance 1 which is stable over the duration θslot of a slot but changes from one slot to the another (quasistatic channel). Note that the minus sign is inserted in (14.56) for convenience, in order to turn the problem into a maximization problem. In (14.56), each element of the summation quantifies the damage that eavesdropper k is able to cause on the secrecy capacity of user i when tapping into its signal during the corresponding time slot. The eavesdroppers aim to minimize the summation in (14.56) in every eavesdropping cycle by maximizing the damage caused through the eavesdropping capacities Cke ,i , ∀k ∈ K, i ∈ N . Due to the fading and path-loss between the eavesdropper and the user, these eavesdropping capacities may be small, thus, reducing the overall effectiveness of the eavesdropping process of all eavesdroppers. Hence, efficient techniques for combatting this fading are needed by the eavesdroppers in order to improve their performance. For example, the eavesdroppers can engage in distributed collaborative receive beamforming [26–28], whereby the radio signals received by a group of single-antenna eavesdroppers with nondirectional antennas can be combined using advanced signal processing techniques to improve the capacities Cke ,i , ∀k ∈ K, i ∈ N . Therefore, to improve their performance in terms of eavesdropping capacities, the eavesdroppers in our model can cooperate by forming groups of eavesdroppers, i.e., coalitions. Every coalition of eavesdroppers, S ⊆ K, can be regarded as a single eavesdropper with multiple receive antennas and, within a single slot, this coalition can use collaborative receive beamforming to tap into the signal of one of the transmitters. For every coalition S, a two-stage cooperation protocol is defined whereby the coalition divides its slot into two phases as follows (this protocol is used every slot to eavesdrop on a particular user i ∈ N ): (1) The first phase of the slot is dedicated to information exchange between eavesdroppers. Hence, sequentially, each eavesdropper k ∈ S broadcasts its information (channel, control, etc.) to the other members of coalition S in this duration of the slot.

410


(2) In the remainder of the slot, the members of coalition S perform collaborative receive beamforming, i.e., the coalition directs its beam towards the user that its members are currently interested in attacking. Once the coalitions in the network are formed, during each time slot in an eavesdropping cycle all the coalitions (each coalition acting on its own) eavesdrop on one user i ∈ N in a round-robin manner. During the information exchange phase, the users are able to transmit without being tapped into since the eavesdroppers are communicating with each other to exchange their channel and control information. Further, during this first phase, the users can overhear the information exchange between the eavesdroppers (act as eavesdroppers on the eavesdroppers!) and, thus, detect the presence of the eavesdropping threat. Consequently, while in the second phase the eavesdroppers improve their eavesdropping capacity using receive beamforming, this performance improvement is hindered by the time and security costs during the information exchange phase. Given this benefit–cost tradeoff, for any coalition S ⊆ K of eavesdroppers, the total secrecy capacity reduction that a coalition S can cause for the users during an eavesdropping cycle can be given by the following utility function: + e θS,i · Cid + (1 − θS,i ) Cid − CS,i , (14.58) u(S) = − i∈N

where

e CS,i

is the receive beamforming eavesdropping capacity, which is given by P˜ · h2 e , (14.59) CS,i = W · log2 1 + σ2

where h is the |S| × 1 channel vector and each row element hk = gi,k with gi,k the channel gain between user i and eavesdropper k ∈ S as given by (14.57). The eavesdropping capacity in (14.59) is achieved by the eavesdroppers through maximal ratio combining which is well known as the optimal SNR maximizing technique for combining the received signals and directing the beam towards a particular direction [26]. Moreover, θS,i is a time cost that accounts for two types of cost for cooperation: (i) the time required for information exchange during which users are transmitting securely; (ii) the possibility that the users may overhear the transmission (and act as eavesdroppers on the eavesdroppers!) between the eavesdroppers during the information exchange phase. This fraction of time is given by − i θS,i = θk , (14.60) k ∈S

with b− min (b, 1) and θki the fraction of time required for exchanging information between an eavesdropper k ∈ S and the other members of coalition S without being tapped into by transmitter i ∈ N (in the slot when the coalition’s


411

beam is directed towards user i). In the first phase of the slot, every eavesdropper k ∈ S exchanges its information with the members of S by sending its data to the farthest member kˆ = arg maxl∈S (dk ,l ) in S as the other members of S simultaneously receive this information due to the broadcast nature of the wireless i i channel. Consequently, θk = θk , kˆ /θslot with θki , kˆ =

L , Ckexch , kˆ ,i

(14.61)

e + where Ckexch = (Ckd, kˆ − Ci,k ) represents the secrecy capacity for exchange of , kˆ ,i information between eavesdropper k and the farthest eavesdropper kˆ ∈ S when

being eavesdropped on by user i and L is the size (in bits) of the packet containing control and channel information. Every element in the summation of (14.58) represents the secrecy capacity reduction for the slot where coalition S was eavesdropping on a user i ∈ N using the two-stage cooperative protocol proposed. For instance, during the eavesdroppers information exchange period θS,i , user i is able to transmit freely with no eavesdropping, hence the term θS,i · Cid . For the rest of the slot (1 − θS,i ), coalition S is able to eavesdrop on user i with an improved perfore in the term mance due to the receive beamforming gain as exhibited by CS,i d + e (1 − θS,i ) Ci − CS,i . The objective of the eavesdroppers (coalitions) is to maximize the damage on the users as captured by (14.58). For a better understanding of (14.58) one can consider some extreme cases. For example, when the eavesdroppers in coalition S, who are eavesdropping on user i, (θS,i = 1,), spend the whole time slot θc exchanging information, user i will have transmitted all of its data without any tapping and, cooperation is not beneficial for attacking i (although it may be beneficial for eavesdropping on another user j = i in another time slot). On the other hand, if θS,i = 0, then coalition S spends no time for information exchange, and, hence, the attack on user i is most efficient as coalition S is able to perform receive beamforming on user i during the whole slot θc . Finally, whenever S is a singleton, then u(S) in (14.58) reduces to the expression given in (14.56) (for a singleton coalition of size 1 there is no information exchange, i.e., θS,i = 0). Given this cooperative model for eavesdropping, the key question that remains to be answered is: how can a network of eavesdroppers form cooperative coalitions in a distributed manner taking into account the benefit–cost tradeoff for cooperation previously described. The following subsection is dedicated to answering this question using coalitional game theory.

14.4.1

Coalition formation games for distributed eavesdroppers cooperation To model the eavesdroppers cooperation problem mathematically, coalitional game theory [29, 30] provides a set of suitable analytical tools. In fact, the

412


eavesdroppers cooperation problem can be modeled as a coalitional game with a nontransferable utility which is defined as follows [29, Chap. 9]. Definition 14.6 A coalitional game with nontransferable utility is defined by a pair (K, V ), where K is the set of players and V is a mapping such that for every coalition S ⊆ K, V (S) is a closed convex subset of R|S | that contains the payoff vectors that players in S can achieve. In other words, a coalitional game has a nontransferable utility whenever the total utility achieved by any coalition S cannot be arbitrarily apportioned among the members of S, hence there is a need for a set of payoff vectors, i.e., a mapping V to describe the utilities achieved by the players in a coalition S. In the eavesdroppers cooperation model, the set of eavesdroppers K is the set of players in the coalitional game. In addition, given a coalition S and denoting by φk (S) the payoff of eavesdropper k ∈ S achieved during an eavesdropping cycle, the following property is highlighted. Property 3 The proposed cooperative eavesdropping game has a nontransferable utility where the payoff φk (S) received by any eavesdropper k ∈ S during one eavesdropping cycle, i.e., the overall secrecy capacity reduction caused during one cycle by eavesdropper k when acting as part of S, is equal to the overall secrecy capacity reduction u(S) achieved by the coalition S as given by (14.58). Given Property 3, the mapping V for the eavesdroppers coalitional game can be defined as follows: V (S) = {φ(S) ∈ R|S | | φk (S) = u(S), ∀k ∈ S},

(14.62)

where φ(S) is a vector of payoffs achieved during one eavesdropping cycle by the eavesdroppers when acting in coalition S, u(S) is the overall secrecy capacity reduction incurred on the users in N as given by (14.58). Clearly, the set V (S) in the proposed game is a singleton since a coalition S can only achieve a single utility value as dictated by (14.58). Consequently, this set is closed and convex, and the eavesdroppers cooperation problem is cast into a (K, V ) coalitional game with nontransferable utility, where the eavesdroppers aim to maximize their payoffs and hence minimize the overall secrecy capacity achieved by the users (achieve maximum damage to the users) by forming coalitions. Moreover, as explained in the previous section, the damage achieved by any coalition as per (14.58) takes into account the cost for cooperation. Consequently, given the cost of information exchange, the eavesdroppers coalitional game for cooperation satisfies the following property.


413

Remark 14.1 For the (K, V ) eavesdroppers coalitional game, due to the cost of cooperation, the grand coalition of all users seldom forms. Instead, independent disjoint coalitions will appear in the network. This can be easily seen by noting that the cost of cooperation grows as: (i) the number of eavesdroppers in the coalition increases as seen in (14.60) and (ii) the channel (distance) between the eavesdroppers in the coalition, as well as the channel (distance) between the eavesdroppers and the users varies as seen from (14.61). For example, by considering a network of two eavesdroppers separated by a very large distance, the time required for information exchange as seen from (14.60) can be close to 1, hence yielding no benefit for cooperation as per (14.58). Therefore, due to the various cooperation costs, the grand coalition of all users forms only in very favorable conditions which can be quite unrealistic for a large-scale wireless network. Hence, the network structure consists of disjoint independent coalitions. Therefore, the proposed game for eavesdroppers cooperation is classified as a coalition formation game due to the presence of cooperation costs and the fact that the grand coalition is not always the optimal solution [30, Sec. IV]. In this regard, coalition formation games have been a topic of great interest in game theory [30, 31, 33] and have also attracted attention in wireless and communication networks [30]. The goal is to find algorithms for characterizing the coalitional structures that form in a network where the grand coalition is not optimal. By using game-theoretical concepts from coalition formation games, a distributed coalition formation algorithm is devised for the proposed (K, V ) eavesdroppers cooperation game. For this purpose, an algorithm can be built based on two simples operations, called “merge” and “split” borrowed from coalition formation games [32] and defined as follows. Definition 14.7 Merge rule. Merge any set of coalitions {S1 , . . . , Sl } whenever A the merged form is preferred by the players, i.e., where { lj =1 Sj } {S1 , . . . , Sl }. A Therefore {S1 , . . . , Sl } → { lj =1 Sj }. A Definition 14.8 Split rule. Split any coalition lj =1 Sj whenever a split A form is preferred by the players, i.e., where {S1 , . . . , Sl } { lj =1 Sj }. Thus, A { lj =1 Sj } → {S1 , . . . , Sl }. In these definitions, the operator represents a comparison relation, i.e., an operator that allows the players to quantify their preferences over the different coalitional structure. For instance, for the proposed eavesdroppers coalitional games, the Pareto order is selected as a comparison relation , and is defined as follows:

414


Definition 14.9 Consider two collections of coalitions R = {R1 , . . . , Rl } and S = {S1 , . . . , Sm } that are partitions of the same subset A ⊆ K (same players in R and S). For a collection R = {R1 , . . . , Rl }, let the utility of a player j in a coalition Rj ∈ R be denoted by Φj (R) = φj (Rj ) ∈ V (Rj ). R is preferred over S by Pareto order, written as R S, iff R S ⇐⇒ {Φj (R) ≥ Φj (S) ∀ j ∈ R, S} with at least one strict inequality (>) for a player k.

(14.63)

Using the Pareto order, the merge and split rules are interpreted as follows. On the one hand, using the merge rule, a number of coalitions can cooperate and form a larger coalition if this merge yields a preferred collection based on the Pareto order. This implies that a group of players can agree to form a larger coalition, if at least one of the players improves its payoff without decreasing the utilities of any of the other players. On the other hand, any formed coalition can decide to break up into smaller coalitions, using the split rule, if splitting yields a preferred collection by Pareto order. The idea of merge and split is based on a family of coalition formation games, known as games with partially reversible agreements. In such games, once the players agree to sign an agreement to form a coalition (e.g., using merge), this agreement can only be broken if all the players approve (e.g., using split). In the proposed eavesdroppers game, performing merge or split using the Pareto order defined in (14.63) requires that the eavesdroppers have full knowledge of the instantaneous channel gain, including the fading amplitude as per (14.57). As the fading amplitude varies from one slot to another, utilizing the Pareto order as per (14.63) can require a continuous estimation of the instantaneous fading amplitude of the channel, which can be quite a complex process for the eavesdroppers. Thus, in order to avoid this complexity, the eavesdroppers can use a far sighted approach to the merge and split rules whereby the eavesdroppers use the Pareto order in (14.63) based on their long-term payoff ¯(S). φ¯k (S) = u This long-term payoff is defined as the utility that the eavesdroppers receive during an eavesdropping cycle averaged over the fading amplitude realizations. Using the quasi-static channel mode, one can easily note from (14.57) and (14.58) that the secrecy capacities, and payoffs φ¯k (S) averaged over the channel realizations depend mainly on the path-loss (distance) between the nodes (eavesdropper–eavesdropper, eavesdropper–user, or user–BS). As a result, to form coalitions, the eavesdroppers can use the far sighted merge and split rules. Then, any coalition formation algorithm based on the far sighted merge and split rules no longer requires a knowledge of the instantaneous fading amplitude as the decisions are based on long-term utilities averaged over the fading amplitude. Using the far sighted merge and split rules, one can devise a coalition formation algorithm based on three phases: neighbor discovery, adaptive far sighted coalition formation, and cooperative eavesdropping. In the neighbor discovery


415

phase (phase 1), each coalition (or eavesdropper) surveys its neighborhood to locate nearby eavesdroppers with whom cooperation is possible. At the end of this phase, each coalition constructs a list of its neighboring partners and proceeds to the next phase of the algorithm. In the second phase, the coalitions (or individual eavesdroppers) interact with their neighbors to assess whether to form new coalitions or whether to breakup their current coalition. For this purpose, an iteration of sequential far sighted merge and split rules occurs in the network, whereby each coalition decides to merge (or split) depending on the long-term utility improvement that merging (or splitting) yields. This phase starts with an initial network partition T = {T1 , . . . , Tl } of K. Subsequently, any random coalition (individual eavesdropper) can start with the merge process. For practicality purposes, consider that the coalition Ti ∈ T which has the highest long-term utility in the initial partition T starts by attempting to merge with a nearby coalition. On the one hand, if merging occurs, a new coalition of eavesdroppers T˜i is formed and, in its turn, T˜i will attempt to merge with nearby eavesdroppers (coalitions), if possible. On the other hand, if Ti is unable to merge with the first neighbor it finds, it tries to find other coalitions that have a mutual benefit in merging. The search ends with a final merged coalition Tif in al composed of the eavesdroppers in Ti and one or several of coalitions in its vicinity (Tif in al = Ti , if no merge occurred). The algorithm is repeated for the remaining Ti ∈ T until all the coalitions have made their merge decisions, resulting in a final partition F . Following the merge process, the coalitions in the resulting partition F can next perform split operations, if any are possible. An iteration consisting of multiple successive merge and split operations is repeated until there is convergence. Note that the decisions on whether to merge or split can be taken in a distributed way by the eavesdroppers without relying on a centralized entity. The convergence of an iteration of merge and split rules is guaranteed [32]. Further, as shown in [33], this convergence always leads to a partition that is stable in the sense that no coalition has any further incentive to perform merge and split. Also, under certain conditions, as per [33], the network partition can be both stable and Pareto optimal, in terms of the eavesdroppers payoffs. In the cooperative eavesdropping phase (phase 3), within every slot of an eavesdropping cycle, the coalitions exchange their information and begin their cooperative eavesdropping process, in a time-slotted manner, one coalition per slot. Hence, in this phase, the eavesdropper coalitions perform the actual receive beamforming, to efficiently tap into the signal of the network’s users within the corresponding slot. For a stationary network, the last phase of the algorithm, i.e., the cooperative eavesdropping phase, is performed continuously over a large number of eavesdropping cycles. On the other hand, in a network where the eavesdroppers and/or the users are mobile, periodic runs of the first two phases of the proposed algorithms are performed which allows the eavesdroppers to autonomously self-organize and adapt the network’s topology through appropriate merge-and-split decisions during phase 2. This adaptation to environmental

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changes is performed in mobile networks periodically every M eavesdropping cycles. In general, the number M of cycles can be chosen arbitrarily but, to adapt to mobility, M must be small as mobility increases in order to allow adequate adaptation of the network. The proposed coalition formation algorithm can be implemented in a distributed manner. At the beginning, the eavesdroppers can detect the strength of the users’ uplink signals, and, thus, estimate the location of these users. Note that, due to the far sighted merge and split rules considered, the eavesdroppers are not required to estimate the instantaneous fading amplitude of the channel (only estimates of the users’ locations are needed to evaluate the long-term payoffs needed for coalition formation). Further, nearby coalitions (eavesdroppers) can be discovered in phase 1 through techniques similar to those used in the ad-hoc routing discovery process. Once the neighbors are discovered and the users’ locations are estimated, the coalitions can perform merge operations in phase 2. Moreover, each coalition formed can also internally decide to split if its members find a preferred split structure. During phase 3, in every slot, the distributed eavesdroppers exchange their information (channels, control, etc.) and then cooperate to perform receive beamforming using the cooperative protocol previously described.

14.4.2

Simulation results The performance of the coalition formation algorithm for the eavesdroppers was assessed by simulations. Thus, given a square network of 4 km × 4 km with the BS located at the center, the eavesdroppers were randomly placed in the upper 4 × 2 rectangle while the users were randomly deployed within the lower 4 × 2 rectangle. The simulation parameters used were as follows: the number of bits for information exchange was taken as L = 128 bits, the power constraint per eavesdropper/user was P˜ = 10 mW, the noise level was −90 dBm, the channel propagation loss was set to α = 3, and the bandwidth was W = 100 kHz. The time slot duration was taken as θc = 42.3 ms which corresponds to the coherence time of a network with very low mobility (e.g., Doppler frequency of around 10 Hz). Figure 14.17 shows a snapshot of the network structure resulting from the proposed coalition formation algorithm for a randomly deployed network with K = 10 eavesdroppers, and N = 10 users. In this figure, one can see how the eavesdroppers were able to self-organize into four coalitions, hence forming the network structure T = {T1 , T2 , T3 , T4 }. This structure is a direct result of the far sighted merge-and-split coalition formation algorithm. For example, eavesdropper 2 is unable to find nearby partner to improve his payoff and hence decides to act alone. In contrast, eavesdroppers 5 and 9 merge into a single coalition T1 = {5, 9} due to the fact that V ({5, 9}) = {φ({5, 9}) = [−135 × 104 , −135 × 104 ]} which is a clear improvement on the noncooperative utilities which were φ5 ({5}) = −177.32 × 104 and φ9 ({9}) = −174.44 × 104 . Similar results can also


417

T T

T

y

T

x

Figure 14.17. A snapshot of a coalitional structure resulting from our proposed coalition formation algorithm for a network with K = 10 eavesdroppers, and N = 10 users (circles).

be seen for the formation of coalitions T3 and T4 . In summary, Figure 14.17 shows how the eavesdroppers can self-organize into disjoint independent coalitions to perform cooperative eavesdropping through receive beamforming. In Figure 14.18, for a network having N = 10 users, the payoff (secrecy capacity reduction) per eavesdropper achieved per eavesdropping cycle is shown during a period of about 4.2 minutes, i.e., M = 600 eavesdropping cycles (each eavesdropping cycle consists of N = 10 slots) averaged over the random locations of the eavesdroppers and the users as a function of the eavesdroppers network size K. The payoff shown is the actual payoff achieved by the eavesdroppers over this period given the instantaneous fading amplitudes of the channel following the coalition formation process. The performance of the proposed eavesdropper coalition formation algorithm is compared to that of the noncooperative case. For the cooperative case, the average eavesdropper’s payoff increases with the number of eavesdroppers since the possibility of finding cooperating partners increases. Moreover, this increase is interpreted that, as more eavesdroppers are available, the efficiency of attacking several users also improves. In contrast, the noncooperative approach presents an almost constant performance with different network sizes. Clearly, Figure 14.18 demonstrates that cooperation presents a significant advantage over the noncooperating case in terms of average payoff per eavesdropper per eavesdropping cycle for all network sizes, and this advantage

418


K

Figure 14.18. Payoff per eavesdropper per eavesdropping cycle (averaged over random locations of the eavesdroppers and users) achieved during M = 600 eavesdropping cycles (around 4 minutes) in a network with N = 10 users as the number of eavesdroppers K varies.

increases with K, reaching 27.6% of improvement relative to the noncooperating case at K = 40 eavesdroppers.

14.4.3

Conclusion We have introduced a model for cooperation among the eavesdroppers in a wireless network. Using a coalition formation game model, a number of single-antenna eavesdroppers interact to form cooperative coalitions that can utilize receive beamforming techniques to improve their attacks on the wireless users. For forming coalitions, a distributed algorithm has been devised based two simple rules of merge and split that allow the eavesdroppers to take autonomous decisions to form or breakup a coalition depending on their utility improvement. The utility of every coalition corresponds to the overall secrecy capacity reduction that the coalition can inflict on the network’s users over the duration of an eavesdropping cycle. For the derived model, we have highlighted the key properties and characterized the resulting network structures. By simulations, it has been shown that, using coalition formation, the eavesdroppers can self-organize while improving the average payoff per eavesdropper up to 27.6% per eavesdropping cycle

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Part V Standardization activities

15 Cooperative communications in 3GPP LTE-Advanced standard Hichan Moon, Bruno Clerckx, and Farooq Khan

15.1

Introduction A cellular communication system is designed based on the concept of frequency reuse, in which the same frequency resources are reused at a certain distance from a cell site [1, 2]. Traditionally, a cellular system has been composed of cell sites operating independently except in some inevitable scenarios like handover. Independent operation of each cell site makes it possible to deploy a wireless system at a low cost, while maintaining the quality of the voice service. However, due to the large amount of interference from neighboring cell sites, cell-edge users experience bad channel conditions. Furthermore, the cell-edge interference becomes more severe, when the frequency reuse factor is 1, which is a common assumption for cellular systems designed for high capacity. Therefore, with the conventional cellular designs, it is difficult to achieve high data throughput for users located at cell edges. However, as the need for high-speed data communication increases, cooperative communications between the neighboring cell sites and UEs1 are being more intensively studied not only in academia but also in industry. One of the main focuses of these studies is to increase the data throughput for the cell-edge UEs. To increase the throughput of the cell-edge UEs, neighboring eNodeBs2 cooperate to enhance the signal quality and/or decrease the interference level. Coverage extension through a wireless relay is another research focus of cooperative communication. Interference management and cooperation between eNodeBs are important issues in a heterogeneous network. The third generation partnership project (3GPP) long-term evolution (LTE)Advanced is one of the most promising standards for the next generation wireless communications systems. LTE-Advanced is a candidate for the International Mobile Telecommunication Advanced (IMT-Advanced) of InternationTelecommunications-Union-R (ITU-R) and is being designed based on the 3GPP 1 2

The UE is the common terminology used to denote mobile terminal in LTE. Note that eNodeB is the terminology used in LTE to denote (or eNB) the base station.


426

Cooperative communications in 3GPP LTE-Advanced standard

Table 15.1. LTE system attributes Bandwidth Duplexing Mobility Multiple access Downlink Uplink MIMO Downlink Uplink Peak data rate Downlink in 20 MHz Uplink Modulation Channel coding Other techniques

1.25 ∼ 20 MHz FDD, TDD, half-duplex FDD 350 Km/Hr OFDMA SC-FDMA 2×2, 4×2, 4×4 1×2, 1×4 173 and 326 Mbps for 2×2 and 4×4 MIMO 86 Mbps with 1x2 antenna configuration QPSK, 16-QAM and 64-QAM Turbo code Channel sensitive scheduling, link adaptation, power control, ICIC and hybrid ARQ

LTE system, which utilizes orthogonal frequency-division multiplexing (OFDM) technology in the air interface [3]. In this chapter, standardization trends in cooperative wireless communications are presented for the 3GPP LTE-Advanced system. The rest of this chapter is organized as follows. Section 15.2 introduces the 3GPP LTE and LTE-Advanced systems. Cooperative multipoint (CoMP) transmission techniques are investigated in Section 15.3. Sections 15.4 and 15.5 present the wireless relay and the heterogeneous networks considered in the LTEAdvanced standard, respectively.

15.2

LTE and LTE-Advanced The 3GPP LTE standard was developed between 2004 and 2009 with the goal of providing a high-data-rate, low-latency and packet-optimized radio-access technology supporting flexible bandwidth deployments. In parallel, a new network architecture was designed with the objective of supporting packet-switched traffic with seamless mobility, quality of service (QoS) and minimal latency. The air-interface-related attributes of the LTE system are summarized in Table 15.1. The system supports flexible bandwidths thanks to OFDMA and single carrier frequency division multiple access (SC-FDMA) schemes. In addition to frequency-division duplexing (FDD) and time-division duplexing (TDD), halfduplex FDD is allowed to support low-cost UEs. Unlike FDD, in half-duplex FDD operation, a UE is not required to transmit and receive at the same time. This avoids the need for a costly duplexer in the UE. The system is primarily

15.2 LTE and LTE-Advanced

427

optimized for low speeds, up to 15 km/h. However, the system specifications allow mobility support in excess of 350 km/h with some performance degradation. The uplink access is based on SC-FDMA, which promises increased uplink coverage due to low peak-to-average power ratio (PAPR) relative to OFDMA [4]. The system supports a downlink peak data rate of 326 Mbps with 4 × 4 MIMO within 20 MHz bandwidth. Since uplink MIMO is not employed in the first release of the LTE standard, the uplink peak data rate is limited to 86 Mbps within 20 MHz bandwidth. In addition to the peak data rate improvements, the LTE system provides 2–4 times higher cell spectral efficiency than the Release 6 high-speed packet access (HSPA) system. Similar improvements are observed in cell-edge throughput while maintaining the same site locations as deployed for HSPA. In terms of latency, LTE radio-interface and network are capable of delivering a packet from the network to the UE in less than 10 ms. We refer the readers to [3] for a detailed description of the LTE system. The LTE standard was completed in 2009 and some initial commercial LTE deployments are already underway in the USA, Japan, and Europe to accommodate the growing data traffic demands. The mobile data traffic continues to grow and is expected to grow at a compound annual growth rate (CAGR) of 131% [5] over the next years, increasing more than 65 fold in 5 years. In order to meet this spectacular growth in data traffic, continuous improvements in air-interface efficiency as well as allocation of new spectrum are of paramount importance. The decisions on IMT spectrum allocation at the World Radiocommunication Conference 2007 (WRC-07) have set the stage for the future evolution of radio technologies towards IMT-Advanced. IMT-Advanced is an ITU-R initiative for developing the fourth generation global mobile broadband wireless standard. A major effort is underway by the 3GPP and IEEE 802.16 standard bodies to develop the IMT-Advanced compliant fourth generation mobile broadband standards. With only two candidate technologies proposed for IMT-Advanced, it is expected that the fourth generation mobile broadband market will be less fragmented compared with the previous generations of cellular technologies. At WRC-07, the bands identified for IMT in addition to the existing IMT2000 bands include: 450-470 MHz, 698-862 MHz, 790-862 MHz, 2.3-2.4 GHz, 3.4-4.2 GHz, and 4.4-4.99 GHz, as shown in Figure 15.1. A maximum of 428 MHz new spectrum has been identified for IMT-2000/IMT-Advanced (including TV bands). The IMT-Advanced set peak data rate targets are 1 Gbps in nomadic environments and 100 Mbps in high mobility scenarios. Also, the cell throughput or spectral efficiency target is set at around two times higher than existing LTE [3] and WiMAX [6] systems. In order to meet the peak data rate and spectral efficiency targets set by IMT-Advanced, the air interface needs to be evolved by incorporating new radio technologies as well as improving performance of the existing techniques. In April 2008, 3GPP started LTE-Advanced standardization activities as part of Release 9 work. The LTE-Advanced study item was completed in 2009 forming

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3300 3400 3500 3600 3700 3800 3900 4000 4100 4200 4300 4400 4500 4600 4700 4800 4900 5000 IMT-2000 bands

Candidate bands for IMT-Advanced

Figure 15.1. Candidate bands for the IMT-Advanced spectrum.

the basis for LTE-Advanced standardization in Release 10. The Release 10 LTEAdvanced standard, with expected completion in 2011, incorporates the following new features [7, 8]:

r r r r

carrier aggregation, latency reductions, enhanced downlink multiple-antenna transmission, uplink multiple-antenna transmission.

Additionally, a work item on LTE-Advanced relays targeted to improve coverage and cell edge throughput was approved separately.

15.2.1

Carrier aggregation LTE-Advanced is expected to operate in spectrum allocations of different sizes including wider spectrum allocations of up to 100 MHz to achieve the target peak data rate of 1 Gbps. The main focus for a wider bandwidth than the 20 MHz used for LTE is on a consecutive spectrum. However, carrier aggregation over noncontiguous component carriers is also permitted. Another requirement is that the LTE-Advanced system should be backwardly compatible with the earlier releases of the LTE system in the sense that for an LTE terminal, an LTE-Advanced network should appear as an LTE network. One way of achieving such backward compatibility while supporting larger bandwidths for LTE-Advanced is to use carrier aggregation where multiple component carriers are aggregated on the physical layer as shown in Figure 15.2. When an LTE-Advanced system supports multiple component carriers, not all component carriers may necessarily be LTE

15.2 LTE and LTE-Advanced

429

Component carriers

20 MHz

20 MHz

20 MHz

20 MHz

20 MHz

100 MHz

Figure 15.2. An example of carrier aggregation with 20 MHz component carriers to provide 100 MHz bandwidth for LTE-Advanced terminals.

Release 8 compatible. This means that as long as there is a single carrier that is LTE Release 8 compatible, LTE terminals can use this carrier for communication. A terminal may simultaneously receive or transmit signals over one or multiple component carriers depending on its capabilities:

r An LTE-Advanced terminal with reception and/or transmission capabilities for carrier aggregation can simultaneously receive and/or transmit on multiple component carriers. r An LTE Release 8 terminal can receive and transmit on a single component carrier only, provided that the structure of the component carrier follows the Release 8 specifications. Carrier aggregation is supported for both contiguous and noncontiguous component carriers with each component carrier limited to a maximum of 110 resource blocks in the frequency domain using the LTE Release 8 numerology. It is possible to configure a UE to aggregate a different number of component carriers originating from the same eNodeB and possibly different bandwidths in the uplink (UL) and the downlink (DL). In typical TDD deployments, the number of component carriers and the bandwidth of each component carrier in the UL and DL will be the same. The spacing between the center frequencies of contiguously aggregated component carriers is a multiple of 300 kHz. This is in order to be compatible with the 100 kHz frequency raster of LTE Release 8 and at the same time preserve orthogonality of the subcarriers with 15 kHz spacing.

15.2.2

Latency improvements The LTE-Advanced target is to further reduce the latency to improve the user experience for Internet applications. The target for the transition time from Idle mode (with the IP address allocated) to Connected mode is for it to be less than 50 ms including the establishment of the user plane. The target for the transition time from the “Dormant state” in Connected mode to the “Active state” is less than 10 ms as depicted in Figure 15.3. Several mechanisms are being considered to further reduce the latency in the LTE-Advanced system including the following:

430


Connected Dormant Idle

10 ms 50 ms Active

Figure 15.3. State transitions time in the LTE-advanced system.

r Combined RRC connection request and nonaccess stratum (NAS) service request Combining allows those two messages to be processed in parallel at the eNodeB and mobility management entity (MME), respectively, reducing overall latency from Idle mode to Connected mode by approximately 20 ms. r Reduced processing delays The processing delays in different nodes form the major part of the delay (around 75% for the transition from Idle mode to Connected mode assuming a combined request). Therefore, reducing processing delays will have a large impact on the overall latency. r Reduced random access channel (RACH) scheduling period Decreasing the RACH scheduling period from 10 ms to 5 ms results in decreasing the average waiting time for the UE to initiate the procedure to transit from Idle mode to Connected mode by 2.5 ms. In order to reduce the transition time from the “Dormant state” in Connected mode to the “Active state,” the following mechanisms are considered for LTEAdvanced:

r Shorter physical uplink control channel (PUCCH) cycle A shorter cycle of PUCCH would reduce the average waiting time for a synchronized UE to request resources in Connected mode. r Contention-based uplink Contention-based uplink allows UEs to transmit uplink data without having to first transmit a scheduling request on PUCCH, thus reducing the access time for synchronized UEs in Connected mode.

15.2.3

DL multiantenna transmission The current LTE system supports a maximum of four MIMO layers in the DL. LTE-Advanced extends DL spatial multiplexing with support for up to eightlayer spatial multiplexing. In the DL, up to 8 × 8 single-user spatial multiplexing per DL component carrier is supported. A maximum of two transport blocks can be transmitted to a scheduled UE in a subframe per DL component carrier. Each

15.3 Cooperative multipoint transmission

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transport block is assigned its own modulation and coding scheme and coded separately using Turbo coding and the coded bits from each transport block are scrambled. For hybrid automatic repeat request (HARQ) ACK/NAK feedback on the UL, one bit is used for each transport block separately. Two types of DL reference signals are considered for LTE-Advanced, namely reference signals for data demodulation and reference signals targeting channel state indication (CSI) estimation for reporting channel quality indicator (CQI), precoding matrix index (PMI), and rank information. These reference signals can be used to support multiple LTE-Advanced features, e.g., CoMP and spatial multiplexing. These reference signals introduced in LTE-Advanced are different from the common reference signals in the LTE system, where the same reference signals are used for demodulation and CSI estimation.

15.2.4

UL multiantenna transmission The UL in the current LTE system does not support spatial multiplexing. LTEAdvanced extends LTE Release 8 with support for UL spatial multiplexing of up to four MIMO layers. In the case of UL single-user spatial multiplexing, up to two transport blocks can be transmitted from a scheduled UE in a subframe per UL component carrier. The rate can be adapted independently for each transport block with each transport block having its own modulation and coding scheme (MCS) level. The uplink MIMO transmission chain is similar to the downlink transmission chain with the differences that the maximum number of layers (and antennas ports) in the UL is limited to four and that SC-FDMA is used as the multiple access scheme in the UL. The MIMO transmission rank can be adapted dynamically.

15.3

Cooperative multipoint transmission A wireless system is commonly evaluated based on its average cell throughput and its cell-edge throughput [9, 10]. Improving both the cell average and cell edge performance is the target in the standardization of wireless systems. While the average cell performance can be improved by increasing the received signal strength using power boosting techniques, cell-edge users experience low received signal strength and the cell-edge performance is therefore primarily affected by the intercell interference (ICI). This is especially true for systems designed to operate with a frequency reuse factor of 1 or close to 1, which is a key objective of OFDM-based fourth generation networks. Such frequency reuse implies that systems become primarily interference limited as all cells transmit on all time and frequency resources simultaneously. Unfortunately, power boosting does not improve-cell-edge performance as both the serving cell signal and the interfering signal strengths would be increased. This motivates the development of other techniques that particularly target improving cell-edge performance.

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System level simulations of a frequency reuse 1 network composed of 57 sectors with an inter-site distance of 100 m indicate that around 5% of the users have a wideband carrier-to-interference-plus-noise ratio (CINR) lower than -4 dB with a two-dimensional antenna pattern at the eNodeB and lower than −2 dB with a three-dimensional antenna pattern at the eNodeB (the three-dimensional radiation pattern includes 15 degrees down-tilting of the antenna array). 30% of the users have a wideband CINR lower than 0 dB with a two-dimensional pattern and lower than 2.5 dB with a three-dimensional pattern. Hence, especially with a two-dimensional antenna pattern, a large proportion of users in the cell experience very low CINR and therefore unsatisfactory throughput performance. The goals of LTE-Advanced are to improve the peak throughput (or spectrum efficiency) by increasing the numbers of transmit and receive antennas and to further boost the average cell throughput by enhancing DL multiuser MIMO [9]. In addition, a particularly challenging task of standardization organizations like 3GPP LTE-Advanced is to improve the cell-edge performance further [9] using novel interference mitigation technologies that are expected to outperform the classical mitigation techniques originally introduced in LTE Release 8. Those techniques have received a lot of attention in the standards community as well as in academia [7, 8, 10, 11] and are commonly referred to as CoMP in the LTE-Advanced community. CoMP stands for coordinated multiple point transmission/reception and is a candidate technology for cooperative communications where antennas of multiple cell sites are utilized in such a way that the serving cell as well as the neighboring cells can contribute to improving the received signal quality at the mobile terminal, as well as to reducing the co-channel interferences from neighboring cells.

15.3.1

Interference mitigation techniques in previous releases of LTE ICI mitigation is not new in cellular systems. Universal terrestrial radio access (UTRA) Release 7 classified these mitigation techniques into three types [11]. The ICI randomization techniques apply random scrambling or frequency hopping to randomize the interference. The ICI cancellation techniques suppress interference through the use of multiple receive antennas at the UE and cancel interference by detecting and subtracting the inter-cell interference. The ICI coordination/avoidance techniques apply restrictions (on the available time/frequency resources and on the transmit power applied to those resources) to the DL resource management using coordination between cells in order to improve the signal-to-interference ratio (SIR) and cell-edge throughput and coverage. Such coordination may require some additional measurement and feedback on top of the usual CQI reports. For instance, the average path-loss of serving and interfering cells can be reported every 100 ms. In static interference coordination, the reconfiguration of the scheduler restriction is rare, occurring only with


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a rate of the order of days, therefore avoiding internode signaling (over the X2 interface). In semistatic interference coordination, reconfigurations are carried out much more frequently, with a rate of the order of seconds. Internode signaling (over the X2 interface) contains the necessary information to reconfigure the scheduler restrictions. Those techniques require a low feedback overhead on the UL control channels as well as over the internode (e.g., X2) interface. Moreover, the coordination between cells is done at a relatively low pace. CoMP can be seen as an extension of the ICI coordination techniques with faster decisions, faster backhaul, and higher overhead in order to share CSI and data information among cells. In the following subsection, we provide an overview of the CoMP techniques discussed in the literature and by the 3GPP LTE-Advanced standardization body.

15.3.2

Overview of CoMP techniques CoMP categories In order to categorize the techniques, two major kinds of CoMP transmission for application in the DL are identified in LTE-Advanced [7]. Coordinated beamforming/coordinated scheduling [7] (denoted as CB/CS) is characterized by the fact that it does not require data sharing between cells. The data are only available at the serving cell and are transmitted from that cell. However, the user scheduling and beamforming decisions are made with coordination among the cells in the set of cooperating cells (denoted as the CoMP cooperating set). CB/CS can operate with and without sharing CSI among cells. The ICI coordination/avoidance techniques first introduced in UTRA Release 7 and discussed in the previous subsection can be thought of as a subset of the CB/CS techniques as data are not shared between cells. CB/CS techniques are motivated by the interference channel in information theory. Joint processing [7] (denoted as JP) is characterized by the fact that data are shared between eNodeBs and are available at each cooperating cell. JP is further categorized into dynamic cell selection and joint transmission (JT). If at a given time instant, data (more rigorously the physical DL shared channel (PDSCH)) are transmitted from a single cell in the CoMP cooperating set, JP is referred to as dynamic cell selection. However, if the data (i.e., PDSCH) to a single UE are transmitted simultaneously from multiple points in the CoMP cooperating set, by performing coherent or noncoherent beamforming, JP is referred to as JT. Like CB/CS, JP can also operate with and without CSI exchange. JP with CSI exchange is aimed at increasing the beamforming gain on top of interference mitigation. JP techniques are motivated by the MIMO broadcast channel for which cooperation between transmitters is possible. CoMP reception coordinates multiple cells to perform joint reception (JR) of the transmitted signal at multiple receiving eNodeBs and/or coordinated scheduling (CS) decisions among cells to control interference. UL CoMP

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Table 15.2. Categories of CoMP schemes No CSI sharing

a

CSI sharing

No data Frequency reuse sharing Static FFR (CB/CS)

Adaptive FFR Rate splitting Coordinated beam patterns PMIa -coordination Coordinated beamforming Interference alignment Coordinated scheduling

Data sharing (JP)

Dynamic cell selection Joint transmission (Network MIMO)

Distributed OL MIMO

PMT – precoding matrix indication.

techniques are motivated by the multiple access channel for which receivers can cooperate. UL CoMP has less impact on the standard specifications from a physical layer perspective. Therefore, we will mainly focus on DL CoMP. In Table 15.2, we summarize the potential DL CoMP techniques based on their requirements in terms of data and CSI sharing. Each technique mentioned in Table 15.2 will be discussed in the following subsections.

CoMP sets LTE-Advanced has defined various kinds of CoMP sets [7]. The CoMP measurement set Mk of the user k is defined in LTE-Advanced [7] as the set of cells about which CSI/statistical information related to their link to the UE k is reported. The actual UE may downselect cells for which actual feedback information is reported. The CoMP-requested user set of cell i is the set of users that have cell i in their measurement set, i.e., Ri = { l| i ∈ Ml , ∀l}. Note that the CoMP-requested user set can also be viewed as the victim user set of cell i as it is the set of users who could be impacted by cell i if cooperation is not performed. The CoMP cooperating set is defined in LTE-Advanced [7] as the set of (geographically separated) points directly or indirectly participating in PDSCH transmission to the UE. Ck ⊂ { j| k ∈ Rj , ∀j = i} denotes the CoMP cooperating set of user k whose serving cell is i. As defined, the CoMP cooperating set does not include the serving cell i. The CoMP cooperating set is a subset of the CoMP measurement set. The CoMP measurement set may be the same as the CoMP cooperating set. In order to avoid feeding back CSI that is not used by the eNodeB, it is preferable for the CoMP measurement set and the cooperating set to be as similar as possible.


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Two types of cooperating set are frequently mentioned: one is the network predefined cooperating set, and the other is the user-centric cooperating set. With a network predefined cooperating set, a fixed set of eNodeBs is cooperating. This is a simple approach. However, due to shadowing, the strongest interference to a certain UE may not always come from the cells in the cooperation set. The CoMP transmission point(s) as defined in LTE-Advanced [7] is a subset of the CoMP cooperating set given by the points or set of points actively transmitting PDSCH to UE. For JT, the CoMP transmission points are the points in the CoMP cooperating set. For dynamic cell selection, a single point is the transmission point at each subframe. This transmission point can change dynamically within the CoMP cooperating set. For coordinated scheduling/beamforming, the CoMP transmission point corresponds to the serving cell.

CS/CB with no CSI sharing CS/CB with no CSI sharing covers the static interference coordination introduced in the previous subsection. (1) Frequency reuse partitioning Frequency reuse partitioning involves dividing the available spectrum into multiple frequency partitions and assigning a given partition to a given cell (sector) in such a way that ICI is minimized. A pure three-reuse is achieved by dividing the frequencies into three parts f1 , f2 , and f3 and by setting the maximum power in / fn each frequency f as Pmax (f ) = P (> 0) for f ∈ fn , and Pmax (f ) = 0 for f ∈ for each cell. In a three-sector cell plan, each sector can be allocated one frequency partition. Unfortunately, such frequency reuse partitioning based on, for example, three-reuse only slightly improves the performance of cell-edge users by decreasing the interference. However, the average cell throughput is degraded [12]. The complexity of such a scheme is minimal since a fixed assignment is predefined. (2) Static fractional frequency reuse (static FFR) Static FFR is a resource partitioning scheme that applies different reuse factors for cell-center users and cell-edge users in the serving cell. Interference is mitigated by assigning resources for cell-edge users with high frequency reuse such that they do not overlap with neighboring cells. Resources for cell-center users are allocated in a frequency reuse 1 (or close to 1) fashion. Power transmitted to the cell-center region on frequency resources not used by cell-edge users is lower than the power allocated to the cell-edge region. In such a way cell-center users interfere with users in an adjacent cell but with a lower transmit power. The SINR of a cell edge user is improved. Therefore, the cell-edge throughput is expected to increase. However, the use of large frequency reuse factors for cell-edge users also induces some loss in throughput as only a small portion of the bandwidth is available. The performance ultimately depends essentially on

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whether the eNodeB decides to allocate a user in the frequency reuse 1 region or in a higher frequency reuse region. There are several ways to assign the frequency resources. In one approach users close to eNB operate in all frequency partitions (e.g., F = f1 + f2 + f3 ) available, while for the edge users, each cell operates only in a specific frequency partition (e.g., f1 only). Another approach is to allocate f1 , f2 , f3 to the cell-edge region in each cell, and F − f1 , F − f2 , F − f3 to the corresponding cell-center region of each cell. Static FFR has been shown to provide additional gain in terms of sector throughput compared to the frequency reuse partitioning scheme based on a frequency reuse factor of 3. However, FFR can decrease the sector throughput compared to a full reuse 1 system due to the efficiency loss induced by the higher reuse factor. Therefore, the gain obtained in terms of SINR for cell-edge users does not compensate for the loss due to spectral efficiency. Despite such a loss, FFR is known to expand the coverage significantly compared to a frequency reuse 1 system and can actually achieve a coverage similar to a frequency reuse-3 system [12, 13]. LTE Release 8 supports ICI coordination with limited interaction between neighboring sites via the internode interface X2. In the DL, the exchange of relative narrowband Tx power (RNTP) messages [14] over X2 enables static FFR-like inter-cell interference coordination (ICIC) techniques with slow coordination in the frequency domain.

CS/CB with CSI sharing While frequency reuse partitioning and static FFR can help to reduce the ICI, their contribution to increasing the spectral efficiency is relatively limited. It is preferable to use more advanced techniques that use a reuse factor of 1 and provide faster interference coordination based on multipoint transmission. In this scenario where no data are shared but CSI is shared, many different kinds of processing can be undertaken. The ICI is mitigated with the aid of some form of CSI exchange such that the beamforming vectors, the scheduling decisions, or the transmit powers can be adequately chosen in a dynamic way. This scenario is closely related with the multiuser MIMO interference channels (IC). (1) Adaptive FFR In an adaptive FFR scheme, the same resources are shared among cell-centered users and cell-edge users. By performing frequency selective scheduling (based on CQI feedback), by adapting the frequency partition assignment (based on interference measurements and cell loading), and by using transmit power control, the performance and efficiency of cell-edge users can be increased while maintaining the performance of cell-center users. The complexity of adaptive FFR is proportional to the number of UEs served by an eNodeB. Moreover, adaptive FFR requires exchange of information related to transmit power among eNodeB. To operate adaptive FFR, the serving eNodeB


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can instruct the UEs to perform some interference measurement over specific frequency partitions and to report the interference information to the serving eNodeB as well as the preferred frequency partition. Adaptive FFR is a popular interference mitigation technique in IEEE 802.16m [10]. (2) Han–Kobayashi (HK) rate splitting Unlike in FFR, which uses power control to mitigate interference, in the Han–Kobayashi (HK) scheme [15, 16], originally proposed for a two-cell two-user scenario, the interference is mitigated by choosing appropriately the transmission rate of a part of the data (denoted as the common message) to be transmitted in the serving cell such that it is decodable to a cell-edge user located in a neighboring cell. By canceling the interference created by the common message, the interference to the cell-edge user can be mitigated without reducing the transmission power. The operation of such a scheme is presented below and more details can be found in [17]. Assume a serving cell communicating with a user and a neighboring cell communicating with a cell-edge user subject to interference from the serving cell. The serving cell splits the transmit information ds into two parts: a common ds,c and a private ds,p message. The common message ds,c is transmitted with a transmission power fraction α and the private message with a fraction 1 − α. The neighboring cell transmits message dn to the cell-edge user. The parameter α is computed by the cell-edge user and reported to the neighboring cell along with two CQIs. The first CQI, CQIn , is the CQI that the celledge user would experience while decoding its message dn if the interference from the common message with power fraction α were removed, i.e., the celledge user only experiences interference from the private message ds,p . Parameter α could be computed by the cell-edge user in such a way that the interference level caused by the private message has the same level as the noise level [16]. The second CQI, CQIn ,c , corresponds to the CQI measured by the cell-edge user when decoding the common message ds,c sent by the serving cell and experiencing the interference from its own message dn transmitted from the neighboring cell and the private message ds,p sent by the serving cell. The serving cell is informed of parameter α. The serving cell indicates α to the serving cell user such that this user can compute two CQI. The first CQI is the CQI of the common message in the serving cell, denoted as CQIs,c , while experiencing the interference from the private message ds,p and from dn transmitted from the neighboring cell. The second CQI is that of the private message, CQIs,p , assuming that the common message has been correctly decoded and therefore experiencing only the interference from message dn . Given CQIn ,c and CQIs,c , it is possible to compute the rate of the common message ds,c decodable by both users. The rate of the private message ds,p can be computed based on CQIs,p and the rate of message dn is computed based on CQIn . The cell-edge user decodes the common part first and subtracts the common message from the received signal to decode message dn . The common message

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ds,c is discarded by the cell-edge user. The serving cell user decodes both the private and common messages and the total rate experienced by the serving cell user is the sum of the rates of the common message and the private message. While the operation of the HK scheme for the two-cell two-user case is relatively well understood, the extension to multicell operations and multiple users is far from clear. Given that in the two-user case, the HK scheme gets only a degree of freedom of 1/2 in the medium interference range [16] (i.e., the capacity per user would scale as 0.5 log(SN R)), it was conjectured that in the K-user case, the degree of freedom would be of the order of 1/K. However, interference alignment techniques, which are discussed later, have provided some refreshing views on this conjecture. Overall, the HK scheme has the advantage of requiring a relatively small amount of information to be shared among cells, since only scheduling information, CQI, the power fraction for common, and private messages need to be communicated over the X2 interface. However, the HK scheme requires a more advanced receiver enabling successive interference cancellation and increases the DL overhead to indicate the modulation and coding scheme (MCS) of the common message in order to be decoded correctly. Its biggest drawback is that its extension to a more general setting with more than two users is not straightforward. (3) Coordinated beam patterns – opportunistic beamforming To benefit from HARQ and adaptive coding and modulation, wireless communication systems significantly rely on fast link adaptation which requires accurate CQI estimation. However, in a beamformed multiantenna system, interference fluctuates very severely between the time of UE measurement and the time of UE demodulation as the beamformers in interfering cells change in a very dynamic way. Such a situation occurs frequently if there is no coordination between cells. The dynamic interference is sometimes referred as the flashlight effect. In IEEE 802.16m, an open-loop region was defined [10]. The open-loop region is a resource in the frequency partition with a reuse factor 1 where open-loop transmission with one or two streams is performed. This resource is aligned for all cells and sectors which apply a fixed and predefined precoder to prevent dynamic interference and guarantee small CQI mismatch (and therefore accurate link adaptation). To do so, rank adaptation is prohibited in the open-loop region. The UE is requested to feedback its preferred subbands and best streams. Given that the precoders are predefined, the CQI(s) can be estimated accurately. In [18, 19], a somewhat similar but more flexible approach was proposed. Each eNodeB in the CoMP cooperating set determines its own beam cycling pattern (it can be predefined or can be defined based on the cell load and user distribution). The central controller that calculates the optimal cycling period (in time and/or frequency domain) is informed of the pattern and reports the optimal period to all eNodeB in the CoMP cooperating set. Given the cycling period and beam pattern, the eNodeBs cycle through the fixed set of beams. The UE is requested to


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feedback its best CQI per cycling period and the subframes/frequency subbands where the maximum CQI is experienced during that cycling period. Unlike in closed-loop operations, the UE does not have to report a preferred PMI nor a restricted/recommended PMI as in PMI coordination schemes. Moreover, the UE does not have to estimate the channel of an interfering cell. The CQI is measured based on the demodulation reference signal (DM-RS) as the UE is not aware of the beam pattern. Therefore, the CQI is calculated as a function of the complete interference that the UE will experience at the time of demodulation and is not based only on the dominant interference as in PMI coordination. The UE is informed about the cycling period in order to keep the CQI report synchronized with the beam cycling period. Based on the report, the eNodeB will decide the best beam subframes/frequency subbands on which to schedule a particular beam for the UE. Examples are provided in [19]. Like all opportunistic beamforming schemes, the major drawback of such a scheme is that its performance gains are expected only when the number of UEs is relatively large (i.e., larger than the ten users commonly assumed in a cell). For a limited number of UEs, a more accurate coordination based on CSI feedback is desirable to achieve performance gains. (4) PMI coordination PMI coordination [20–22] is a relatively simple concept that uses the multiple antennas at the eNodeB to mitigate the ICI. Two variants exist, namely PMI restriction and PMI recommendation. Assuming that the users and the eNodeB have knowledge of a codebook C composed of codewords, PMI restriction and PMI recommendation techniques aim to improve cell-edge user throughput by constraining the interfering cells to use only a subset of the codebook C. In the case of PMI restriction, the cell-edge users in each cell measure the channel of the interfering cells belonging to the CoMP measurement set Mk and calculate the worst PMI or the set of bad PMIs that would create the highest interference if used as the precoder in the interfering cells. The restricted PMI set can be calculated as the set of codewords in the codebook whose correlation with the dominant eigenvector of the interfering cell channel is larger than a certain predefined value. Let us denote that PMI restricted set as Rr estr. . Alternatively, in the case of PMI recommendation, the cell-edge users calculate the best PMI or the set of good PMIs that would generate low interference if used as precoders in the interfering cells. The recommended PMI set can be calculated as the set of codewords in the codebook whose correlation with the dominant eigenvector of the interfering cell channel is lower than a certain predefined value. Let us denote that PMI restricted set as Rr ec. . In order to help the interfering cell make appropriate decisions on whether to accept or reject the request of PMI restriction/recommendation and to resolve potential PMI conflict between different requests, additional quantities, e.g., differential CQI (difference between CQIs with and without PMI coordination), can provide information about the gain achievable if the restriction/recommendation

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is accepted. UEs feed back to the serving eNodeB the cell and sector IDs, along with the restricted/recommended PMI or PMI set and the differential CQIs. The necessary information is forwarded to the interfering eNodeBs in order for them to accept or reject the coordination request. If an interfering eNodeB decides to accept the request of PMI restriction, this eNodeB restricts the precoders in Rr estr. from being used by the inner-cell users that it serves. To do so, the eNodeB broadcasts information about the restricted set to the users in the cell (using, e.g., bitmap [10]). After reception of such information, the inner-cell users are forced to use and feedback only PMI included in the reduced codebook set C\Rr estr. (i.e., the set defined as the difference between C and Rr estr. ). Cell-edge users on the other hand are allowed to use the full codebook C. If the request of PMI recommendation is accepted, the interfering cell indicates to its inner-cell users to feedback only PMI included in Rr ec. . Cell-edge users on the other hand are allowed to use the full codebook C. Such an approach targets a practical scenario where the UL feedback overhead would be too large to accommodate the feedback of full CSI of many interfering cells. It primarily targets rank-1 PMI feedback in highly correlated channels enabling the feedback of a single wideband restricted/recommended PMI to further decrease the uplink overhead. (5) Coordinated beamforming Coordinated beamforming refers to the use of a coordinated design of the transmit precoders in each cell to eliminate or reduce the effect of ICI. In contrast to PMI coordination, the eNodeB computes a new transmit filter based on the CSI/PMI feedback from cells in the CoMP measurement set. Zero-forcing beamforming (ZFBF) based coordinated beamforming [23, 24] is one of the most popular schemes in standardization communities such as the LTE-Advanced and in the literature. In the presence of multiple antennas at the eNodeBs, such an approach consists in forcing the interference to zero. The number of interfering links that can be eliminated depends on the number of transmit antennas at the eNodeB. There is no coordinated scheduling among cells in such an approach. This means that each eNodeB must first decide which user will be scheduled in each cell. Once this is decided, the transmit beamforming can be accommodated in order to avoid creating interference to other cells. Such an approach requires CSI feedback of both the interfering cell in the CoMP measurement set and the serving cell, i.e., a given UE feeds back to the serving eNodeB not only its serving cell channel (between the UE and the serving eNodeB) but also the interfering cells channels (between the UE and the interfering cells in the CoMP measurement set). Note that it would also work if the UE did not feedback its serving cell channel. However, this is not the common scenario under investigation. The information required to be communicated over the backhaul (e.g., X2 interface) consists of the interfering cell CSI and the information related to which users will be scheduled simultaneously by the eNodeBs


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in the CoMP cooperating set. ZFBF filter design has the advantage of being relatively simple to implement as it does not require any iteration. Unfortunately, such an approach is very sensitive to the accuracy of the CSI feedback. Performance is significantly impacted by the quantization error induced by the limited feedback based on a codebook. Another popular scheme in LTE-Advanced is a joint leakage suppression (JLS) scheme [24–26]. Such a filter design does not maximize the SINR or the sum-rate but does maximize the SLNR which is the signal-to-leakage-plus-noise ratio. Compared with the zero-forcing solutions, SLNR does not impose a condition on the number of degrees of freedom as there is no pure suppression (hence there is no constraint on the relation between the number of transmit antennas, the number of receive antennas, and the number of users to mitigate interference), and it also avoids noise enhancement. However, one issue is that the leakage signal power has to be relatively small compared with the received signal power of the scheduled user in the interfering cell. Otherwise, a ZFBF-like solution would be more appropriate as it fully cancels the interference. As in ZFBF, such schemes require both serving cell and interfering cell CSI as well as the information related to which users will be scheduled simultaneously by the eNodeBs in the CoMP cooperating set. The interfering cell CSI is shared with other cells over the backhaul. The beamforming design does not require iterations since the filter design is obtained as a solution of a generalized eigenvalue problem. Therefore, the complexity is similar to that of ZFBF. It is important to note that ZFBF and JLS may have different requirements or preferences in terms of feedback. The JLS solution typically requires the channel covariance matrices, while the ZFBF filter is a function of the channel matrix itself. (6) Interference alignment (IA) Interference alignment (IA), originally introduced in [27, 28], is a single-user MIMO (SU-MIMO) coordinated beamforming scheme that has attracted a lot of attention in the literature but not much in the standards community. Regarding the degrees of freedom of a K-users interference channel, it has been shown [29] that it is possible to achieve 1/2 degree of freedom (i.e., in the limit of high SNR, the capacity per user would scale as 0.5 log(SNR)) despite the presence of K interfering users. In other words, as the transmit power of each eNodeB increases, every user will be able simultaneously to achieve half of the capacity it could achieve in the absence of the interference from other users. Assume a K-user, K-cell network with Nt transmit antennas at each eNodeB and Nr ≤ Nt receive antennas at each mobile where each mobile receives d < Nr data streams from its serving cell in a closed-loop SU-MIMO mode. The IA scheme consists of dividing the Nr -dimensional observation space at the receiver into a d-dimensional signal space and a (Nr − d)-dimensional interference space and designing jointly the transmit and receive filters such that every interference is aligned into the (Nr − d)-dimensional interference space. Unlike coordinated

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beamforming schemes, which optimize the transmit filter based on the feedback, IA jointly optimizes the transmit and receive filters. The necessary and sufficient condition for interference alignment is that the column space of each interference to a given user should be aligned. Interference is aligned before receive shaping in such a way that after receive shaping, it is completely canceled out and the received signal after filtering lies in the d-dimensional signal space. Such a scheme requires the global CSI to design the transmit and receive filters and is very computationally demanding. (7) Coordinated scheduling The aforementioned techniques such as coordinated beamforming and IA rely on only transmit and/or receive filter design to mitigate interference. However, as is well known in single-cell multiuser MIMO (MUMIMO), an appropriate scheduler is highly beneficial to reduce further the multiuser interference. Similarly, in a multicell scenario, a coordinated scheduler has a significant impact on the performance. The scheduler design is not standardized as it is left as an implementation issue for the vendors and operators. Depending on the network architecture, centralized and distributed schedulers can be identified. In the centralized scheduler, a central controller collects all CSI from all cells in the network and makes all scheduling decisions for all cells before passing those scheduling decisions onto each individual eNodeB. The central scheduler may be implemented at one of the eNodeBs in the network. In the distributed scheduler of [30], cells make scheduling decisions (e.g., UE decision and transmit precoding) one after the other for their own users based on the scheduling decisions made by other cells (belonging to the CoMP cooperating set) and then broadcast those decisions so that other cells (belonging to the CoMP cooperating set) can make their own decisions. As an example, cell 1 makes the scheduling decisions assuming no cooperation between cells and broadcasts those decisions. Cell 2 can make decisions based on cell 1 scheduling knowledge and then broadcasts the decisions. Cell 3 makes decisions based on those of cells 1 and 2. Such procedure is completed when all cells have made their decisions. In the distributed schedulers of [25, 31], scheduling decisions at each cell are reconsidered and updated in an iterative way prior to scheduling a UE in a given subframe based on decisions taken by all other cells at the previous iteration. Note that in its general form, the coordinated scheduler is actually a coordinated beamformer and scheduler and all techniques described in the previous subsections (e.g., coordinated beamforming, IA) are performed in each iteration of the iterative scheduler. Hence, at each iteration, each cell makes decision on the beamformer and on the UE to schedule. For both centralized and distributed schedulers, the importance of defining a network utility metric is stressed in [31, 32]. The goal of the scheduler is to maximize the utility metric through coordination. In its most advanced form, the


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network utility metric should account for the spectral efficiency associated with a particular cooperative transmission scheme (i.e., the exact type of cooperative scheme), the transmission modes (e.g., SU-MIMO, MU-MIMO), the relative priorities of the UEs (to account for fairness/QoS requirements), the backhaul constraints, the CSI accuracy as well as certain UE/network capabilities (e.g., centralized or distributed). A typical procedure of an iterative coordinated scheduler (and beamformer) can be summarized as follows [25, 31]:

r Initialization step Each cell decides upon which UEs to schedule in the SUor MU-MIMO mode and the corresponding transmit precoding, assuming no coordination between cells (i.e., single-cell processing). The decision is taken based on some priority metric according to, e.g., proportional fairness and the most recent CSI available at the eNodeB. In SU-MIMO, precoding would be chosen, e.g., as the dominant eigenvector(s) of the short-term covariance matrix, the number of eigenvectors being determined by the rank of the transmission. Such an approach is generally referred as singular value decomposition (SVD) precoding. In MU-MIMO, precoding is computed based on, e.g., ZFBF or JLS criteria, similarly to single-cell MU-MIMO precoding designs. r Iteration-n Each cell revisits its decision on the UEs to schedule and their transmit precoding based on decisions taken by other cells in iteration n − 1. In order for each cell to maximize a network-wide utility metric (and therefore guarantee some convergence of the iterative scheduler), the scheduling decision in a given cell i is a function of not only the utility metric of users scheduled by that cell but also the utility metric of victim users that have been tentatively scheduled by other cells in iteration n − 1. Interestingly, the results in [33] show that performing coordinated scheduling with SVD precoding and with JLS precoding both provide the same performance, suggesting that the scheduler itself is much more critical than the beamforming design.

JP with no CSI sharing Distributed open-loop MIMO The joint transmission based on distributed openloop (OL) MIMO can be seen as a direct extension of the single-cell OL MIMO where space-time encoding is done over multiple antennas of all eNodeBs in the CoMP cooperating set rather than just on the multiple antennas of the serving cell. It is sometimes referred to as macrodiversity. As an example, assuming two single-antenna eNodeBs, orthogonal space-time coding is obtained by encoding data over those two antennas as if they belong to a single eNodeB. Such schemes naturally require data sharing between cells but no CSI sharing. A simple scenario of this scheme is the intra-eNodeB (intrasite) transmission where there is cooperation between multiple sectors of the same cell.

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JP with CSI sharing (1) Dynamic cell selection Dynamic cell selection refers to the coordinated scheduling technique in which instantaneous single-point (i.e., from a single eNodeB) transmission is performed to a single user. Based on the instantaneous channel condition of a UE, fast selection of the most appropriate eNodeB is performed. eNodeBs in the CoMP cooperating set share the data in order to enable the fast switching. An example of the fast cell selection is provided in [34]. Once a cell-edge user is identified based on its average received power from multiple cells, a central scheduler allocates frequency resources to that cell-edge user in such a way that the cell with the highest interfering power to that cell-edge user is muted and the power allocated to that frequency resource in the serving cell is boosted by a factor of 2. Resource allocation is ended once the transmission power for each cell reaches its maximum value. (2) JT with CSI sharing Joint transmission with CSI sharing is commonly called network MIMO in the literature. In this scheme, all cells in the CoMP cooperating set effectively form a super eNodeB whose effective number of transmit antennas is equal to the sum of the numbers of transmit antennas of the cells in the CoMP cooperating set. Transmission to a UE is performed from multiple cells simultaneously. In such scenarios, it is typically assumed that multiple cells in a cellular network are connected to a central processing unit, which has knowledge of the transmit messages for all the users and the channels from different cells to all the users. In these fully cooperative multicell systems, the optimization problem reduces to a MIMO broadcast channel with the number of transmit antennas equal to the sum of those of all cells in the CoMP cooperating set. A major difference from the single-cell MIMO broadcast channel is that the transmit signals are subject to a per-cell power constraint rather than a sum-power constraint. Such a technique is expected to provide significant performance gain over single-cell operation as it provides beamforming gain and interference mitigation. Unlike CB techniques, JP is very beneficial even for single transmit antenna cells as it enables spatial interference nulling as well as transmit channel gain combining across multiple cells. Unfortunately, the complexity of such a system increases exponentially with the number of cells and the number of links, making the task of the scheduler extremely complicated if it has to be centralized. To provide sufficient beamforming gains from multiple cells, coherent transmission is recommended, i.e., the UE needs to feedback the aggregated channel containing the phase shift between the channels of the cells. It is quite demanding in terms of feedback overhead. Another form of JT is non-coherent JT, where the phase shift between the channels of the cells is not fed back. In such a scenario, feedback overhead is decreased but coherent combining is not achieved and therefore beamforming gain is decreased compared with the coherent transmission.


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Like single-cell MU-MIMO (single-cell broadcast channels), transmission strategies can be classified into linear and nonlinear precoding schemes. Linear filters based on ZFBF and JLS are far more popular than nonlinear schemes due to their lower complexity [24]. Popular nonlinear schemes include dirty paper coding (DPC) and Tomlinson–Harashima precoding (THP). Note that while computing those transmit filters, a per eNodeB power constraint should be taken into account. The original paper [35] dealing with JTs assumed a ZF-DPC approach based on a sum power constraint, i.e., the power is shared among all eNodeBs in the CoMP cooperating set. Later, filter design with per-eNodeB power constraints was considered [36–39]. Theoretical limits (DPC) with per-eNodeB power constraints were derived in [40].

Some practical considerations Some important factors should be taken into account in the design of CoMP schemes. (1) Scheduler architecture and complexity The overall complexity of CoMP depends on the scheduler architecture and the size of the CoMP cooperating set. To reduce the complexity, cell clustering has been investigated. Two popular clustering methods for identifying the CoMP cooperating sets are the user-centric cooperating set and the network predefined cooperating set [33, 41, 42]. The former has the advantage of efficiently suppressing the interference by allowing each UE to have its own cooperating set. However, it is extremely complex and challenging as the cooperating sets are selected dynamically and could overlap with each other. If the scheduling is performed in a centralized way, the number of cells to manage is very large in order to cover the cooperating sets of all users and avoid performance degradation for boundary UEs. In the networkcentric cooperating sets, cells are clustered in a more static way and UEs are served only by one of the clusters. Hence, clusters do not overlap with each other. Unfortunately, users at the boundary of the clusters are subject to poor performance. A hybrid approach enabling partial overlap of the clusters has also been proposed [41]. (2) Intra-eNodeB vs. inter-eNodeB CoMP There are two important CoMP deployment scenarios: intra-eNodeB and inter-eNodeB CoMP. Intra-eNodeB (intrasite) CoMP performs cooperation between the cells belonging to the same eNodeB. Intra-eNodeB CoMP does not require any X2 interface, therefore reducing the impact of CoMP on the standard. Efficient JP relies on a low latency and large bandwidth backhaul to convey data to cells that jointly serve a UE as well as to provide fast CSI and HARQ feedback to the scheduler and scheduling decisions, MCS level, and HARQ information to the transmitters. This makes JP more suitable to intercell intra-eNodeB cooperation as well as cooperative transmission within a set of remote radio heads

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(RRHs) or distributed antennas (DAs) interconnected by high-speed broadband links [32]. Inter-eNodeB (intersite) CoMP performs cooperation between cells belonging to different eNodeBs and linked through the X2 interface. Inter-eNodeB CoMP relies on the backhaul link to support the CSI and/or scheduling information exchange among eNodeBs. The backhaul latency and limited capacity is a common issue for all inter-eNodeB CoMP schemes. However, the backhaul requirements are different for JP and CB/CS. Since JP requires data sharing among eNodeBs, its requirements in terms of backhaul capacity are higher than those for CB/CS which only require CSI sharing and scheduling decisions. Such considerations makes CB/CS more for attractive inter-eNodeB with limited backhaul capacity. (3) Backhaul capacity and latency X2 defines the logical interface between two eNodeBs. A typical maximum backhaul delay over the X2 interface is expected to be in the order of 20 ms [43]. However, larger delays can be found in some specific scenarios. A median delay over the X2 interface would be around 10 ms. It is important to note though that the physical realization of the X2 interface can be implemented in many ways, including fiber, copper, and microwave. Such implementation highly impacts network performance. A comprehensive analysis of different types of (current and future) backhaul was provided in [44]. While studies of CoMP with limited backhaul are scarce, some results are available. CoMP has been shown to present a graceful degradation as the backhaul capacity decreases [45]. (4) Impact of delay and mobility on CoMP CoMP schemes experience different delays depending on, e.g., the kind of CSI sharing, scheduler, and transmit filter. Users scheduled based on a scheme like coordinated beam patterns requiring long-term CSI sharing and no iterative scheduler are less sensitive to the backhaul delay than users scheduled based on CoMP using an iterative distributed coordinated scheduler and beamformer. CoMP performance depends on the total delay, which is a function of the CSI/CQI delay (typically of the order of 4–6 ms), the backhaul delay (10 ms oneway on average based on current technology), the delay of periodic exchange of information as long-term CSI (e.g., 50 ms), eNodeB processing time (of the order of milliseconds), and the number of iterations required by an iterative scheduler. In [30], it was shown that the CoMP scheme based on the coordinated beam pattern scheme relying on long-term information exchange would experience a total delay of the order of 5 ms for serving cells’ UEs and 65 ms for UEs in cooperating cells. The CoMP scheme based on short-term CSI sharing and a centralized scheduler (e.g., intrasite CB/CS, JP) would experience a total delay of 5 and 7 ms (for one and three iterations in the centralized scheduler respectively). The CoMP scheme based on short-term CSI sharing and a distributed noniterative scheduler (e.g., intersite CB) would experience about 16 ms total


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delay in cooperating cells and 5 ms total delay in the serving cell. Finally, a CoMP scheme based on short-term CSI sharing and distributed iterative scheduler (e.g., intersite iterative CB/CS) experiences about 16 ms total delay for one iteration and 70 ms total delay for three iterations. Therefore, the CoMP schemes relying on iterative and distributed schedulers would not operate on the classical backhaul but would require a high-speed backhaul. Note, however, that CoMP schemes have different sensitivities to those delays depending on the deployment scenarios. A distributed iterative scheduler experiences a delay that is proportional to the number of iterations and the backhaul delay but users may or may not be impacted by such a delay depending on whether closely spaced antennas are deployed or not at the eNB. Such a configuration leads to spatially correlated channels whose channel directions are stable in the frequency and time domain. In such closely spaced antenna configurations, CB is also believed to be more robust to UE mobility and delay than JP [32]. JP based on JT techniques is mainly limited to only low mobility UEs. CS can also be used to handle high mobility UEs when efficient cooperation through spatial interference nulling is not possible. (5) Downlink reference signals CoMP operations rely on accurate measurement of the channels in the CoMP measurement set. For channel measurement, reference signals (RS), denoted CSI-RS, are introduced in LTE-Advanced. Unlike the common reference signals (CRS) in Release 8 used for measurement and demodulation, CSI-RS is only used for measurement and therefore requires a lower density in the frequency and time domains than CRS. Any CSI-RS design that did not consider multicell operations would result in dramatic CoMP performance losses. Hence, one of the priorities of the CoMP design is CSI-RS design [46, 47]. The goal of CSI-RS design is to guarantee good performance with low overhead by benefiting from power boosting and avoiding RS collisions. The larger the CoMP measurement set is, the more difficult is the design. Typical approaches to design CSI-RS in a multicell environment introduce orthogonal CSI-RS patterns. Methods to introduce orthogonal patterns include shifting in the time domain and/or frequency domain by a certain time/frequency offset or using CSI-RS patterns that are orthogonal to each other in each RB. Note that CSI-RS also depends on the CoMP architecture. For a user-centric cooperating set, the overall number of involved cells for cooperation is much larger than that for a network predefined cooperating set. CSI-RS design for a CoMP architecture-based user-centric cooperating set is more difficult than for CoMP architecture relying on a network predefined cooperating set [33]. The user-specific reference signal (DM-RS) is primarily used as a demodulation signal and is one of the key features of LTE-Advanced (and standards like IEEE 802.16m) to improve system capacity. The use of DM-RS allows for more advanced transmit filtering at the eNodeB (for single-cell and CoMP operations) and more advanced feedback mechanisms at the UE side compared with

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the Release 8 codebook-based precoding approach using CRSs. With the DMRS, the eNodeB transmit filter design becomes an implementation issue and is therefore not standardized. (6) CSI feedback CSI feedback is related to the report of the dynamic channel conditions between the multiple points included in the CoMP measurement set and the UE. It can also include reports that could facilitate the decision on the set of participating transmission points [7]. In FDD, CoMP based on short-term feedback naturally requires higher feedback overhead than single-cell operations, since the channels from the CoMP measurement set need to be reported to the serving cell. Depending on the CoMP transmission scheme, the feedback accuracy requirement might differ. Very accurate feedback is required for techniques based on interference nulling such as JT, CB, or IA. Inaccurate feedback would significantly reduce the interference nulling capability as in single-cell MU-MIMO. Moreover, JP based on JT and coherent combining typically also requires more feedback than CB schemes or noncoherent combining beamformers [48]. To provide the expected gains, JT requires an individual per-cell feedback and an intercell feedback that contains information about the phase shift between individual per-cell feedback information. As in single-cell MU-MIMO, advanced feedback mechanisms (in the form of adaptive codebooks, differential codebooks, hierarchical codebooks, etc.) are essential to support and fully benefit from the advanced CoMP deployed with high-speed backhaul. In TDD, channel reciprocity can provide some advantages. The transmission of a single sounding sequence on the UL can be received simultaneously from multiple cells. LTE-Advanced supports both a FDD mode and a TDD mode for which channel reciprocity may be exploited [7]. Another important design principle of the feedback mechanisms is to develop a universal and scalable structure supporting various downlink transmission schemes including single-cell SU-MIMO, single-cell MU-MIMO, CoMP CB/CS, and CoMP JP [48, 49]. Feedback scalability was defined such that the feedback in support of CoMP JP is a superset of the feedback in support of CoMP CB/CS. Such feedback structure can easily and dynamically switch from one transmission scheme to another and avoids standardizing multiple feedback and transmission modes. LTE-Advanced has identified three main categories of CoMP feedback mechanisms [7]:

r Explicit feedback of the channel state/statistical information consists in feeding back the channel as it is observed by the receiver without assuming any hypothetical transmission scheme or any receiver processing. Explicit feedback information may include the short-term channel matrix, the instantaneous transmit covariance matrix, or its average in time or frequency [25]. For both the channel matrix and the covariance matrix, the full


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information or just its dominant eigencomponents may be reported. Additionally, any intercell channel properties can be reported. As well as the information originating from the CoMP measurement set, additional information related to the interference outside the CoMP measurement set can be reported, e.g., the full matrix or the dominant eigencomponents of the noise-plus-interference covariance matrix. r Implicit feedback of the channel state/statistical information is the feedback mechanism used in Release 8. It makes some hypotheses on the transmission and/or reception processing at the time of feedback. Typical contents of the implicit feedback are the well-known CQI, PMI, and rank indicater (RI). As examples of the hypotheses, the UE could assume at the time of feedback that it will be scheduled in SU-MIMO or MU-MIMO mode, in single or coordinated transmission using single- or multi-point transmission [50, 51]. It could also make assumptions on the receiver processing (e.g., MMSE, ML), or on the way the interference is processed given the transmit and receive processing. r Sounding reference signals (SRSs) transmitted by a UE can be used for CSI estimation at an eNB exploiting channel reciprocity. A key issue of CoMP design is to identify the UL overhead vs. DL performance tradeoff achievable with each feedback mechanism. To support CoMP, the UL overhead will necessarily be increased compared to Release 8. This calls for enhanced UL control channels that can carry this increased traffic. Two options can be considered in LTE-Advanced [7]: either expand the physical uplink control channel (PUCCH) payload sizes or use periodic/aperiodic reports on the physical uplink shared channel (PUSCH). (7) Time and frequency synchronization Time and frequency synchronization errors can have a severe impact on the performance of CoMP if appropriate requirements are not satisfied. To illustrate the issue, assume two single-antenna cells are communicating with a single UE. Assume cell 1 transmits the passband signal over carrier frequency f1 and cell 2 transmits the passband signal over carrier frequency f2 . The ideal central frequency is denoted as f0 . The difference ∆f = f2 − f1 is the frequency offset between the cell 1 and cell 2 carrier frequencies. The differences f1 − f0 and f2 − f0 are the frequency errors of cell 1 and cell 2, respectively. Assume also narrowband and static channels such that the channel from cell 1 to the UE is modeled as 1 and the channel from cell 2 to the UE is modeled as a complex scalar h. The UE receives the signals from cell 2 with a delay τ compared with the signals from cell 1. Assuming the UE locks its receiver on frequency f1 , we can easily show that the equivalent baseband channel h from cell 2 to the UE becomes h = hej 2π (−f 1 τ +∆ f (t−τ )) . Hence, the phase of the channel is affected by two factors: the phase shift due to the time delay τ and the phase shift due to the phase offset ∆f .

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The quantity 2πf1 τ represents the phase shift due to the time delay τ . The time delay creates a frequency selective channel. Due to the increased frequency selectivity of the channel, multiple PMI feedback is required over the whole bandwidth in order to reasonably limit the losses due to the mismatched beamforming [52]. This significantly increases the signaling overhead. Such a situation would be even more critical in a CoMP scenario. Inter-eNodeB CoMP coherent JT is more sensitive to time synchronization errors than other CoMP schemes. A maximum delay of 0.5 µs for JT schemes is recommended in [53], while the maximum delay should be smaller than the cyclic prefix for other types of CoMP transmission schemes. The quantity 2π∆f (t − τ ) represents the phase shift due to the frequency offset ∆f . Such a phase offset induces a time varying channel due to the product ∆f t. Requirements for the frequency errors are provided in [54] for different classes of eNodeBs. The minimum requirement allows the frequency error to be smaller than ±0.05 ppm for wide-area eNodeBs, ±0.1 ppm for medium range eNodeBs, ±0.1 ppm for local area eNodeBs and ±0.25 ppm for home eNodeBs. An error of ±0.05 ppm corresponds to ±2 GHz ∗ 0.05/1e6 = ±100 Hz for a carrier frequency of 2 GHz. Assuming a 5 ms backhaul delay and ∆f = 100 Hz, the channel phase can change by π between the measurement time and the transmission time. Both backhaul delay and frequency synchronization errors have to be significantly decreased in order to avoid such phase mismatch. Time and frequency synchronization issues are much more serious for JT techniques than for CB/CS, since two signals from multi-eNodeBs are coherently combined in JT. Requirements on the frequency synchronization accuracy are higher for the JT technique. Considering frequency offset of the order of ±0.005 ppm for inter-eNodeB CoMP JT is suggested in [53]. A maximum frequency offset of one order of magnitude smaller than current requirements used in a commercial eNodeBs is suggested in [55]. For intra-eNodeBs CoMP JT, it is possible to achieve a much better accuracy, since the same reference clock can be used to calibrate the clocks of the cells attached to the same eNB. For CoMP CB/CS, accuracies similar to that required by Release 8 would be sufficient, since CB/CS is less sensitive to the frequency offset. Higher frequency and time synchronization accuracies can be obtained using GPS assistance or network-based synchronization [53, 55, 56].

15.3.3

Release 10 of LTE-Advanced CoMP has been heavily discussed for Release 10 of LTE-Advanced. The system has been designed and built in such a way that even if only some types of CoMP are supported in Release 10, more advanced features can be supported in future releases of LTE-Advanced. As discussed previously, the CSI-RS design for accurate measurement of multicell channels is a fundamental issue in the design of CoMP and is under investigation. Feedback mechanisms and the performance vs. overhead tradeoff are other core problems under discussion.

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Below is a summary of the major decisions on CoMP for Release 10 [7]:

r As the baseline of CoMP design in LTE-Advanced, the UE is not explic-

r

r r r

itly informed of the CoMP transmission point(s) and the UE reception and demodulation of CoMP transmissions (CS/CB, or JP) are the same as those for non-CoMP (SU/MU-MIMO). For CoMP schemes that require feedback, individual per-cell feedback is considered as the baseline. Complementary intercell feedback may be supported. As the baseline, the feedback information is reported to the serving cell when the X2 interface is available and suitable enough in terms of latency and capacity to support CoMP operations. For other scenarios (X2 interface not available or not suitable due to latency and/or limited capacity), more discussions are required. For Release 10, any DL CoMP scheme will not include a new standardized X2 interface communication to support multivendor inter-eNodeB CoMP. In other words, CoMP will assume only intra-eNodeB techniques. CSI RS design should take the potential needs of DL CoMP into account and should allow for accurate intercell measurements. No additional features are specified in Release 10 to support DL CoMP.

Companies recommend considering further studies on DL-CoMP within the Release 10 timeframe in the framework of a new study item [57]. A new study item on CoMP has been introduced with the objectives of evaluating the performance benefits of CoMP and the required specification support in the physical and higher layers [67]. LTE and LTE-Advanced have been submitted to ITU as IMT-Advanced candidates. Extensive simulation results were provided at that time to assess the performance of LTE-Advanced vs. ITU requirements [8]. Generally speaking, it appeared that MU-MIMO based on DM-RS provides significant gains over SU-MIMO relying on Release 8. CB/CS provides negligible gains over advanced MU-MIMO. JP outperforms MU-MIMO significantly in some specific scenarios like Urban Micro. Note that these results and conclusions that could be drawn should be considered with caution as they greatly depend on the simulation assumptions. Hence, careful investigation of the simulation assumptions is required before drawing any meaningful conclusions [8].

15.4

Wireless relay Wireless relay is one of the most important features of the 3GPP LTE-Advanced standard. In a conventional cellular system, a wired backhaul is one of the major sources of the maintenance cost of a cellular network. Wireless relay is introduced to reduce the cost of the wired backhaul. A wireless relay can forward user data between a neighboring macro-eNodeB and UEs. Therefore, it can be regarded as a kind of cooperative communication. There has been a lot of research on several types of wireless relays including the

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Table 15.3. Comparison of two types of wireless relay Type 1 relay Cell ID

Data transmission SYNC, CRS transmission Notes

Relay has a unique cell ID (relay operates as an independent cell) Transmits all DL data channel Transmits Major work item for Release 10

Type 2 relay Cannot have a unique cell ID Retransmits PDSCH HARQ Does not transmit

decode-and-forward relay, and the amplify-and-forward relay. The 3GPP LTEAdvanced standard considers only decode-and-forward wireless relays, which can forward the user data after successfully decoding the corresponding data packet.

15.4.1

Key technologies Types of wireless relays Two different types of wireless relays are discussed in the LTE-Advanced standard. Table 15.3 compares these two different types of wireless relays. A type 1 relay node has an independent cell ID and operates as an independent eNodeB. The only difference from the conventional macrocell is that a type 1 relay has a wireless backhaul link instead of wired one. Therefore, a type 1 relay node has all the scheduling and resource allocation functionalities in addition to the physical layer functionalities. Unlike a type 1 relay, which has an independent cell ID, a type 2 relay cannot have an independent cell ID. Hence, it is not possible for it to operate as an independent eNodeB. A type 2 relay is used to retransmit HARQ packets after the relay node has successfully received the PDSCH packets sent to UEs. Therefore, a type 2 relay can send only the retransmissions of PDSCH and the related reference signals for demodulation. A type 2 relay node is not allowed to transmit SCH, RSs, or PDCCH. Therefore, it is difficult to consider the signal quality from a type 2 relay in computing the CQI used for adaptive modulation and coding.

Operation of wireless relay There are several design issues for the backhaul link between a macro-eNodeB and a relay node. Depending on the frequency band used for the wireless backhaul, the wireless backhaul link is categorized as [7]:

15.4 Wireless relay

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(1) Inband The macro-eNodeB to relay link uses the same frequency band used for the macro-eNodeB to UE links. (2) Outband The macro-eNodeB to relay link uses a different frequency band from the macro-eNodeB to UE links. The macro eNodeB is required to support both UEs in the cell and the wireless backhaul link. For a relay node operating as an inband relay, it is difficult to receive data from the macro-eNodeB, while transmitting a DL signal at the same frequency band. This may result in discontinuity in the DL signal sent from a relay node, during the subframes when the relay receives data from the macroeNodeB. The solution used for the inband relay is not to transmit any signal in the DL by creating “gaps” in these subframes. Therefore, timing alignment is one of the important issues in designing the wireless backhaul link. As described in [7], the DL subframe boundary from a macro-eNodeB should be aligned with the backhaul downlink subframe boundary at the relay node, although there could be some adjustment to allow for the relay node transmitting/receiving time switching. A wireless relay node should also support LTE Release 8 UEs. Since LTE Release 8 UEs are not designed for the wireless relay operation and do not know the subframes when a wireless relay node switches to the DL reception mode, they may experience problems from these subframes configured as the gaps. To the LTE Release 8 UEs located in a relay cell, the relay node declares these subframe as the multimedia broadcast over a single-frequency network (MBSFN) subframe, which the UEs do not have to receive. The MBSFN subframes are used for broadcasting services in an LTE system. With this information, the LTE Release 8 UEs can discard the DL PDSCH of these subframes configured as the gaps. Figure 15.4 shows an example of the timings of a macro-eNodeB and a relay node. The figure shows only two subframes. It can be observed that the subframe boundaries are aligned between the macro and the relay. The first subframe is not used for the backhaul link. Therefore, the macro-eNodeB and relay node transmits data to the UEs in each cell. The second subframe is used for the backhaul link and the macro-eNodeB can send data to the relay node. The macro-eNodeB sends data to the relay node (and to the UEs in the macrocell if necessary). Therefore, the relay node stops DL transmission after the transmission of PDCCH in the second subframe and switches its mode to receive the data sent over the wireless backhaul link. The second subframe is noticed as an MBSFN subframe to the UEs in the cell served by the relay node. UEs in a relay cell can decode only the data from the relay node. Since a wireless relay node should transmit the PDCCH even in the gap subframe shown in Figure 15.4, it may not demodulate the PDCCH sent from the macro-eNodeB. Therefore, new physical channels need to be designed that include R-PDCCH and R-PDSCH for the inband type 1 relays, where R-PDCCH

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Subframe MacroeNB

Control

Data

Control

Relay

Control

Data

Control

Data

Transmission gap (MBSFN subframe)

Figure 15.4. Downlink subframes of macro eNB and relay node. and R-PDSCH are the channels to send the control information and data to the relay nodes, respectively. In addition to R-PDCCH and R-PDSCH, other channels are being considered and will be defined if they are necessary for efficient operation of the wireless relay.

15.4.2

Standard trends on Release 10 and future works Even though the concept of a wireless relay was introduced in the LTE-Advanced standard to reduce the backhaul cost, only the most fundamental and simplest designs will be embodied in the Release 10 standard. There are some technical concerns with the type 2 relay and its benefit is not clear. Hence, it was decided that the standardization of LTE-Advanced Release 10 will be based on the type 1 relay only [58]. It is expected that more complicated and efficient PHY/MAC designs and procedures will be added after the Release 10. These may include the issues that are actively being discussed in the heterogenous network, which will be introduced in the next section. In addition to these issues, more efficient airinterface designs may be included in the standards after Release 10.

15.5

Heterogeneous network One of the research topics in the LTE-Advanced standard is the heterogeneous network. The purpose of the heterogeneous network is to ensure reliable communication links and to increase system capacity, when the network is configured with different types of eNodeBs in addition to the conventional eNodeBs. In this section, the standardization trends for the heterogeneous network will be investigated.

15.5.1

Key technologies Heterogeneous network scenarios The heterogeneous network issue concerns the deployment environments, where many low-power nodes are placed in a macro-cell layout. The configurations

15.5 Heterogeneous network

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Table 15.4. Summary of heterogeneous network scenarios

RRH Pico-eNodeB (nodes for femto-cells) Home eNodeB (nodes for femto-cells) Relay nodes

Backhaul

Access

Notes

Several µs latency to macro X2 interface

Open to all UEs

Placed indoor or outdoors Placed indoor or outdoors

Open to all UEs

For further study

Closed subscriber group (CSG)

Placed indoors

Through air-interface with a macro-cell

Open to all UEs

Placed outdoors

that are currently considered for the heterogeneous network are (Table 15.4) [7]: (1) (2) (3) (4)

Macro-eNodeB Macro-eNodeB Macro eNodeB Macro-eNodeB

+ + + +

RRH; pico-eNodeB; home eNodeB; relay nodes.

The RRH is one of the promising solutions for implementing a distributed network. It can geometrically separate the radio frequency (RF) modules from the baseband signal processing module using fibers. With RRH, the locations of the baseband processes are concentrated and the RF modules are placed in the geometrically separated nodes. The backhaul to the macrocell uses optical fibers and its latency can be assumed to be several microseconds. With this low delay backhaul, it is possible to coordinate resources among geometrically separated nodes in real time. Therefore, RRH is one of the widely studied frameworks for implementing CoMP technology. The pico-eNodeB is used for hotzone cells, which are intended for areas with a small cell radius and densely located UEs. The maximum transmission power of a pico-eNodeB is typically about 30 dBm. Basically, a pico-eNodeB is located with planned deployment as normal cellular eNodeBs and open to all UEs. The backhaul is assumed to be the X2 interface, which is the same as the conventional cellular networks. Wireless relay is used to extend coverage of a cellular system. The backhaul is the wireless one as explained in Section 15.4. Performance enhancement is an important issue in the environments, where UEs are located between the macro-eNodeB and the wireless relay node.

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The home eNodeB is used for femto-cells, which are targeted for an independently operated node by a personal user (customer deployed). The backhaul for a home eNodeB is another item for study. While the other three heterogeneous network scenarios are designed to be open to all users, the home eNodeB is targeted for a closed subscriber group (CSG). Therefore, only limited UEs are allowed to access the home eNodeB.

Performance requirements When standardizing LTE-Advanced, the performance of several heterogeneous networks is evaluated. To evaluate the benefit of adding low-power nodes to the macrocell only network, several performance metrics are considered. In addition to the existing traffic performance metrics, some additional important performance metrics are considered for the heterogenous network:

r the macrocell area throughput, r the fraction of throughput over low-power nodes, r the UE throughput ratio between the macro- and the low-power node. For the performance simulation, there are several key assumptions including the channel model, traffic model, and operation scenarios. Details of these assumptions can be found in [7].

Important technical issues In deploying a heterogeneous network, there are several technical issues to be considered. The interference problem is one of the main issues of a heterogeneous network. Due to the interference between the neighboring macro-eNodeBs and newly deployed nodes (pico, femto, and wireless relay nodes), it is difficult to establish a stable communication link with high data throughput. In particular, interference on the control channel can make a serious impact on maintaining a reliable communication link. The interference on the data channel region can reduce the data throughput drastically. Therefore, it is essential to mitigate and coordinate the interferences in a heterogeneous network. One of the most interference-dominated areas is the boundary between a macro-eNodeB and a femto-eNodeB. Since a femto-cell is custom deployed and targeted for CSG, it may be difficult to control the interference from a femtocell. In particular, when a UE is located near a femto-cell, it may be difficult to acquire the signal from a macro-eNodeB. If the UE can acquire the signal from the macro-eNodeB and make a communication link, the transmitted signal from the UE can be a large interference to the femto-receiver. Therefore, it is very important to measure and coordinate the interference generated by the femtoeNodeBs and UEs. This becomes more difficult to do in a femto-cell scenario, since all UEs are not allowed to access the femto-cell.

15.6 Conclusion

457

There are many technical contributions to coordinate the interference generated from neighboring eNodeBs and UEs [59–63]. For further reduction of interference, ICI cancelation is considered as a receiver technology [64]. Efficient serving eNodeB selection is another important technical issue [65, 66]. Unlike in conventional cell selection in a homogeneous network, the service capability and delay are different depending on the type of eNodeBs. Therefore, selecting a proper serving eNodeB can be an important issue determining the data throughput and service quality in a heterogenous network. Measurement is also an important issue. For both interference coordination and cell selection, it is essential to detect and measure the neighboring and interfering sources. Without proper measurement, it is impossible to make an efficient decision about interference coordination and cell selection. Specific eNodeB signals should be designed with measurement in mind. The candidates for the measurement signals are the CSR and the CSI-RS. Measurement based on these channels is being discussed for heterogeneous networks.

15.5.2

Standard trends on Release 10 and future work The heterogeneous network issue was adopted as a study item in the fourth quarter of 2009 and added to the work items in the first quarter of 2010. It is premature to say that a separate section for the heterogenous network will be included in Release 10 of LTE-Advanced standard. This is because some essential techniques can be included in other work items, such as the wireless relay, feedback and measurement issues, if they are necessary for heterogeneous network operation. It is widely believed that the heterogeneous network is important from both technical and business perspectives. Therefore, many companies will focus on the heterogeneous network issue. It is expected that heterogeneous-network-related issues will be one of the major work items in the later versions of the LTEAdvanced standard and future wireless systems. The heterogenous network scenarios will be the baseline for the cooperative communication technologies of wireless cellular systems.

15.6

Conclusion The standard trends in cooperative wireless communication are investigated in the 3GPP LTE-Advanced system. In particular, CoMP transmission, wireless relay, and heterogeneous network issues are presented in addition to the general LTE-Advanced concepts. CoMP is being intensively discussed as a means to enhance the throughput of cell-edge users. Wireless relay links between a donor eNodeB and a relay node are also being designed. Heterogenous networks are being investigated for the scenarios where different kinds of eNodeB are deployed.

458


It is expected that only simple concepts will be included in the Release 10 version of the LTE-Advanced standard. However, more complicated and advanced cooperative communication techniques will be considered for the later versions of LTE-Advanced and other future wireless systems.

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16 Partial information relaying and relaying in 3GPP LTE Dong In Kim, Wan Choi, Hanbyul Seo, and Byoung-Hoon Kim

16.1

Introduction Direct transmission from source to destination often faces weaker channel conditions when a mobile is moving across the cell border, because of the large propagation loss due to path-loss and shadowing, and the power limitation not to cause undue interference. For this reason, attention has been given to the use of cooperative relaying to mitigate intercell interference to abtain an increased rate and extended coverage at cell edge. There have been many proposals for cooperative relaying, such as amplify-andforward (AF), decode-and-forward (DF), and compress-and-forward (CF), some of which were developed in [1–4]. Such relaying schemes are mainly designed to exploit the multipath diversity for a power gain (or increased rate) that results from combining direct and relayed signals. However, these schemes do not fully utilize the asymmetric link capacity in direct (source–destination) and relay (source–relay) links, e.g., where the latter gives better results in the downlink if line-of-sight (LoS) transmission is realized in the link between the base station and a fixed relay. A partial DF protocol has been proposed in [5] that aims to exploit the asymmetric link capacity more efficiently by forwarding a part of the decoded information to the destination using superposition coding. Further, Popovski and de Carvalho [6] investigated a power division between the basic data and the superposed data that result from superposition coding, for a maximum overall rate capacity. However, the multiple-antenna configurations that cause additional interstream interference due to spatial multiplexing were not considered, and also the partial DF relaying can be designed more efficiently using multiple antennas, which is a crucial issue in realizing next generation cellular systems. The concept of partial DF relaying can be translated into multiple-antenna configurations by applying superposition coding per antenna, termed perantenna superposition coding (PASC), and across antennas, termed multilayer superposition coding (MLSC). However, the extension is not straightforward because the power should be divided not only between the basic and superposed Cooperative Cellular Wireless Networks, eds. Ekram Hossain, Dong In Kim, and Vijay K. Bhargava. Published by Cambridge University Press. C Cambridge University Press, 2011.

16.2 Partial information relaying with multiple antennas

463

layers but also across the spatial layers under multiple-antenna configurations. Furthermore, the power division here interacts with spatial interference. In this context, we describe how to form the partial information to be forwarded, find a proper power division strategy for partial DF relaying with PASC and MLSC, and eventually show how another form of relaying based on PASC and MLSC, termed partial information relaying can be effective in increasing an overall data rate at the cell edge when multiple antennas are employed. In addition, multinode cooperation is introduced for partial information relaying that realizes two-stage superposition coding at the source and relay, in conjunction with relay selection, when multiple relays and destinations exist. This multinode cooperative relaying more effectively increases the overall rate capacity by fast forwarding the partial information in the second cooperating phase, considering asymmetric link conditions. Finally, we summarize the LTE-Advanced standard issues, discussions, and current conclusions on relay, while detailing the functionalities of relay nodes. We also highlight the self-interference issue which is the key point of multiplexing the source-to-relay link and the relay-to-destination link, and provide some discussion on how to resolve it. The rest of this chapter is organized as follows. Section 16.2 describes how to form partial information in multiple-antenna configurations, using PASC and MLSC, where the relaying protocols with PASC and MLSC are given along with their performance comparison. In Section 16.3, the PASC with zero-forcing decorrelation is analyzed to find a proper power division strategy for partial information relaying, leading to an overall rate capacity. Multinode partial information relaying is introduced in Section 16.4, along with two-stage superposition coding, in order to increase further the overall rate capacity, and this is followed by concluding remarks on partial information relaying in Section 16.5. Section 16.6 provides an overview of relaying in 3GPP LTE-Advanced.

16.2

Partial information relaying with multiple antennas Due to the broadcast nature of the wireless channel, an intermediate node can relay the signal from source to destination using either the AF or the DF relaying protocol. When orthogonal channels are used for simple relaying, information loss cannot be avoided because receiving and forwarding at the relays are divided into two hops to avoid the self-interference, resulting in a half-duplex operation. It is also reported in the literature that non-orthogonal AF (NAF) [7] can adopt joint maximum-likelihood (ML) detection for the intersymbol interference channel caused by duplicate relaying, where a new symbol from the source overlaps with the prior symbol from the relay under time-division multiplexing (TDM). This approach attempts to avoid the information loss by virtue of nonorthogonal channelization through joint ML detection.

464


Xi

Pi1 Ri1

Xi

Xi

Pi2 Ri2

Xi

PiL R i L

Xi

1

2

X1

PR

X1

X2

PR

X2

XM

PM R M

Xi

L

1

2

L

M XM

L

M

M m

Pm= P

M m

Rm= R

Figure 16.1. Partial information relaying with multiple antennas.

Unlike in the existing approach, we develop a partial information relaying method in which multiple antennas are available at the source (S), the relay (R), and the destination (D), as shown in Figure 16.1, where Pm and Rm denote the power and rate allocated to antenna m, m = 1, 2, . . . , M . This relaying method realizes transmission of multiple parallel data streams which carry two types of information: (1) basic data streams, (2) superposition coded (SC) data streams, on the condition that the relay forwards only the SC streams, i.e., partial information rather than full information as received in conventional AF and DF protocols. The key idea behind partial information relaying is to exploit the asymmetric link conditions often observed in a cellular environment, where the relay (source– relay) link and the access (relay–destination) link are relatively better than the direct (source–destination) link. Considering this with half-duplexing mode for relaying, the source sends M multiple (basic and SC) streams in the first hop, as shown in Figure 16.1. Then, the relay forwards only L (≤ M ) SC streams in the second hop to the destination. Finally, the destination decodes the SC streams received in the second hop after which the basic streams are decoded by canceling out the SC streams from the original signal received in the first hop. Here, we assume adaptive TDM so that the relatively better access link will forward the SC streams/partial information in the second hop whose duration can be made much shorter than that of the first hop. This leads to an increase in overall rate capacity because of the fast forwarding of partial information/SC streams, thereby reducing the information loss caused by half-duplexing operation. To realize the partial information relaying method, it is a prerequisite to form the partial information to be forwarded in multiple-antenna configurations, based on the superposition coding. Here, the superposition coding refers to a simple


465

linear combining of basic data streams and SC data streams. For this we consider two possible realizations below when M antennas are employed.

16.2.1

Per-antenna superposition coding (PASC) Figure 16.2 shows the structure of PASC where the basic and SC streams (or layers) are serially formed at each antenna, and the per-antenna power Pm is divided between the two layers according to the power division factor αm , m = 1, 2, . . . , M , which considers the asymmetric link conditions. SC layers

ANT #1

xb,1 [(1- 1) P1]

xs,1 [ 1P1]

R1 = Rb,1 + Rs,1

ANT #2

xb,2 [(1- 2) P2]

xs,2 [ 2P2]

R2 = Rb,2 + Rs,2

{ {

Basic layers

....

xb,M [(1-

....

....

.... ANT #M

M

) PM ]

xs,M [

M

PM ]

RM = R b,M + Rs,M

Figure 16.2. PASC with M antennas.

In the multiple parallel transmission under PASC as shown in Figure 16.3, it is necessary to optimally determine the set of power division factors {αm , m = 1, 2, . . . , M } such that an overall rate capacity can be maximized. In fact, to determine the power division factors, we need to acquire the information about asymmetric link conditions for direct and relay links, in terms of the per-antenna signal-to-interference-plus-noise ratio (SINR) after a proper decorrelation process (to minimize the interstream interference), e.g., the minimum mean-square-error successive interference cancelation (MMSE-SIC) algorithm [8]. It is assumed that a low-rate feedback channel is available to report the post-processing per-antenna SINR to the source so as to allow joint power and rate allocation.

R

Basic layer SC layer

S R

D R

Figure 16.3. Partial information relaying via PASC with M = 2.

466


Figure 16.3 shows that two parallel data streams carry both basic and SC layers per stream from each antenna, of which the SC layers only are being forwarded in the second cooperating phase using two antennas at the relay. This allows the fast forwarding of the partial information/SC layers using the relatively better access link, leading to a gain in the overall rate capacity, as anticipated. Description of the PASC (2 × 2 × 2): ♦ Phase 1 • S broadcasts two streams: √ √ stream 1 : 1 − α1 xb,1 + α1 xs,1 , √ √ stream 2 : 1 − α2 xb,2 + α2 xs,2 ; • αi denotes the power division factor between basic data xb,i and SC data xs,i of ith stream; • R decodes the received signal from S, in the order of basic and SC, stream-by-stream, while D keeps the received signal in its memory. ♦ Phase 2 • R forwards only the SC data streams xs,1 and xs,2 from phase 1 after re-encoding; • D decodes the received SC data streams to estimate xs,1 and xs,2 using MMSE-SIC; • Based on the decoded xs,1 and xs,2 , D performs SIC to decode xb,1 and xb,2 from phase 1.

Figure 16.4 shows a flow diagram of partial information relaying via PASC in two phases (hops) under adaptive TDM when two antennas are used at the source, relay, and destination, assuming half-duplexing operation.

16.2.2

Multilayer superposition coding (MLSC) Figure 16.5 shows the structure of MLSC where the basic and SC streams are formed in parallel across antennas, and a specific configuration of L SC streams and (M − L) basic streams with per-antenna power allocation {Pm , m = 1, 2, . . . , M } is determined according to the asymmetric link conditions. In the multiple parallel transmission under MLSC as shown in Figure 16.6, it is necessary to optimally determine the subset of SC streams to be forwarded partially, i.e., the adaptation parameter L such that an overall rate capacity can be maximized. As mentioned above, how to set the parameter L depends on the information about asymmetric link conditions for direct and relay links, in terms of the per-antenna SINR after proper decorrelation process (to minimize the interstream interference), e.g., MMSE-SIC.


467

Decodes received signals

R Broadcasts data streams

S R

D R

(a)

Transmits only SC layers

R 1. Decodes SC layers first 2. Decodes basic layers after SIC

S R

D R

(b)

Figure 16.4. Flow diagram of partial information relaying via PASC with M = 2: (a) phase 1; (b) phase 2.

ANT #L

xs,L (PL, RL)

ANT #L+1

xb,1(PL+1, RL+1)

{ {

xs,1 (P1, R1)

...

ANT #1

...

(M – L) basic layers

x b,M-L (PM, RM)

ANT #M

L SC layers

Figure 16.5. MLSC with M antennas.

R

Basic layer SC layer

S R

D R

Figure 16.6. Partial information relaying via MLSC with M = 2 and L = 1. Figure 16.6 shows the two parallel data streams carrying basic and SC layers, respectively, from each antenna, of which the SC layer only is being forwarded in the second cooperating phase using two antennas at relay. By exploiting the relatively better access link, this partial information relaying can provide a gain in the overall rate capacity.

468


Description of the MLSC (2 × 2 × 2, assume L=1): ♦ Phase 1 • After L is selected to maximize rate, S broadcasts two streams stream 1 : xb,1 , stream 2 : xs,1 ; • R decodes only SC streams xs using MMSE-SIC; • D keeps both SC and basic streams in its memory. ♦ Phase 2 • R forwards only SC streams xs using all antennas; • D decodes xs first, and then decodes xb after SIC; • If L = M , it realizes two-hop transmission with no basic stream; • If L = 0, it reduces to direct transmission with no SC stream.

Decodes only SC streams

R Broadcasts data streams

S R

D R

(a)

Transmits only SC streams

R 1. Decodes SC streams first 2. Decodes basic streams after SIC

S R

D R

(b)

Figure 16.7. Flow diagram of partial information relaying via MLSC with M = 2 and L = 1: (a) phase 1, (b) phase 2. Figure 16.7 Shows a flow diagram of partial information relaying via MLSC with L = 1 in two phases (hops) under adaptive TDM when two antennas are used at the source, relay, and destination, assuming half-duplexing operation.

16.2.3

Rate matching for superposition coding Based on the post-processing per antenna SINRs {¯ ρ0,m , m = 1, 2, . . . , M } of the direct link and per-antenna SINRs {¯ ρ1,m , m = 1, 2, . . . , M } of the relay link, where αm is initially set to zero in order to measure the degree of asymmetry in


469

both links, the power division factor αm at the mth stream for partial information relaying via PASC is set by the following formula: + 1 1 − for m = 1, 2, . . . , M (16.1) αm = ρ¯0,m ρ¯1,m where (x)+ = max(0, x). Here, αm is adjusted to balance between the uneven direct and relay links in terms of the rate capacity, which is discussed in Section 16.3, and the per-antenna power allocations {Pm , m = 1, 2, . . . , M } have been assumed to be performed through the water-filling algorithm as + 1 1 Pm = − for m = 1, 2, . . . , M , (16.2) P λ λ1,m where λ1,m denotes the per-antenna SINR of the relay link at the mth stream if the total power P is allocated to the mth stream, whereas ρ1,m is the pre-antenna SINR if the power Pm is allocated to the mth stream. Here, λ is determined to meet the total power constraint m Pm ≤ P . Based on the post-processing per-antenna SINRs {ρ0,m , m = 1, 2, . . . , M } of the direct link and per-antenna SINRs {ρ1,m , m = 1, 2, . . . , M } of the relay link, the adaptation parameter L for partial information relaying via MLSC is set by the following formula: L=

M u ρ1,m − ρ0,m ,

(16.3)

m =1

where u(x) = 1 if x > δ (some threshold to be tuned) and zero otherwise. Note that the threshold δ is selected properly such that an overall rate capacity can be maximized, since the better condition of the access link can be utilized to fast forward arbitrary L partial SC streams in the second cooperating phase.

16.2.4

Overall rate capacity The overall rate capacity of the partial information relaying via PASC and MLSC is compared with those of existing relaying protocols. First, the rate capacity as a function of {αm , m = 1, 2, . . . , M } and L for PASC and MLSC, respectively, can be evaluated as: 0 M / ρ0,m ) + log(1 + αm ρ¯1,m ) m =1 log(1 + (1 − αm )¯ RP A S C = , (16.4) 1+ M ¯1,m )/R2 m =1 log(1 + αm ρ L M m =1 log(1 + ρ1,m ) + m = L +1 log(1 + ρ0,m ) RM L S C = , (16.5) L 1 + m =1 log(1 + ρ1,m )/R2 where R2 denotes the rate capacity (bits/symbol) of the access link between the relay and the destination. In the above, the overall rate capacity is due to the basic layers of direct transmission after the successive interference cancelation (SIC) at the destination and the SC layers after the SIC at the relay, normalized

470


by the average time spent over two-hop transmission. Here, the average second hop time can be made shorter than the normalized first hop time of 1 because of the better access link, or equivalently the larger R2 , than the rate capacity of the SC layers to be forwarded. For comparison, the average rate capacity (or throughput) of conventional relaying protocols is evaluated as follows: 1. direct transmission (DT): RD T = log(1 + ρ0,m );

(16.6)

2. two-hop transmission (2H): M

R2H =

1+

3. DF: RD F

log(1 + ρ1,m ) ; M m =1 log(1 + ρ1,m )/ m =1 log(1 + ρ0,m + ρ2,m ) m =1

M

1 = min 2

M

log(1 + ρ1,m ),

m =1

M

(16.7)

4 log(1 + ρ0,m + ρ2,m ) ,

(16.8)

m =1

where the maximal-ratio combining (MRC) of direct and access links is assumed, whereas the access link only yields R2 = M m =1 log(1 + ρ2,m ) for its own perantenna SINR ρ2,m at the mth stream. Figure 16.8 shows the average throughput of two partial information relaying methods and conventional relaying protocols, where the direct, relay, and access link SNRs are γi = |hi |2 P/σ 2 , i = 0, 1, 2.

16.2.5

Features of partial information relaying The notable features offered by the partial information relaying developed here are described as follows. First, the asymmetric link conditions are fully exploited in implementing a practical MMSE-SIC receiver rather than the ML receiver with complexity. Second, the near-optimal rate capacity via ML detection can be achieved by the cascaded operation of partial information relaying and SIC with manageable complexity, in conjunction with a low-rate feedback on SINR. Third, the multidimensional rate adaptation via PASC and MLSC in multiple-antenna configurations will give rise to a new adaptive modulation coding (AMC), especially when the relay is adopted for extended coverage and to mitigate intercell interference. The latter is of great interest in that cell-edge users can benefit mostly from this for various quality-of-service (QoS) demands in wireless multimedia communications.

16.3

Analysis of PASC with zero-forcing decorrelation A multiple-antenna configuration is considered with M transmit antennas at the source and N receive antennas at the destination. A half-duplexing mode is

16.3 Analysis of PASC with zero-forcing decorrelation

471

Figure 16.8. Achievable rate capacity (bits/symbol) when M = 4. assumed at relay with N receive and N transmit antennas. It is assumed that the slot length in the first and second hops varies depending on the amount of information to be transferred and the link conditions for efficient link utilization. The transmit signal vector at the source is (16.9) x = [x1 , x2 , . . . , xM ]T , √ √ where xm = 1 − αm xb,m + αm xs,m , {αm } represents the power division factors between the basic and superposed layers of each data stream per antenna, the power allocation to antenna m is Pm = E[|xb,m |2 ] = E[|xs,m |2 ], and (·)T and E[·] denote the transpose and expectation, respectively. Note that the subscript b denotes the basic layer while s indicates the superposed layer on top of basic layer. With path-loss and fading accounted for, the N × 1 received signal vector at destination is of the form √ (16.10) y0 = µ0 H0 x + n0 , where µ0 is the channel attenuation due to path-loss, the N × M channel matrix of the direct link H0 is composed of independent zero-mean complex Gaussian random variables (flat fading), n0 denotes the zero-mean additive white Gaussian 2 H noise (AWGN) vector with E[n0 nH 0 ] = σ IN , (·) and IN denotes the Hermitian transpose and the identity matrix of size N × N . Likewise, the N × 1 received signal vector at relay can be formulated as √ (16.11) y1 = µ1 H1 x + n1 ,

472


where the channel and noise statistics associated with different links and antennas are assumed statistically independent. Note that no precoding across multiple transmit antennas is considered at the transmitter because we assume feedback about per-antenna SINR instead of full channel state information (CSI). Zero-forcing (ZF) V-BLAST [9] is employed at relay for successive interference cancelation and spatial decorrelation of the interstream interference. The ZFnulling vector for the stream to be decoded in the jth order is given by T w1,l j = H+ , (16.12) 1,l j −1

lj

where lj is the index of the stream to be decoded in the jth order, H1,l j −1 is the matrix obtained by zeroing columns l1 , l2 , . . . , lj −1 of H1 , (·)+ denotes the Moore–Penrose pseudoinverse [10], and (·)l j denotes the lj th row of the given matrix. Note that the jth decoding order is determined by lj = argminn ∈/ l 1 ,...,l j −1 ||(H+ 1,l

j −1

)n ||2 .

After spatial decorrelation by the ZF-nulling vector, the basic data are decoded first and then the superposed data are decoded by subtracting the effects of the basic data. Assuming that the data stream through antenna m is decoded at relay in the jth order, the SINRs of the basic and superposed data on the mth antenna are given, respectively, by ρ1b,m

=

ρ1s,m

=

(1 − αm )γ1,m , ||w1,l j ||2 + αm γ1,m αm γ1,m , ||w1,l j ||2

(16.13) (16.14)

where the superscript 1 denotes the relay and γ1,m is the per-antenna link SNR from the source to the relay and is given by γ1,m = µ1 Pm /σ 2 . The relay forwards only the superposed layers in the second hop. In the adaptive slot length protocol, the duration of the second hop can be much shorter than that of the first hop since only partial information needs to be transferred over the relatively better link. This might contribute to an increase in the overall rate owing to the fast forwarding of partial information. Once the destination successfully decodes the superposed layers,1 the effects of the superposed layers are canceled out from the signal received in the first hop. Consequently, the basic layers become free from interference by superposed layers. Applying ZF V-BLAST, the ZF-nulling vector for the stream to be decoded in the ith order is given by T w0,k i = H+ , (16.15) 0,k i −1

1

ki

Sufficient energy for successful decoding can be accumulated by the variable duration in the second hop.

16.3 Analysis of PASC with zero-forcing decorrelation

473

where ki is the index of the stream to be decoded in the ith order and determined by ki = argminn ∈/ k 1 ,...,k i −1 ||(H+ 0,k

i −1

)n ||2 .

The data stream through antenna m is assumed to be decoded at the destination in the ith order; the SINR of the basic layer on the mth antenna is given by ρ0b,m =

(1 − αm )γ0,m , ||w0,k i ||2

(16.16)

where the superscript 0 denotes the destination and γ0,m is the per-antenna link SNR from the source to the destination and given by γ0,m = µ0 Pm /σ 2 . Then, the achievable rates for the basic layer and the SC layer through antenna m are determined, respectively, by Rb,m = log(1 + ρb,m ),

(16.17)

Rs,m = log(1 + ρs,m ),

(16.18)

where ρb,m = min(ρ0b,m , ρ1b,m ). Based on the feedback from the destination and the relay to the source about per-antenna SINRs, the optimal power and rate allocation between the basic and superposed layers and across antennas is perfermed to maximize an overall data rate. That is, the overall rate offered by partial information relaying with multiple antennas, denoted by Rsc (M, N ), is maximized by finding optimum combinations of power division factors {αm } and per-antenna power allocation {Pm }. Considering the adaptive slot length protocol, the problem for optimizing the power allocations above can be formulated as {αm }, {Pm } Rsc (M, N ) = = argmax {α m }, {P m } (16.19) M

P m ≤P T

4 R (α , P ) + R (α , P ) b,m m m s,m m m m =1 , (16.20) 1+ M m =1 Rs,m (αm , Pm )/R2 (N )

M

m =1

where (αm , Pm ) denote explicitly the dependence of Rb,m and Rs,m on these parameters. Here, the capacity of the relay-to-destination link (the R–D link) R2 (N ) is evaluated as R2 (N ) =

N n =1

R2,n =

N

log(1 + ρ2,n ),

(16.21)

n =1

where the post-detection SINR at the nth receive antenna of the R–D link is γ2,n ρ2,n = . (16.22) ||w2, ˜l j ||2 Here, γ2,n = µ2 Pñ /σ 2 is the R–D link SNR at the nth antenna, and Pñ denotes the power allocation to nth antenna of the R–D link. Note that the ZF-nulling

474


vector of the R–D link w2, ˜l j can be obtained similarly as in (16.12) with H1 replaced by the N × N channel matrix of the R–D link H2 . Given {Pm }, the overall rate Rsc (M, N ) is maximized if the rates are matched as ρ0b,m = ρ1b,m because of decorrelation after the projection by each ZF-nulling vector. To achieve the rate matching, i.e., ρ0b,m = ρ1b,m , the power division factors should be set to + ||w1,l j ||2 ||w0,k i ||2 − for m = 1, 2, . . . , M . (16.23) αm = γ0,m γ1,m Now, the overall capacity offered by partial information relaying with PASC is simplified to M γ1,m log 1 + m =1 ||w1,l j ||2 Rsc (M, N ) = (16.24) µ1 ||w0,k i ||2 Big/R 1+ M θ(α ) log (N ) m 2 m =1 µ0 ||w1,l j ||2 for 0 ≤ αm < 1, where θ(αm ) = 0 if αm = 0 and otherwise is 1.

16.4

Multinode partial information relaying In a single-node scenario as shown in Figure 16.1, the superposition coding for partial information relaying is performed at the source using the per-antenna SINRs of the direct and relay links, for which the rate matching is achieved to balance the two links by adjusting the power division factors {αm } and adaptation parameter L for PASC and MLSC, respectively. In this method the aim is to fast forward the partial information, i.e., SC layers, through the rate matching, which helps to reduce the average time for the second hop, provided relay and access links are in a better condition than the direct link. It is noted that adaptive TDM is a prerequisite for enabling this method, which may not be feasible in the channel structure designed for current and next-generation cellular systems. To circumvent this limitation, we consider a generalized partial information relaying in multinode configurations, as shown in Figure 16.9, where two-stage superposition coding is performed at the source and relay, and the SC layers intended for multiple destinations are superposed again at the relay. A fixed TDM can be implemented by superposing multiple SC layers at the relay and forwarding them in the second cooperating phase. Figure 16.10 illustrates the resulting partial information relaying method in multinode configurations with M relays, N destinations, and L (≤ N ) SC layers to be superposed at a relay, where a single antenna is assumed (although it can easily be generalized to multiple-antenna configurations), resulting in a specific (M, N, L) multinode configuration. Here, the best relay is selected to perform the second-stage superposition coding when multiple relays M > 1 are available.

475

16.4 Multinode partial information relaying

S R

RM

DN

R2 R1 D2 D1

Figure 16.9. Multinode configurations with M relays and N destinations.

Listening phase Time

xb,1

Cooperating phase Time

xs,1 xs,2

xs,1

1st

xb,2

xb,N

xs,2 2nd

xs,L xc,L+1xc,L+2

(N+1)th

(N+2)th

xs,N

N th

xs,2L

xs,N-L+1xs,N-L+2

xs,N

(N+N/L)th

Figure 16.10. Multinode patial information relaying with (M, N, L) configuration.

16.4.1

Two-stage superposition coding With multiple relays and destinations, all SC layers decoded correctly in the first listening phase are superposed at a relay before forwarding them in the second cooperating phase, and the best relay is selected to maximize the overall rate capacity. It is also possible to superpose the SC layers at multiple relays to exploit the heterogeneous path-losses between multiple relays and destinations, but this requires undue information exchange to share the total available power among multiple relays. Hence, the latter case is not dealt with, instead the best relay is involved in the second-stage superposition coding. The procedure and related signaling for multinode partial information relaying is illustrated in Figure 16.11 where N = L = 2 is assumed. Here, the power division factors {αi , i = 1, 2, 3} are determined to achieve the rate matching for two-stage superposition coding at the source and relay, which interact with each other in view of the overall rate capacity derived in the sequel.


Description of the scheme (e.g., M = 1, N = L = 2): ♦ Phase 1, 2 (listening phase) • S broadcasts x1 and x2 to D1 and D2 , respectively and R √ √ phase 1 : 1 − α1 xb,1 + α1 xs,1 √ √ phase 2 : 1 − α2 xb,2 + α2 xs,2 ♦ Phase 3 (cooperating phase) • R forwards superposed SC layers xs,1 and xs,2 simultaneously √ √ phase 3 : 1 − α3 xs,1 + α3 xs,2 where α3 is the power division factor between the two SC layers.

D1 2

D1 x

s,

x s,1

s, 1

x b,1

x

476

S R

x b,1 x b,2

x s,1 x s,2

R R

S R

R R ,1

xs

2

(a)

2

xs,

x s,

xb,

2

D2

D R2 (b)

Figure 16.11. Flow diagram of multinode partial information relaying with N = L = 2: (a) listening phase; (b) cooperating phase. To achieve the rate matching for the first-stage superposition coding, the power division factors αi , i = 1, 2 are set to

+

1 1 − , (16.25) αi = γsd,i γsr where γsr and γsd,i denote the link SNRs associated with the relay link and the direct link intended for destination i, respectively. The above power division is not strictly optimal, but it is an attempt to increase the overall rate capacity as derived in (16.35) by balancing the asymmetric link capacities over direct and relay links. The latter can be found in balancing the rate capacities of basic layer i over both links, since their minimum rate should be allocated at both ends for successful decoding, as derived in (16.36).

16.4 Multinode partial information relaying

16.4.2

477

Successive decoding in cooperating phase L superposed SC layers at a relay are forwarded in the second cooperating phase and then decoded at N multiple destinations, one-by-one, using the SIC, where the order of decoding will largely affect the overall rate capacity. To illustrate the decoding procedure, we consider a practical scenario with N = L = 2 for which the forwarded signal is represented by √ √ (16.26) sr (t) = 1 − α3 xs,1 (t) + α3 xs,2 (t). Here, xs,i denotes the transmitted signal associated with SC layer i = 1, 2, where P = E[|xs,i |2 ], and 0 ≤ α3 ≤ 1 is the corresponding power division factor. Then, the received signal at destination j can be expressed by yr d,j (t) = hr d,j sr (t) + nj (t),

(16.27)

where hr d,j is the channel gain of the complex Gaussian with variance normalized to 1 for the access link from the relay to the destination j and nj (t) is the AWGN with variance σ 2 . Suppose |hr d,1 | > |hr d,2 |, then SC layer 2 directed to destination 2 should be decoded at both ends to utilize the better link condition when SC layer 1 is decoded at destination 1 after canceling out SC layer 2. Therefore, it turns out that the link capacities for carrying SC layer i are Rr d,1 Rr d,2

= C((1 − α3 )γr d,1 ), α3 γr d,2 , = C 1 + (1 − α3 )γr d,2

(16.28) (16.29)

where C(x) = log2 (1 + x) and γr d,i = |hr d,i |2 P/σ 2 , i = 0, 1, 2. Likewise, if |hr d,1 | < |hr d,2 |, SC layer 1 is first decoded at both ends, and SC layer 2 is then decoded at destination 2 after canceling out SC layer 1. In this case, the above link capacities are rewritten as (1 − α3 )γr d,1 , (16.30) Rr d,1 = C 1 + α3 γr d,1 Rr d,2 = C(α3 γr d,2 ). (16.31) Figure 16.12 shows the decoding procedure at both ends depending on the link conditions when M > 1 and N = L = 2.

16.4.3

Relay selection for maximum capacity In (M, N, L) multinode configurations with M > 1, the best relay is selected to maximize an overall rate capacity when adaptive TDM is assumed for optimum performance. In practice, the second-stage superposition coding is likely to be performed with the configuration of M > 1 and N = L = 2 because of the successive decoding at a mobile handset with limited complexity. In this case, the frame messages i = 1, 2 intended for destination i are sent in time slots i = 1, 2

478


Case 1: Relay to D1 channel gain is better

D R1 xs,1

xs,2

D R2 xs,1

D R1 xs,1

Decode xs,1 after SIC xs,2

Decode xs, 2

D R1

SIC

xs,2

S R

D R1 D R2

xs,2 Decode xs,2 after SIC xs,1

Decode xs, 1

D R2

Case 2: Relay to D2 channel gain is better

xs,1

xs,1

xs,2

SIC

D R2 xs,2

Figure 16.12. Successive decoding of superposed SC layers when M > 1 and N = L = 2. whose length is normalized to 1 (i.e., Ti = 1), and the superposed SC layers i = 1, 2 are then forwarded to destinations i = 1, 2 in time slot 3 with variable length, determined by their maximum transmission time Rs,1 Rs,2 . (16.32) , T3 = max Rr d,1 Rr d,2 Here, Rs,i denotes the rate capacity of SC layer i over the relay link, given that the basic layer i is removed after the SIC at a relay, which is evaluated as Rs,i = C(αi γsr )

(16.33)

for the power division factor αi between the basic layer and the SC layer i. Finally, the overall rate capacity can be derived as Rtot

= =

Rb,1 + Rs,1 + Rb,2 + Rs,2 T1 + T2 + T3 Rb,1 + Rs,1 + Rb,2 + Rs,2 , Rs,1 Rs,2 1 + 1 + max , Rr d,1 Rr d,2

(16.34) (16.35)

where Rb,i denotes the rate capacity of basic layer i over direct and relay links. Note that basic layer i over the direct link is decoded at destination i after the SIC to remove SC layer i, whereas it is decoded at a relay in the presence of SC layer i as interlayer interference. To allow successful decoding at both ends, the rate selection should be made by choosing the minimum, which is evaluated as

(1 − αi )γsr . (16.36) , (1 − αi )γsd,i Rb,i = C min 1 + αi γsr In Figure 16.13, the overall rate capacity in (16.35) is plotted as a function of direct link SNR γsd,i (dB) when other link SNRs are set to γsr = γr d,i = 20 dB, M = 1, 2, 3, and N = L = 2. It is observed that the overall rate increases with increased M because of the increased diversity order, and most of this gain

16.5 Concluding remarks on partial information relaying

479

Figure 16.13. Overall rate capacity with increased diversity order when M = 1, 2, 3 and N = L = 2. is achieved when M = 2, thereby suggesting two-relay cooperation for multinode partial information relaying. To see the rate increase with multinode partial information relaying, the rate capacity for the partial information relaying with a dedicated single relay without second-stage superposition coding is compared with the former in Figure 16.14 when M = 2. Here, we assume that the relay and (dedicated) access link SNRs are γsr = γr d,i,i = 20 dB (i = 1, 2) from relay i to destination i, whereas the cross-access link SNRs are γr d,1,2 = γr d,2,1 = 15 dB. We see that the multinode cooperation with second-stage superposition coding outperforms the partial information relaying without it, which validates the usefulness of second-stage superposition coding at a relay, along with relay selection for increased diversity. Moreover, if the power allocation between the source and the relay is jointly performed subject to a fixed total power (i.e., 2P ), the rate capacity is further increased because the rate matching can be more effective in maximizing the overall rate capacity.

16.5

Concluding remarks on partial information relaying We have shown that partial information relaying via PASC and MLSC allows perfect rate matching among the asymmetric links often observed at the cell edge, resulting in significant capacity gain over full information relaying. In additon, PASC with ZF decorrelation has been analyzed to show how to achieve the rate matching while maximizing the overall rate capacity, thereby balancing the asymmetric link capacities through a proper power division between the basic

480


Figure 16.14. Comparison of overall rate capacity without and with second-stage superposition coding when M = N = L = 2.

and SC layers. Furthermore, the extension to multinode cooperation with twostage superposition coding has shown that the overall rate capacity can be significantly increased by making the cooperating phase more effective in forwarding the partial information through second-stage superposition coding at a relay. In particular, relay selection to achieve the diversity gain has been shown to be effective in increasing the overall rate capacity, in conjunction with the secondstage superposition coding, which can be generalized to distributed superposition coding using multiple relays under the multinode cooperation.

16.6

Relaying in 3GPP LTE-Advanced The 3GPP has been considering the wireless relaying operation for long-term evolution advanced (LTE-Advanced). The relay node (RN) is wirelessly connected to radio access network via a donor eNodeB2 and serves the user equipment (UEs) under its coverage as illustrated in Figure 16.15. The wireless link between a donor eNodeB and an RN is called the backhaul link and the link between an RN and UEs associated with the RN is called the access link. The link between an eNodeB and a UE directly associated to the eNodeB is called the direct link to differentiate from the links in which an RN is involved. 2

eNodeB means evolved NodeB, the base station of 3GPP LTE systems.

16.6 Relaying in 3GPP LTE-Advanced

481

Figure 16.15. Illustration of a relay network.

The relaying operation can have various uses. First, an RN can be deployed to enhance the system throughput and improve the coverage of high data rate transmissions. By locating an RN in a crowded hotspot area, the direct link can be replaced by the backhaul and access links in which the channel conditions are more favorable and high rate transmissions are allowed more frequently. Second, an RN can improve the user experience at the cell edge where the signal strength from the network is weak. In this case, the RN can be a cost-effective solution for providing service coverage in new areas as no additional cost is required to deploy the wireline backhaul link to connect the RN to radio access network. Third, an RN deployed in a bus or train can support the group mobility efficiently. UEs under the RN coverage do not need to perform handover as the “mobile” RN on their behalf takes care of the group mobility which requires the individual UE handover procedure when such a mobile RN does not exist. Fourth, an RN can be used for temporary network deployment (also known as a portable or nomadic RN) in cases such as concerts, exhibitions, and sports events. The issues, discussions, and current conclusions on the relaying agenda of 3GPP LTE-Advanced will be described in the following sections.3 Section 16.6.1 is about the functionalities of an RN in view of the protocol layer. Section 16.6.2 describes how to separate the backhaul and access links in a single RN.

16.6.1

Functionality of RNs One topic discussed in 3GPP is with what functionality should an RN be equipped (e.g., [12–14]). The decision on this topic determines the “functionalities” of the relaying operation of the RN in view of the protocol stack, i.e., at which protocol layer the relaying operation is performed. Depending on the functionalities of the RN, control/data signals of some lower layers are managed and forwarded by the RN while signals of the remaining higher layers are directly exchanged between the UE and eNodeB bypassing the RN. Also, this topic is 3

The content of this chapter is based on [11].

482


related to how the RN appears to the UEs – as a part of the donor cell or as a separate cell. In the following, RNs are classified in three categories based on the layer in which the user data are relayed.

Layer 1 relay – repeater Layer 1 (L1) RNs simply act as repeaters, amplifying the input signal while they do not carry out any decode/reencode processing. Figure 16.16 depicts the protocol layers of this type of RN. As an L1 RN simply amplifies and forwards the input signal, the RF layer is the only protocol layer with which it is equipped. The operation of each layer in this figure can be summarized as follows:

r RF layer: passband signal processing including filtering and amplification; r PHY layer: baseband signal processing including modulation/demodulation and channel coding/decoding;

r MAC+ layer: operation of high-layer radio resource management from the viewpoint of the PHY layer. This includes the medium access control (MAC) layer performing operations such as scheduling and hybrid automatic repeat request (HARQ), the radio link control (RLC) layer performing operations such as segmentation/reassembly, high-level ARQ, and flow control, and the packet data convergence protocol (PDCP) layer performing operations such as IP header compression and sequence number maintenance; r IP layer: management of IP packets.

IP

IP

MAC+

MAC+

PHY

PHY

RF

RF

RF

eNodeB

Relay node

UE

Figure 16.16. Protocol stack of an L1 RN. One benefit of an L1 RN is that it incurs very little delay (typically less than a microsecond), which is mainly due to filtering carried out within the repeater. Another benefit is the possibility for operation without “duplex” loss, i.e., it may be possible to operate the backhaul and access links simultaneously on the same frequency. As the latency incurred by the relaying operation is significantly less than the length of the cyclic prefix of a typical OFDM system, the two signal components – one directly from/to the eNodeB and the other forwarded by the RN – are seen as nothing but two different multipath components of the same signal which can be resolved by the corresponding OFDM processing.


483

The drawback with an L1 RN is that, due to the absence of decoding/reencoding, the noise added in the receiver side of the RN is amplified and forwarded together with the desired signals. As a result, the SINR cannot be improved between the repeater input and the repeater output, i.e., the SINR at the input of an L1 RN is an upper limit on the SINR experienced by the UE. It is also possible to consider an enhancement of the L1 RN (i.e., “advanced repeater” or “smart repeater”) by adding some further capability to the RN. One possibility is a power control capability which enables the L1 RN to limit any unnecessary interference to the other transmissions and reduce the RN power consumption. Another possibility is time/frequency-selective repetition which implies that the RN repeats only a part of the input signal which corresponds to some specific frequency/time resources. This selective repetition enables the RN to forward the relevant part (e.g., the signal of the UEs that require the RN’s assistance) only, thereby limiting the unnecessary interference caused by the RN and allowing for more efficient utilization of the available RN power.

Layer 2 relay – decode and forward Layer 2 (L2) RNs are also known as decode-and-forward RNs: they decode the physical layer signal, and may also decode some MAC parameters by decoding control signals and so on. After successfully decoding the received signal, an L2 RN reencodes the data and then forwards them to the destination (e.g., UEs associated with it in the downlink). Figure 16.17 depicts the protocol stack of a L2 RN. IP

IP

MAC+

MAC+

PHY

PHY

PHY

RF

RF

RF

eNodeB

Relay node

UE

Figure 16.17. Protocol stack of an L2 RN.

As an L2 RN carries out a decode–reencode operation, the noise added in the receiver side of the RN can be removed during the decoding process and, as a result, the output signal SINR can be improved. In addition, it becomes possible to change the modulation and coding scheme and the amount/location of resources allocated to each packet during the relaying operation, which implies that for an L2 RN it is allowed to separate the link adaption and optimization in the backhaul and access links.

484


IP

IP

MAC+

MAC+

MAC+

PHY

PHY

PHY

RF

RF

RF

eNodeB

Relay node

UE

Figure 16.18. Protocol stack of an L3 RN.

One drawback of an L2 RN is that a substantial delay (typically a couple of milliseconds) occurs during the relaying operation (especially during the decoding process). This implies that, at a given time, the signal directly from/to the eNodeB and the signal forwarded by RN can no longer be seen as multipath components of the same signal as they are in an L1 RN. As a result, the input signal and the output signal of an L2 RN interfere with each other, and this may cause a duplex loss which has to be known in order to separate the input and output signals. An L2 RN is not involved in controlling the operation of the layers higher than the PHY layer. In other words, it does not issue scheduling information or a control signal about HARQ and channel feedback. The control signaling is handled by the donor eNodeB. Thus, an L2 RN cannot generate a complete cell and is only a part of the donor cell from the UE’s perspective. As a result, an L2 RN has to intervene in the MAC or higher-layer operation (e.g., delivery of the scheduling message, HARQ ACK/NACK transmission/reception, retransmission of error packets, channel quality measurement/feedback, etc.) performed between the donor eNodeB and the relay–UE. This intervention may require a sophisticated operation protocol among the eNodeB, RN, and UE.

Layer 3 relay – self-backhauling Layer 3 (L3) RNs perform the same operation as eNodeBs, so they are equivalent to new eNodeBs with their own cell identity from a PHY and MAC viewpoint.4 Here, “self-backhauling” means that an L3 RN is provided with the backhaul link (connecting it to the other eNodeBs) by itself, not relying on the interfaces other than the operating radio spectrum. Figure 16.18 depicts the protocol stack of an L3 RN. 4

It is possible to consider RNs in which the relaying operation is performed within the MAC+ layer in Figure 16.18, i.e., at MAC, RLC, or PDCP layer. But they are not very feasible and efficient because one part of radio resource management (RRM) function is located in the donor eNode while the rest is in the RN.


485

One advantage of an L3 RN is that the mechanisms designed for the link between the eNodeB and the UE (e.g., scheduling, HARQ, handover) can be applied to the access link (the link between the RN and the UE) with no change, which is helpful in reducing the UE implementation complexity. However, this simplicity comes with the cost that an RN should be equipped with all the eNodeB’s functionalities which may increase the RN’s implementation cost.

Type 1 vs. type 2 relay After discussions about the different types of RNs described in the previous subsections, 3GPP has specified two different types of RNs – type 1 relay and type 2 relay – for more detailed discussion and description. A type 1 relay is an L3 RN which is characterized by the following:

r It controls cell(s), each of which appears to a UE as a separate cell distinct from the donor cell.

r The cell has its own cell identity which can be recognized by legacy LTE LEs; the RN transmits its own control signals such as synchronization channels and reference signals. This means that the RN appears as a legacy eNodeB to legacy LTE UEs (i.e., it is backward compatible). r In the context of single-cell operation, the UE receives scheduling information and HARQ feedback directly from the RN and sends its control channels to the RN. r To LTE-Advanced UEs, a type 1 RN should appear different from a legacy eNodeB to allow for further performance enhancement. It has been agreed that type 1 relay will be supported as a part of LTE-Advanced and the corresponding specification work is ongoing. A type 2 RN is an L2 RN which is characterized by the following:

r It does not have a separate cell identity and thus does not create any new cells.

r It is transparent to legacy LTE UEs; a legacy LTE UE is not aware of the presence of a type 2 RN.

r It can transmit the downlink physical data channel but it does not transmit the downlink physical control channel and cell-specific reference signal which is used for the demodulation of the downlink control channel and the legacy UE’s channel measurement. One important feature of a type 2 RN is that the UEs facilitated by the RN rely on the downlink physical control channel and cell-specific reference signal transmitted from the donor eNodeB. No agreement on the support of the type 2 relay for 3GPP has been reached as a conclusion has not yet been made about its features and advantages. This topic is still under the study item of 3GPP. It is widely understood that the type 1 relay may be a solution for coverage extension while the type 2 relay may be more suitable for throughput enhancement. A type 2 relay cannot be an effective solution for coverage extension as

486


Donor eNodeB

UE1

Type 1 RN

UE2

Cell created by the donor eNode B

Cell created by the RN

(a)

Donor eNodeB

UE1

Type 2 RN

UE2

A single cell is created by the donor eNodeB and RN

(b)

Figure 16.19. Illustration of cell creation in case of: (a) type 1 relay and (b) type 2 relay.

it does not transmit the downlink control channel to the UEs which the donor eNodeB’s control signal cannot reach (e.g., UE1 in Figure 16.19). On the other hand, a type 1 RN can provide strong control channels to these UEs, thereby improving the control channel coverage of the radio access network, i.e., the range of the “connectivity.” Figure 16.19 compares the cell coverages of type 1 and type 2 RNs. A type 2 relay has the potential to improve the UE throughput (especially when located between the donor eNodeB and the RN such as UE2 in Figure 16.19) by exploiting the tight coordination between the donor eNodeB and the RN, which is not possible in a type 1 relay. In a type 1 relay, the transmission between the donor eNodeB and the RN is a kind of inter-eNodeB communication which is not usable in view of a UE. Thus, even though this backhaul transmission contains information to be forwarded to a UE, it is impossible for that UE to utilize this transmission and the backhaul link transmission appears as intercell interference to that UE as shown in phase 1 of Figure 16.20(a). However, as a type 2 RN is invisible to UEs, the transmission from an eNodeB to an RN for the purpose of data forwarding to a UE can be seen as the direct transmission to that UE which is overheard by the RN as depicted in phase 1


487

Transmission from eNodeB to RN

Donor eNodeB

Donor eNodeB

Not received

Transmission from RN to UE

Type 1 RN

UE

UE

Phase 1

Phase 2

Type 1 RN

(a)

Transmission from eNodeB to UE Donor eNodeB

Donor eNodeB

Overhearing

Transmission from RN to UE if needed

Type 2 RN

UE

UE

Phase 1

Phase 2

Type 2 RN

(b)

Figure 16.20. Examples of downlink data relaying: (a) a type 1 relay and (b) a type 2 relay. of Figure 16.20(b). Consequently, it becomes possible to reduce the probability of the decoding error remaining after the RN-to-UE transmission in phase 2 by properly combining the signals received in phases 1 and 2. The operation in Figure 16.20(b) can be interpreted as a kind of intervention of a type 2 RN in order to assist the HARQ procedure between the donor eNodeB and the UE. In other words, the RN overhears the transmission from the donor eNodeB (the initial transmission) to UE in phase 1 and participates in the retransmission in phase 2 for more robust error recovery as shown in Figure 16.20(b).

488


16.6.2

Separation of the backhaul and access links Another important topic in the 3GPP relaying discussions is how to separate the backhaul and access links. This link separation is necessary in order to avoid the self-interference shown in Figure 16.21. In this figure the RN is receiving a backhaul link signal from the donor eNodeB while transmitting an access link signal to the UEs at the same time. Therefore, from the perspective of the RN’s receiver, the RN’s transmission signal is an interference which may corrupt the signal reception especially for L2 and L3 RNs where the transmitting access link signal is different from the receiving backhaul link signal. This self-interference can be much stronger than the desired signal when the distance between the transmission antenna and the reception antenna is small, for example, when the transmission/reception antennas are co-located.

Self-interference

eNodeB

UE

RN

Figure 16.21. Example of self-interference in a relay node.

There are two approaches that have been discussed to avoid this selfinterference: One is to separate the backhaul and access links in the time domain while operating the two links within a single frequency band. This kind of relaying is called inband relaying. The other is to separate the two links in the frequency domain, which implies that there are at least two different frequency bands, one is used for the backhaul link and another is used for the access link. This kind of relaying is called outband relaying. To be precise, the inband relaying explained above corresponds to inband halfduplex relaying which implies that either the backhaul or the access link is activated at a given time. 3GPP also discussed the possibility of inband full-duplex relaying in which both backhaul and access links are activated simultaneously within a single frequency band. To support this inband full-duplex relaying, some other type of link separation is needed, such as separate transmission/reception antennas. This scenario is considered as one possibility in the indoor relay case where the backhaul link antenna is located out of a building and the access link antenna is located inside a building (or even underground). It was decided that further study is needed to determine the feasibility and detailed uses of inband full-duplex relaying, so inband half-duplex relaying and outband relaying operations are in the current specification work.


489

Inband relay This subsection discusses the time-domain link separation of inband half-duplex relaying. Inband relaying hereinafter means inband half-duplex relaying. In order to allow inband backhauling, some resources in the time-frequency space are set aside for the backhaul link and cannot be used for the access link on the respective node. The general principles for resource partitioning at the RN are:

r eNodeB-to-RN and RN-to-UE links are time division multiplexed in a single frequency band (only one is active at any time).

r RN-to-eNodeB and UE-to-RN links are time division multiplexed in a single frequency band (only one is active at any time). The basic rule agreed for the backhaul link transmission is quite straightforward: eNodeB-to-RN transmissions are done in the downlink resource while RN-to-eNodeB transmissions are done in the uplink resource.5 In the case of a type 1 relay, this operation seen as a noncontinuous existence of the serving cell from the viewpoint of a UE associated with the RN because the RN sometimes does not transmit any signal to the UE. This implies that the RN creates “gaps” in the RN-to-UE transmission when it receives the eNodeB-to-RN transmission. Since a legacy LTE UE expects a cell-specific reference signal in every subframe for the purpose of channel measurement, the relay-UEs should be informed of the location of these “gaps” in order to prevent the UEs from unnecessarily trying to measure the cell-specific reference signal during the gaps when there is only noise. In a type 1 RN, a “partial blanking” method is used for a downlink subframe which is allocated to the eNode-to-RN transmission as shown in Figure 16.22. Here, “partial blanking” means that the RN transmits a few OFDM symbols at the beginning of a subframe to transmit the downlink control channel to the relay-UEs, and it does not transmit any signal in the remaining symbols.6 A relay-UE does not try to measure the cell-specific reference signal during the 5

6

Here, downlink (uplink) resource means downlink (uplink) frequency band in a frequency domain duplex system (FDD) where downlink and uplink transmissions are separated in frequency. Downlink (uplink) resource means and downlink (uplink) subframe in a time domain duplex (TDD) system, where downlink and uplink transmissions are separated in time. This “partially blank” subframe appears as multicast broadcast multimedia service (MBMS) single-frequency network (MBSFN) subframe to the relay-UEs. The original purpose of the MBSFN subframe was to support the simultaneous transmissions (usually multicast or broadcast traffic) from the serving eNodeB and all the neighboring eNodeBs within a predefined area. In an MBSFN subframe, a few downlink control symbols are transmitted in a cell-specific manner at the beginning of the subframe but, after those control symbols, no cell-specific transmission (including cell-specific reference signals) occurs to send the multicast/broadcast traffic. Consequently, a relay-UE does not perform the measurement of the cell-specific reference signal of the associated RN in this partially blank subframe and the RN is allowed to halt the downlink signal transmission to receive the backhaul signal without causing performance degradation in the relay-UE’s measurement.

490


transmission gap of a partially blank subframe, and its measurement performance is not affected by the RN’s half-duplex operation.

eNodeB

One subframe

Partially blank subframe

Control

Data

Control

UE

UE

UE

Transmission gap (no RN-to-UE signal)

Figure 16.22. Example of RN-to-UE communication using a normal subframe (left) and eNodeB-to-RN communication using a partially blank subframe (right). Figure 16.23 illustrates the basic rule of the backhaul and access link separation in a half-duplex relaying system. Downlink (uplink) resource activation in the backhaul and access links is separated in time from the perspective of the RN. DL resource

UL resource

eNodeB

Separated in time

Separated in time

Relay node

UL resource DL resource


UE UE

Figure 16.23. Illustration of the backhaul transmission multiplexing methods based on the basic multiplexing rule (DL – downlink; UL – uplink).

Outband relay If backhaul and access links are isolated enough in frequency, then there is no interference when activating both links simultaneously. Figure 16.24 shows an example of an outband relaying operation where the RN uses frequency band 1 for the backhaul link and frequency band 2 for the access link. In general, a guard band is required to avoid self-interference across the frequency band and


491

it is also possible to assist the link separation by an additional means such as antenna separation which can be used for inband full-duplex relay. As the two links are completely separated, there is no correlation between the operations in the two frequency bands. Thus, it is possible for an RN to operate as a normal UE in frequency band 1 while operating as a normal eNodeB in frequency band 2. eNodeB

Guard band Band 1

Band 2

Frequency

UE

Figure 16.24. An example of outband relaying operation.

Hybrid of inband and outband relay In most cases, the backhaul link capacity becomes the bottleneck in the performance of a relaying system. As shown in Figure 16.15, all the transmissions for the backhaul link and direct link share the same resource of the donor cell. Thus, with only the inband or outband relaying operation discussed in the above subsections, a relaying system usually suffers from backhaul resource shortage, so that the amount of the backhaul link resource is not enough to achieve satisfactory performance improvement. To be specific, in inband relaying, half-duplex operation requires frequent switching between the transmission and reception modes of an RN. As this mode switching typically requires around 20 microseconds which is larger than the length of the cyclic prefix, an OFDM symbol cannot be used if an RN switches its operation mode during that symbol time. This OFDM symbol loss degrades the throughput of the backhaul link which is the bottleneck in the system. In outband relaying, a guard band is required to separate the two frequency bands (typically more than 10 MHz separation) as shown in Figure 16.24, thereby wasting some frequency resource. In addition, the outband relaying operation cannot provide flexible resource allocation between the backhaul and access links as the bandwidth of each frequency spectrum is usually predefined to a fixed value. One solution that can resolve the above-mentioned backhaul resource shortage is to use additional frequency resource (i.e., frequency spectrum or frequency band) in the backhaul link. Let us assume that an inband RN suffers from backhaul resource shortage and it is decided to use an additional frequency band to

492


resolve the shortage problem.7 In this case, the RN does not necessarily open the access link in the newly added spectrum as the access link does not require additional resources in most case. Therefore, as long as the two frequency bands are well separated, it is desirable to use one frequency band solely for the backhaul link while performing the half-duplex operation in the other frequency band. In other words, if an RN is provided with two well-separated frequency bands, a hybrid RN which uses both bands for the backhaul link but uses only one band for the access link can be considered as an attractive solution. Figure 16.25 illustrates the operation of this hybrid RN in comparison with Figure 16.24. A hybrid of inband and outband relaying provides more flexible resource allocation between the backhaul and access links when compared with the pure outband relaying, while it can reduce the OFDM symbol waste caused by the RN’s mode switching when compared with the pure inband relaying. Outband relaying can be regarded as a special case of the hybrid relaying in which all the time resources are used only for the access link in a frequency band. eNodeB

eNodeB

Separated in time

Guard band Band 1

Band 2

Frequency

UE

Figure 16.25. An example of hybrid of inband and outband relaying operation.

As a special example of the hybrid of inband and outband relaying, hybrid relaying operation across downlink and uplink frequency bands can be considered in an FDD relaying system. As downlink traffic is much heavier than uplink traffic in most data communication scenarios, the uplink frequency band can sometimes be borrowed for the purpose of eNodeB-to-RN communication on top of the basic rule discussed above [15]. This operation falls within the category of hybrid relaying as, from the perspective of the transmissions in downlink frequency band (i.e., eNodeB-to-RN and RN-to-UE link), there is no access link (i.e., RN-to-UE link) in the uplink frequency band and thus eNodeB-to-RN transmission in the uplink frequency band can be regarded as a kind of outband relaying operation. The donor eNodeB sometimes uses the uplink resource 7

Communication over multiple frequency carriers can be achieved by “carrier aggregation” which is in development in 3GPP as a work item of LTE-Advanced.


493

Table 16.1. Types of relay nodes defined in 3GPP LTE-Advanced

Inband

Half duplex Full duplex Outband

a

L3 relay

L2 relay

Type 1a Type 1b Type 1aa

Type 2 Not defined Not defined

It has been agreed that this will be supported as a part of LTE-Advanced and

the specification work is currently ongoing.

DL resource UL resource

Separated in time

UL resource eNodeB UL resource DL resource

Separated in time

Separated in time

Relay node


UE UE

Figure 16.26. Illustration of the backhaul transmission multiplexing methods based on the uplink resource borrowing for eNodeB-to-RN communication. (DL – downlink; UL – uplink.) for the backhaul link transmission to the RN while stopping all the uplink transmission of the direct link. Figure 16.26 illustrates this multiplexing method based on this uplink resource borrowing. Table 16.1 summarizes the “types” of RN defined so far in 3GPP. As has been discussed before, there are two types of RN according to the RN’s functionality: type 1 and type 2 RNs. In view of the separation between the backhaul and access links, both type 1 and type 2 RNs fall within the category of inband relaying (specifically, inband half-duplex relaying). Two more RN types are defined in the type 1 family: type 1a and type 1b RNs. A type 1a RN has the same characteristics as a type 1 RN except that it operates as an outband RN. The only difference for a type 1b RN is that it is an inband full-duplex RN.

494


References [1] J. Laneman, D. Tse, and G. Wornell, “Cooperative diversity in wireless networks: Efficient protocols and outage behavior,” IEEE Trans. Info. Theory, vol. 50, no. 12, pp. 3062–3080, Dec. 2004. [2] A. Nosratinia and A. Hedayat, “Cooperative communication in wireless networks,” IEEE Commun. Mag., vol. 42, no. 10, pp. 74–80, Oct. 2004. [3] R. Nabar, H. Bolcskei, and F. Kneubuhler, “Fading relay channels: Performance limits and space-time signal design,” IEEE Journal Sel. Areas Commun., vol. 22, no. 6, pp. 1099–1109, Aug. 2004 [4] T. Cover and A. El Gamal, “Capacity theorems for the relay channel,” IEEE Trans. Info. Theory, vol. IT-25, no. 5, pp. 572–584, Sept. 1979. [5] M. Yuksel and E. Erkip, “Broadcast strategies for the fading relay channel,” in Proc. of IEEE MILCOM 2004, vol. 2, pp. 1060–1065, Oct. 2004. IEEE, 2004. [6] P. Popovski and E. de Carvalho, “Improving the rates in wireless relay systems through superposition coding,” IEEE Trans. Wireless Commun., vol. 7, pp. 4831–4836, Dec. 2008. [7] K. Azarian, H. Gamal, and P. Schniter, “On the achievable diversitymultiplexing tradeoff in half-duplex cooperative channels,” IEEE Trans. Info. Theory, vol. 51, pp. 4152–4172, Dec. 2005. [8] S. T. Chung, A. Lozano, H. C. Huang et. al., “Approaching the MIMO capacity with a low-rate feedback channel in V-BLAST,” EURASIP J. Appl. Signal. Proc., pp. 762–771, May 2004. [9] P. W. Wolniansky, G. J. Foscini, G. D. Golden, and R. A. Valenzuelar, “V-BLAST: an architecture for realizing very high data rates over the richscattering wireless channel,” in Proc. of URSI International Symposium on Signals, Systems, and Electronics (ISSSE ’98), pp. 295–300, Pisa, Italy, Sept. 1998. IEEE, 2008. [10] G. H. Golub and C. F. Van Loan, Matrix Computations. Johns Hopkins University Press, 1983. [11] 3GPP TR 36.814 V9.0.0, 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Further Advancements for EUTRA; Physical Layer Aspects (Release 9). [12] Technical document R1-083533, Decode and Forward Relays for E-UTRA enhancements, Texas Instruments, 3GPP TSG RAN WG1 #54bis. [13] Technical document R1-083752, Wireless Relaying for the LTE Evolution, Ericsson, 3GPP TSG RAN WG1 #54bis. [14] Technical document R1-083568, Discussion on L3 Relay for LTE-A, Samsung, 3GPP TSG RAN WG1 meeting #54bis. [15] Technical document R1-084206, UL/DL Band Swapping for Efficient Support of Relays in FDD Mode, LG Electronics, 3GPP TSG RAN WG1 Meeting #55.

17 Coordinated multipoint transmission in LTE-Advanced Sung-Rae Cho, Wan Choi, Young-Jo Ko, and Jae-Young Ahn

17.1

Introduction Coordinated multipoint (CoMP) transmission is considered as a promising multiple-input multiple-output (MIMO) technique that can be a primary element for better intercell interference (ICI) control in the next generation cellular networks. The classical MIMO technique uses a colocated antenna array for beamforming to the direction of an intended user while trying to reduce interstream and interuser interference. However, such single-cell MIMO transmissions cause intensified narrow beams and can interfere with other cells’ users. In multicell simulations, interference from adjacent cells is even more detrimental. It is found that, depending on the scenario, no less than 30% of the user equipment (UEs) in a cell will have a wideband signal-to-interference-and-noise ratio (SINR) below 0 dB. Various techniques to combat this problem have been proposed by standardization organizations such as 3GPP LTE and IEEE 802.16e/m. Typical examples [1] include sectorization using directional antenna, ICI randomization with interference cancelation at the receiver, and ICI avoidance techniques, such as ICI-aware power control, fractional frequency reuse (FFR), and intercell scheduling. These techniques can be deployed in addition to MIMO but often lead to either loss of average sector throughput or increased receiver complexity. CoMP transmission has been proposed and supported by many companies, including Ericsson, Motorola, Alcatel-Lucent, Huawei, Qualcomm, Samsung, LGE, ETRI, DoCoMO, Nortel, and is believed to be a promising ICI mitigation solution that can improve cell-edge throughput as well as average sector throughput with little complexity increase at the receiver side. The basic idea behind CoMP is to extend the conventional single-cell-tomultiple-UEs transmission to a multiple-cell-to-multiple-UEs transmission by base station cooperation [2]. Similar concepts have also been discussed in IEEE 802.16m and the advantages especially for cell-edge users have been evaluated by many companies. To enhance competitiveness with regard to other standards, the CoMP agenda has been discussed since July 2008. Preliminary studies on


496

Coordinated multipoint transmission in LTE-advanced

the requirements of LTE-Advanced [3] have been undertaken as 3GPP RAN 1 study items in LTE Release 9. The proposals and current conclusions regarding the CoMP program for LTEAdvanced will be outlined as follows: Section 17.2 gives an overview of the architecture of the CoMP transmission scheme. Section 17.3 describes the necessary CoMP design parameters. Section 17.4 outlines the performance evaluation methodologies related to link level and system level simulations.

17.2

CoMP architecture In a universal frequency reuse system, it is well known that interference from neighboring cells substantially degrades performance compared to what can be achieved in a single-cell scenario and it is also recognized that reducing the interference from only one neighboring cell can significantly improve the performance, e.g., 8.12% (5 percentile) cell-edge gain was obtained in [4] and about 20% gain was obtained in [5]. Two categories of CoMP are used to reduce the ICI: coordinated scheduling and beamforming (CS/CB) and joint processing (JP). JP is further divided into (noncoherent and coherent) joint transmission (JT) and dynamic cell selection (DCS). For JT, data are shared among multiple eNodeBs1 that belong to a CoMP cooperating set and the physical downlink shared channel2 (PDSCH) is constructed from multiple eNodeBs of the entire CoMP cooperating set, but for DCS there is a single-transmission eNodeB at every subframe time and this transmission eNodeB can dynamically change within the CoMP cooperating set. For CS/CB, data are transmitted from the serving cell but user scheduling and beamforming decisions are made with coordination among the eNodeBs in the CoMP cooperating set. Some terminologies to facilitate discussions for CoMP proposals were agreed in [6], despite being revisited in work items for specification impact:

r A CoMP cooperating set is a set of eNodeBs participating in transmitting over the PDSCH to the UE.

r A CoMP transmission set is a set of eNodeBs actively transmitting data to the UE over the PDSCH. This is a subset of the CoMP cooperating set. Different CoMP categories require different levels of coordination in terms of channel state information (CSI) and data sharing, e.g., sharing both CSI and data, either or neither of them where each entails different CoMP operation costs, such as the backhaul limit, thus providing different performance gains [4, 7]. 1 2

eNodeB denotes the base station of 3GPP LTE systems. The PDSCH is a shared data channel that can be multiplexed over frequency and time by a number of UEs.

17.2 CoMP architecture

17.2.1

497

Joint processing and transmission (JPT) Joint processing and transmission (JPT) basically changes interference signals into desired signals with a cooperation gain by combining the signals as constructively as possible over the same radio resources. Many companies have discussed many different ways to find a realistic balance between performance gains and effort; and have built scalable design parameters to decide the level of cooperation. Three main topics have been addressed in this context [8]: (1) reference signal design for multicell channel estimation; (2) an uplink control overhead increase for channel knowledge at the transmitter; and (3) the choice of precoding techniques to combine the signals from multiple cells effectively. Details are given in Section 17.3.

17.2.2

Coordinated scheduling and beamforming (CS/CB) CS/CB is a kind of beam coordination among coordinated cells that dynamically reduces the dominant interference from interfering cells. Beam coordination tunes the interfering beam toward a null space of the desired signal, thereby nullifying the interference to the UE, and otherwise avoids pointing the beam toward the direction that has high correlation, which can be done by reporting a recommended precoding matrix index (PMI) and a restricted PMI, respectively. A subset of most efficient PMIs is chosen and exchanged to reduce backhaul overheads. As discussed in [9], multibeam coordination can be improved by enhanced UE feedback, additional reports that indicate how the interference level can be reduced (in the form of Delta-CQI [10]). The UEs can report (say) best-companion or worst-companion PMIs for a number of interfering cells and then serving cells can schedule the UEs in such a way that they experience lower interference by improved user pairing. For better beam coordination, the coordination can be updated according to channel variation and also scheduling information can be exchanged. The reported PMIs may be statistically processed in terms of time, frequency, and user domain so that the most efficient beam can be found from the beam selection pool. When the serving cell wants not to finalize UE scheduling prior to beam information exchange but to maintain a plural number of UE candidates, the multiple PMIs collected can be delivered to the interfering cell and then the interfering beam can be tuned toward the null space of all the beams [11].

17.2.3

Cell clustering In cellular networks, all users are potentially coupled by interference and the performance of one link depends on the other links. In general, a joint optimization approach is desirable but full cooperation between the users over a large

498


network is in practice infeasible. Dynamic cell clustering to identify dominant interfering cells according to UE position is a reasonable choice and hence a limited number of cooperation cells are determined in a geographical sense to form a cooperation area [12]. To identify candidate cooperation cells, post-CoMP SINR (SINR after CoMP), as a measure of ICI mitigation, is calculated by turning (one or two) interfering signals into the desired signal. As was observed in [13], the gain of the coordination saturates when the number of coordinating eNodeBs goes beyond some threshold value; therefore further study is required to find an exact threshold to be incorporated with UE geometry and interference level information. The complexity dramatically increases with the number of coordinating eNodeBs. Furthermore, backhaul latency is also a limiting factor for cell clustering. Cluster can be formed in a UE-centric, network-centric, or a hybrid fashion. In UE-centric clustering, each UE chooses a small number of cells that give the greatest cooperation gain. In general, UE-centric clustering is, however, very complex from a scheduling point of view. Coordinated clusters corresponding to different UEs may overlap and coordination among all overlapping clusters can span the whole network. Arguing that pure UE-centric dynamic clustering was impractical for real implementation, a UE-centric clustering was proposed in [14] in which the cluster serving a particular UE is a subset of a larger fixed cluster rather than the whole network and the subset can change in different frequency subbands and different times. A semi-fixed cell clustering (SFCC) was proposed in [15] in which the clustering of the cells is fixed during a certain time period but varies over frequency and/or time in order to dynamically adapt to the changing environment. When the network predefines a set of cooperation cells, the cooperation area can be determined by network-centric clustering or in a hybrid fashion [16]. In network-centric clustering the clustering is done in a static way and hence the performance of boundary UEs can be compromised, whereas in a hybrid approach multiple clusters that possibly overlap are formed but this alleviates the boundary problems among clusters by having flexibility in resource allocation between the clusters [17]. Comparing rate geometries with and without CoMP transmission, the choice of a better UE is considered important to enhance the CoMP gain. In [18] a criterion for deciding which UEs should be served by comparing pre-CoMP and post-CoMP rates under given cluster was proposed. The geometry viewpoint shows that most gain achieved by CoMP transmission is in the 5% throughput regime (cell edge). Confining CoMP to cell-edge UEs is justified by less arrival timing mismatch because obviously cell-centric UEs are far from transmission points of other cells. It has also been realized that if the transmission delay from cooperating cells is significant, the CoMP transmission gain is drastically diminished and clustering is forbidden at points far from a UE [19, 20].

17.3 CoMP design parameters

17.2.4

499

Inter-eNodeB and intra-eNodeB coordination Coordination among eNodeBs carried out through the X2 interface,3 so that users can be served by different eNodeBs, is called inter-eNodeB coordination, whereas coordination within the eNodeB, so that users can be served by a number of co-located or distributed antenna system (DAS) connected to the same eNodeB by a physical connection, e.g., fiber, is called intra-eNodeB coordination. While the latency of the X2 interface is specified to be about 20 ms [21], some companies are inclined to skepticism about whether inter-eNodeB coordination is feasible because of the functionalities limited by the X2 interface, and hence they consider the intra-eNodeB coordination scheme more realizable in practice [22]. Scheduling information, dynamic channel knowledge, and user data may not be reflected promptly by cooperating cells so that the performance gain of inter-eNodeB coordination scheme is restricted [17]. Nevertheless, some companies [23–25] have expressed strong interest in the scheme. JPT schemes are considered feasible in practice for intra-eNodeB scenarios due to the fact that the cooperating sectors are geographically colocated and communication between the sectors is assumed to be fast enough, whereas CS/CB schemes have no severe backhaul constraints since data packets are not shared among cells and thus seem more practical for inter-eNodeB cooperation scenarios.

17.3

CoMP design parameters

17.3.1

Reference signal (RS) A reference signal (RS) is defined at each individual antenna port 4 as the pilot symbols needed at the UE for CSI estimation and data demodulation. The cellspecific RS (CRS) was designed for both purposes. LTE Release 8 provides CRS for at most four antenna ports with an overhead of 14.3% that can support up to 1, 2, and 4 streams for single-user MIMO and up to four users with each being with a single stream for multi-user MIMO. Since CRSs from different cells have different shifts in either frequency or time,5 most companies realize that adding more CRS patterns across the full band in LTE-Advanced introduces too much overhead [27] and that it is better to utilize the current CRS structure than to introduce new CRS patterns for backward compatibility; like CRS, CSI-RS is additionally defined to provide a low-density RS with a different density in the frequency and a different periodicity in time, and is aimed at obtaining CSI especially for CoMP UEs [28]. 3 4

5

It is a direct physical connection for interfacing between neighboring eNodeBs. Each physical antenna is called an antenna port and has a distinguishable RS pattern. Orthogonal reference symbols among coordinating eNodeBs may need to be designed for estimating channels accurately for neighboring eNodeBs. An overhead analysis of different RS patterns is given in [26].

500


An existing CRS may interfere with data transmission by other active cells such that the actual channel is affected by the data symbol [29] and hence the quality of channel measurement is likely to be poorer, resulting in a modulation and coding scheme (MCS) level mismatch and precoding performance degradation. A slightly different CRS design should be considered in which the weaker cells do not suffer from interference from the stronger cells. Interference caused by the stronger cells can be removed by making such cells puncture resource elements (REs) that overlap with the CRS of other cells. Such puncturing is useful only in the presence of UEs that benefit from the cooperation of weak neighbors. It could be enabled based on the assessment of cooperation gains and overhead associated with RE puncturing. This clearly results in an additional waste of REs and the total overhead increases, but the expected performance gain may compensate for the additional overhead. Leaving aside the CRS–data collision issue, the expected CoMP gain can also be degraded due to channel quality indicator (CQI) mismatch with the actual post-processing SINR from existing PMI and CQI feedback. Interference conditions may change significantly across resource blocks (RBs) and subframes and also depend on the beams and transmit power densities used by different cells on each RB. Therefore, periodic CQI feedback that estimates the channel and interference over a larger time–frequency resource6 (potentially the entire bandwidth) would not accurately capture the exact CQI. This, in turn, would impact the ability of the eNodeB to choose the MCS accurately, thereby resulting in a significant throughput loss. In [31] a challenge to investigate whether a new type of CQI would be beneficial was posed, and a resource (channel) quality indicator (RQI) was proposed that would accurately reflect the channel quality, thereby enabling the eNodeB to choose the MCS correctly. Furthermore, in [13] it was proposed that when CoMP is used the UE should report a new type of CQI corresponding to different CoMP transmission schemes and a number of CQIs in order to support a dynamic switch between the transmission schemes. Since CoMP transmission can be transparent to CoMP UEs, a transmission points configuration for CoMP (TPCC) is proposed in [32] so that UE can provide a set of CQI values according to different CoMP configurations and the network can then decide the link adaptation appropriately. It has been agreed [33] that in CoMP a dedicated RS will be used for demodulation and a UE-specific demodulation RS (DM-RS) has been considered for CoMP transmission because weighting of the reference signal from multiple cells can help improve the quality of channel estimation. The operation at the network side is transparent to UEs and whether the signal is emitted from a single cell or from multiple cells is irrelevant. Such overlapping DM-RS is transmitted only in scheduled RBs [28] and can save downlink signaling. 6

The granularity of CQI report defined in LTE Release 8 [30] is divided into three levels, wideband, selected subband, and higher layer configured subband, according to the transmission modes.


501

An extension of the current DM-RS is needed to support more streams for CoMP UEs. There are two basic DM-RS structures to add more DM-RS patterns, i.e., FDM-based and CDM-based. In FDM-based multiplexing, additional DM-RS symbols are transmitted on different REs, while in CDM-based multiplexing they are transmitted on the same REs but are distinguished by different orthogonal codes. Several FDM and CDM DM-RS patterns with different interpolation spacings in time and frequency are evaluated in [34]. In general, FDM-based DM-RS performs better than CDM-based DM–RS but may result in an unacceptable overhead. For instance, if two exclusive FDM-based DM-RS ports are supported, the total overhead including the current four CRS ports will be 28.6% [26]. Indeed, CDM-based DM-RS multiplexing to differentiate multiple streams per UE or multiple UEs could exploit the commonality between RS designs for single-user and multiuser transmissions, but it entails eNodeB coordination to switch between the modes [35]. Although many companies put emphasis on MU-CoMP operation outperforming SU-CoMP operation in the system level perspective (despite the restrictive user pairing problem [36]), employing additional DM-RS patterns needs careful investigation in terms of increased overhead of RS and expected performance gain.

17.3.2

Precoding To change a dominant interference signal into desired signal requires data and CSI sharing between the cooperating cells and can thus cause high backhaul capacity and complexity. To reduce the complexity, several CoMP transmission modes have been defined and are classified primarily into noncoherent and coherent transmissions. Noncoherent transmission does not coherently combine the signals arriving at the UE but does obtain an cooperation gain, approximately 3 dB for the case of two-cell cooperation from the doubled transmission power [19]. In coherent transmission, the signals from multiple cells are combined coherently by adjusting the phase of locally precoded signals and by global precoding of a composite channel among the cooperating cells, with the network obtaining the CSIs of all the cooperating cells. Various precoding techniques are well categorized in [19, 37, 38]. Although CoMP is carried out in synchronized networks, the received signal from several different cells may arrive at the UE at different times due to the different distances between the UE and the cell sites. A mismatch greater than the intersymbol interference (ISI) leads to a diminishing cooperation gain, resulting in a linear phase rotation in the frequency domain. Once the mismatch exceeds a certain threshold associated with a cyclic prefix (CP), the cell is excluded from the CoMP cooperation set, otherwise some timing calibration has to be introduced to compensate for the mismatch. Similar concerns about the arrival timing mismatch problem as well as feedback aging and power mismatch were addressed in [37] and with more elaborate work in [39] including the effect of frequency selective scheduling, codebook quantization, and spatial correlation.

502


The impact of the residual timing mismatch even after the compensation depends on the applied CoMP scheme. Transmitted data separated by the spacefrequency block code (SFBC) mechanism between cooperation cells are robust against the arrival timing mismatch since the channels from cooperating cells are distinguishable, whereas coherent precoding schemes such as local precoding with phase correction, as well as global precoding suffer a performance loss of about 1–2 dB, since linear phase distortion over a span of consecutive subcarriers cannot be recovered by a single phase correction factor [19]. Interestingly, however, arrival mismatch may benefit noncoherent precoding schemes such that single frequency network (SFN) precoding can give extra frequency diversity. Cyclic delay diversity (CDD) based on precoding, in which the signals from cooperating cells are cyclically delayed, may also be affected (if the CDD delay is shortened, the performance is degraded and otherwise improved). In the context of such potential benefit, some companies [19, 40] argue that noncoherent transmission may be a promising multicell precoding method with respect to low realization complexity and backhaul capacity and particularly for the case of TDD systems [38, 41]. Moreover, simple SFN precoding can be enhanced by antenna selection such that only a subset of transmit antennas is used from each of the cooperating cells [42]. Thanks to better resource utilization of the number of transmit antennas and power, it even outperforms codebook-based global precoding, thereby highlighting the importance of antenna selection for CoMP operation. However, it may entail increased complexity with regard to fast antenna selection.

17.3.3

Feedback Once the UE obtains channel knowledge of the serving cell as well as the interfering cells when CoMP is used, this information needs to be transferred to the serving cell. Agreements in CoMP feedback schemes were made on the principles of feedback signal design [6, 43, 44], and since then discussion on CoMP feedback has been focused on feedback types, including the following categories: Explicit channel state/statistical information feedback Direct channel feedback as observed by the receiver, without assuming any transmission or receiver processing,7 is aimed at providing complete channel knowledge of a set of subcarriers (corresponding to a subband or the entire band from CRS) for optimal beamforming. Explicit channel state/statistical information is fed back based on aperiodic or periodic reporting mechanisms [46]. If this information is accumulated over a long period of time, it converges to a statistical correlation and it was shown in [47–50] that significant gains can be obtained for MU-MIMO and CoMP schemes. Possible examples of spatial covariance feedback (SCF) using the statistical correlation were discussed in [48, 51]. 7

A compression technique [45] may be applied to reduce feedback overhead.


503

Each entry of the spatial covariance matrix can be fed back by a direct modulation technique, e.g., by mapping the entries to QPSK/QAM modulation symbols carried in enhanced uplink control channels, i.e., physical uplink control channel (PUCCH) and physical uplink shared channel (PUSCH), or by a generalized quantized codebook by minimizing a combination of entry-wise distance. However, spatial channel feedback with a limited number of bits would be a limiting factor [52]. Implicit channel state/statistical information feedback A transmission format is fed back by using different types of transmission and/or reception processing, e.g., direct extension of LTE Release 8 MIMO feedback, CQI/PMI/RI. In fact, optimal precoding requires the eNodeB to acquire complete channel knowledge on each subcarrier and thus increases feedback overhead. On the other hand, one PMI for full frequency band fed back to the eNodeB results in a simpler implementation but in very small performance gain due to inaccuracy to frequency selective channel [53]. Interestingly, it has been shown that under the assumption of fixed feedback overhead, PMI-based implicit feedback is superior to explicit channel feedback since averaging the transmit covariance matrix over a wideband basis may result in increased mismatch due to quantization errors in a frequency-selective channel [54]. Uplink sounding reference signal (SRS) CSI is estimated at the eNodeB by exploiting channel reciprocity. Due to channel reciprocity, direction of arrival (DOA) information can be obtained through uplink SRS. By sharing DOA and scheduling information of cell-edge UEs, each cell constructs a set of directions that are forbidden while forming beams, and schedules users to maximize the cell throughput [55]. A suitable feedback scheme may well depend on the CoMP scheme used. There is a tradeoff between performance gain and overhead [53]; noncoherent per-cell based precoding can further be improved by adding additional beam-phase correction feedback and explicit channel feedback8 as well as MU-MIMO can also be used to further improve the performance of CoMP UEs [51]. A common feedback framework for single-cell MIMO and different CoMP schemes has been discussed extensively [57, 58] and hierarchical and self-contained feedback structure was proposed to give scalability and flexibility [50, 59, 60]. It has also been agreed that dynamic switching between different CoMP schemes can be supported and that feedback for single-cell MIMO should be a subset of feedback for CoMP operation. For commonality between different CoMP schemes [44], the same feedback can be used for CS/CB and noncoherent JPT operations. UE PMI feedback is used for intercell coordination by interference avoidance and user paring.

8

The performance of the CoMP precoding schemes based on explicit channel feedback is summarized in [56].

504


17.4

CoMP performance evaluation methodologies The performance of CoMP schemes has been evaluated by a number of companies under reasonable but not identical simulation assumptions, such as scheduler, frequency granularity of resource allocation, and MCS determination. Hence, it is difficult to fairly compare the results directly from the work done by different companies and research groups. TR36.814 provides some guidelines for system level evaluations and related simulation results from some typical LTE-Advanced configurations which have been conducted by a number of companies [61]. In this section, we outline the evaluation methodologies especially for CoMP operation in link level and system level simulations.

17.4.1

Link level simulation The link level model implemented for the LTE downlink conforms to LTE Release 8 [62, 63] and employs CoMP JT. As illustrated in Figure 17.1, frequency selective channel coefficients are first generated in the frequency domain and kept to be later convolved in the time domain with generated time-domain OFDM symbols. Modulation symbols are then generated through the modulation symbol generation block [63] and are mapped onto one or several transmission layers. After the layer mapper, the complex-valued modulation symbols are each precoded by PMI fed back from the CoMP precoding block and then mapped for each antenna port to resource elements. Finally a complex-valued time-domain OFDM signal is generated for each antenna port. For the CoMP precoding block, we can consider the following precoding methods, codebook-based precoding schemes proposed in [64] and eigenbeamforming schemes using explicit channel feedback [56].

r Multiple single-cell precoding with identical precoding across cells – SFN transmission All cooperating cells employ the same precoding to the UE. The UE selects the best precoding assuming the same precoding across different cooperating cells. The UE feedback format defined in LTE Release 8 can be reused. r Multiple single-cell precoding allowing different single-cell precoding across cells Different cells can employ different precoding. UE feedback includes the best combination of precoding vectors for a combined multicell channel. The PMI feedback overhead scales with the number of cooperating cells. r Multiple single-cell precoding with additional beam-phase correction The UE first finds the best precoder for each of the cooperating cells, assuming singlecell transmission, and then chooses the best beam-phase factors for coherent combining of beams from different cells. The PMI feedback overhead scales with the number of cooperating cells. r Multiple single-cell precoding with a single eigenbeam vector precoding across cells The UE selects the best common eigenbeam vector, assuming the same precoding across different cooperating cells.

505

17.4 CoMP performance evaluation methodologies

MCS report Modulation symbol generation Source generation

PMI for precoded DM-RS

CRC encoding

RS generation CRS and DM-RS

Channel coding Channel generation

Layer mapping

Resource element mapping

Precoding

Interleaver

OFDM modulation

Rate matching PMI report

Modulation symbol mapper

Time-domain signal

For ideal channel estimation

MCS level HARQ Retains transmitted data when CRC checksum fails Simulation end?

BLER calculation

From DM-RS CRC check

Multipath channel

CoMP precoding

Channel decoding

From CRS Channel estimation Resource element demapping

OFDM demodulation

LLR accumulation for HARQ retransmission

Y Simulation result

Figure 17.1. Link level simulator block diagram of CoMP transmission where shaded blocks incorporate multicell processing.

r Multiple single-cell precoding with additional beam-phase correction using an eigenbeam matrix The precoding at joint transmission eNodeBs is chosen locally, with each based on the eigendecomposition of its own channel. For coherent combining, a phase-correction is additionally computed. The CoMP precoding block for computing either PMIs or eigenbeamforming vectors can directly use the channel coefficients generated in the channel generation block for ideal channel estimation case. The receiver performs the reverse processes to those performed by the transmitter in order to detect the transmitted symbols and to decode them to recover the original bit streams, for which the receiver has to estimate the MIMO channel and the instantaneous effective SINR, feedback CQI to the transmitter and generate the soft bit information, called the log likelihood ratio (LLR), that is the input for the turbo decoder. In the simulation, the LLR that reflects the link reliability is calculated per subframe after the channel decoding block that includes the reverse processes of the modulation symbol generation block. While performing the hybrid automatic repeat request (HARQ) process, to increase redundancy the LLR can be accumulated up to (say) four retransmissions in the case of a block error. Generation of ACK/NACK is based on the CRC check sum error. Whether to generate a new source message is incorporated with the HARQ process. The HARQ protocol enables block error rate (BLER) to be reduced

506


eNodeB Large-scale channel generation

UE distribution

Small-scale channel generation

CoMP scheduling

2 TTI round trip delay

Report CSI for scheduling

CoMP precoding for scheduled UEs

Report ACK/NACK for retransmission

Rate update after retransmissions

Report assigned MCS to UEs

UE Simulation result

End of drops? Y

End of TTIs? Y

Compute CSI

Generate ACK/NACK

Accumulate SINR by HARQ process

Figure 17.2. System level simulator block diagram of CoMP transmission where dashed line blocks are invoked every three TTIs and rate update is done after three retransmissions in this case. CSI feedback includes computed PMIs and phase corrector, MCS values and SINR values for the non-CoMP and CoMP cases, all in per-RB basis, for CoMP scheduling. so that when an ACK is obtained, a new transmission is made and otherwise a retransmission is enqueued. Adaptive modulation and coding (AMC) is also used to maximize throughput while maintaining the BLER below a predefined target value. There are several different MCS options for adapting to varying channel conditions. To find an optimum MCS level, the MMSE post-processing effective SINR obtained from DM-RS is calculated and the best MCS is selected, satisfying a required BLER of about 0.1.

17.4.2

System level simulation Figure 17.2 shows system level simulator that performs CoMP JT. Path-loss and shadow fading are position-dependent and time-invariant (per-drop based) according to the given UE distribution. Small-scale fading is modeled as a timedependent process (per-TTI9 based). The number of drops and TTIs are defined so that the performance of the employed scheme represents statistically converging results. The spatial channel model (SCM) or the SCM extended (SCME) for a larger bandwidth is employed for generating small-scale fading channels. It is a ray-based model using stochastic modeling of scatterers. Six paths formed and each path is made up with 20 spatially separated sub-paths by summing up sinusoidal waves. In general, there are 19 cell-sites with three sectors each where each cell-site receives interference from up to two-tier rings with a wrap-around cell layout that ensures that all cells experience the same interference characteristics, and statistics are gathered from all the 19 cell-sites. 9

Transmission time interval.

17.4 CoMP performance evaluation methodologies

507

Either intersector cooperation within each cell-site (up to two-cell JT) or intercell cooperation between different cell-sites can occur. From a practical point of view, intra-eNodeB CoMP operation has a scheduling algorithm that can be explicitly modeled in each cell-site coordinating only three sectors. The FFR of reuse 3 is typically used for cell-edge users [65] to mitigate intercell interference between the CoMP clusters. Some conditions made for CoMP operation, which comply with typical CoMP operation steps [66] are:

r Decision on CoMP UEs Once UEs are considered as cell-edge UEs based on the downlink average received signal power, CoMP UE is decided by the reference signal received power (RSRP) difference between the received signals from the CoMP cooperation set. In the simulation, a UE is considered to be a cell-edge UE when the SINR averaged over the entire band goes below 0 dB, and a cell-edge UE is considered as a candidate CoMP UE when the largest interfering signal power is within a threshold from the received signal power of the serving cell, in order to facilitate UE-centric cell clustering. The threshold value is set to −3 dB for two-cell cooperation:

η=

mini∈C RSRPi , maxj ∈C RSRPj

(17.1)

where C is the CoMP cooperation set. The UE reports a candidate set of interfering cells based on the RSRP measurement. The eNodeB first broadcasts a threshold and the UE reports the cells whose RSRP difference relative to that of the serving cell is within the threshold (Figures 17.3 and 17.4). r Selection of precoding vector for the cell-edge UE Precoding vectors are selected so that the instantaneous received signal power is maximized as proposed in [64]. We assume error-free feedback signaling in the simulation and that the total number of signaling bits required for the PMI feedback is seven, i.e., two bits for each cell and three bits for the eight-different phase correction factor to let the signals from the two cells coherently combine. In general, the precoding vector is updated every three TTIs.

r CoMP UE MCS selection In practice, the eNodeB may request the CoMP UE to make a certain CoMP feedback related to the full or a subset of the dominant interfering cells in order to choose the MCS accurately. In the simulation, the CoMP UE calculate the received SINR to be improved by the expected precoding vectors, i.e., combined CQIs [13], and correspondingly fed back every three TTIs per-RB MCS selection for the entire band to the serving cell, where the MCS table is obtained from the link level simulation in advance. Given a MCS table, exponential effective SINR mapping (EESM) [67] is used to select an MCS option. It translates the SINR obtained by a linear minimum

508


Figure 17.3. Geometry of candidate CoMP UEs in intra-eNodeB cooperation (two-cell): the darker spot represents greater likelihood of being a candidate CoMP (target center cell).

Figure 17.4. Geometry of candidate CoMP UEs in inter-eNodeB cooperation (two-cell): the darker spot represents greater likelihood of being a candidate CoMP (target center cell). mean square error (MMSE) receiver [68] to effective SINR values in association with available MCS options [69]. The MCS with the largest data rate that simultaneously satisfies the target BLER, is selected. We assume error-free feedback signaling for the MCS report.

r Scheduling algorithm Based on the UE’s CSI feedback, the scheduling algorithm will decide the CoMP type (JPT or CS/CB) and the cooperating cells, UE pairing, and link adaptation. The scheduler performs user selection and link adaptation using parameters, including precoding vectors and MCSs. User

17.5 Conclusion

509

selection is based on the scheduling metric determined by a proportional fairness (PF) criterion for all the UEs served by the cell-site. The scheduler then assigns the RBs of the cells to the UEs in descending order of the scheduling metric, where the scheduling metric is normalized by the number of cooperating cells for the UE. When there is intra-eNodeB operation and JPT is performed, 19 master schedulers are formed so that each can manage the resources available at one three-sector cell site and when an RB is available for the two sectors that perform JT, the scheduler is allowed to assign the RB to the UE. If no CoMP UE is available, the RB is allocated to cell-edge UE that performs a single-cell transmission. In general, cell-centric UEs whose SINRs are above 0 dB operate with all subcarriers of reuse 1.

r ACK/NACK generation The PDSCHs are constructed from multiple cells applying the selected precoding vectors of each with RB-based frequency granularity, and the UE is supposed to decode the data over PDSCH with DM-RS so that the multiple signals are coherently combined at the UE. The SINR obtained by a linear MMSE receiver that accounts for the combined desired signal and interference of precoded beams is translated to the effective SINR in association with the selected MCS. The effective SINR computed per RB basis and averaged over the number of assigned RBs is then used to generate an ACK or NACK according to the BLER.

17.5

Conclusion We have outlined the issues and agreements regarding CoMP. A number of companies have expressed strong interest in CoMP systems and put forth great efforts to determine the necessary design parameters, such as RS design, feedback signaling, and precoding strategies, required for the CoMP operation. Depending on the CoMP schemes used, CoMP operation entails different costs and provides different performance gains. Non-coherent precoding can be improved by adding a beam-phase factor and explicit channel feedback is also employed to improve the CoMP gain further. A scalable control framework for resilient deployment that takes into account the tradeoff between complexity and performance should be carefully investigated as part of the work item phase. Then, some form of eNodeB cooperation can be finalized and this is expected to appear in future standards.

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[22] R1-083050, Inter-eNB and Intra-eNB Schemes for CoMP in LTE-Advanced, Huawei, 3GPP TSG RAN WG1, #54, Aug. 2008. [23] R1-082576, Inter-cell Radio Resource Management for Heterogeneous Network, NTT DoCoMo, 3GPP TSG RAN WG1, #53bis, June 2008. [24] R1-081877, LTE - IMT advanced – Candidate Technologies, Alcatel-Lucent, 3GPP TSG RAN WG1, #53, May 2008. [25] R1-083156, Opportunistic Spacce Time Multiple Access for LTE-Advanced, 3GPP TSG RAN WG1, #54, Aug. 2008. [26] R1-091340, On Demodulation-RS and CSI-RS Design and Overhead, Motorola, 3GPP TSG RAN WG1, #56bis, March 2009. [27] R1-090151, Discussion on RS designs for CoMP in LTE-A, Nortel, 3GPP TSG RAN WG1, #55bis, Jan. 2009. [28] R1-091066, Way Forward on Downlink Reference Signals for LTE-A, 3GPP TSG RAN WG1, #56, Feb. 2009. [29] R1-090129, Further Discussions on the Downlink Coordinated Transmission - Impact on the Radio Interface, Huawei, CMCC, 3GPP RAN WG1, #55bis, Jan. 2009. [30] 3GPP TS36.213, v8.5.0, Evolved Universal Terrestrial Radio Access (EUTRA); Physical layer procedures, Dec. 2008. [31] R1-090366, Impact of Downlink CoMP on the Air Interface, Qualcomm Europe, 3GPP TSG RAN WG1, #55bis, Jan. 2009. [32] R1-091869, CoMP Operational Mode Feedback Discussions, Samsung, 3GPP TSG RAN WG1, #57, May 2009. [33] R1-084377, Downlink Coordinated Transmission – Impact on Specification,” Ericsson, 3GPP TSG RAN WG1, #55, Nov. 2008. [34] R1-090754, Performance Evaluation of DRS Design for Multi-layer Transmission , Nortel, 3GPP TSG RAN WG1, #56, Feb. 2009. [35] R1-090796, Downlink RS Design for Supporting Higher Order SU/MUMIMO and CoMP, Motorola, 3GPP TSG RAN WG1, #56, Feb. 2009. [36] R1-090325, Coordinated Multi-Point Transmission – Coordinated Beamforming/Precoding and Some Performance Results, Motorola, 3GPP TSG RAN WG1, #55bis, Jan. 2009. [37] R1-084465, Discussion and Link Level Simulation Results on LTE-A Downlink Multi-site MIMO Cooperation, Nortel, 3GPP TSG RAN WG1, #55, Nov. 2008. [38] R1-092159, Downlink Non-coherent SU-CoMP Schemes Comparison for TDD Systems, Alcatel-Lucent, 3GPP TSG RAN WG1, #57, May 2009. [39] R1-091916, Further Performance Evaluations of CoMP Solutions, Nortel, 3GPP TSG RAN WG1, #57, May 2009. [40] R1-091133, Further Considerations on MBSFN Precoding for DL CoMP, Sharp, 3GPP TSG RAN WG1, #56bis, March 2009. [41] R1-092160, DL Non-coherent Multi-user MIMO Joint Transmission (MUMIMO JT) Scheme and System Performance Evaluations in TDD Systems, Alcatel-Lucent, 3GPP TSG RAN WG1, #57, May 2009.

512


[42] R1-092337, Simulation Results for SFN and AS-SFN Precoding Schemes for DL CoMP, Sharp, 3GPP TSG RAN WG1, #57bis, June 2009. [43] R1-092290, TP for Feedback in Support of DL CoMP for LTE-A TR, Qualcomm Europe, 3GPP TSG RAN WG1,#57, June 2009. [44] R1-092369, Feedback Design Principles for Downlink CoMP, Huawei, 3GPP TSG RAN WG1, #57bis, June 2009. [45] R1-092032, CQI and CSI Feedback Compression, Alcatel-Lucent, 3GPP TSG RAN WG1, #57, Apr. 2009. [46] R1-091935, CoMP Operation and Evaluation, Motorola, 3GPP TSG RAN WG1, #57, May 2009. [47] R1-090793, Coordinated Multi-Point Transmission–Coordinated Beamforming and Results, Motorola, 3GPP TSG RAN WG1, #56, Feb. 2009. [48] R1-091936, Spatial Correlation Feedback to Support LTE-A MU-MIMO and CoMP: System Operation and Performance Results, Motorola, 3GPP TSG RAN WG1, #57, May 2009. [49] R1-092943, CoMP Operation Based on Spatial Covariance Feedback and Performance Results of Coordinated SU/MU Beamforming, 3GPP TSG RAN WG1, #57bis, Jun. 2009. [50] R1-093034, Discussion on Common Feedback Framework for DL CoMP, Huawei, 3GPP TSG RAN WG1, #58, Aug. 2008. [51] R1-091342, On UE Feedback to Support LTE-A MU-MIMO and CoMP Operations, Motorola, 3GPP TSG RAN WG1, #56bis, March 2009. [52] R1-090866, Multiple Description Coding for Spatial Feedback Payload Reduction, Qualcomm Europe, 3GPP TSG RAN WG1, #56, Feb. 2009. [53] R1-092397, Further Consideration on CoMP Feedback, Texas instruments, 3GPP TSG RAN WG1, #57bis, June 2009. [54] R1-092938, Implicit Feedback in Support of Downlink MU-MIMO Beamforming, Texas Instruments, 3GPP TSG RAN WG1, #57bis, June 2009. [55] R1-084290, Proposal of Multiple Sites Coordination for LTE-A TDD, CATT, 3GPP TSG RAN WG1, #55, Nov. 2008. [56] R1-092304, UE Feedback for Downlink CoMP Schemes, ETRI, 3GPP TSG RAN WG1, #57bis, June 2009. [57] R1-093720, CoMP E-mail Discussion Summary, Qualcomm Europe, 3GPP TSG RAN WG1, #58, Aug. 2009. [58] R1-093912, Downlink Feedback Framework for LTE-Advanced, Nokia, 3GPP TSG RAN WG1, #58bis, Oct. 2009. [59] R1-092056, Hierarchical Feedback in Support of Downlink CoMP operation, Qualcomm Europe, 3GPP TSG RAN WG1, #57, May 2009. [60] R1-094217, Feedback in Support of Downlink CoMP: General Views, Qualcomm Europe, 3GPP TSG RAN WG1, #58bis, Oct. 2009. [61] 3GPP TR 36.814, Further Advancements for E-UTRA Physical Layer Aspects, Release-9, V9.0.0, March 2010. [62] 3GPP TS 36.211, Evolved Universal Terrestrial Radio Access (E-UTRA); Physical Channels and Modulation.

References

513

[63] 3GPP TS 36.212, Evolved Universal Terrestrial Radio Access (E-UTRA); Multiplexing and Channel Coding. [64] R1-083546, Per-cell Precoding Methods for Downlink Joint Processing CoMP ETRI, 3GPP TSG RAN WG1, #54bis, Sept. 2008. [65] R1-091490, Multi-cell PMI Coordination for Downlink CoMP, ETRI, 3GPP TSG RAN WG1, #56bis, March 2009. [66] R1-091484, Evaluation of DL CoMP Gain Considering RS Overhead for LTE-Advanced, NTT DOCOMO, 3GPP TSG RAN WG1, #56bis, Mar 2009. [67] R1-031303, System-level Evaluation of OFDM – Further Considerations, Ericsson, 3GPP TSG RAN WG1, #35, Nov. 2003. [68] R1-092429, Different Types of DL CoMP Transmission for LTE-A, Fujitsu, 3GPP TSG RAN WG1, #57bis, Jun. 2009. [69] R1-062050, Initial Characterization of E-UTRA UL VoIP Capacity, Qualcomm Europe, 3GPP TSG RAN LTE, Sep. 2006.

Index

3GPP, 480 802.16j, 7 adaptive precoding order (APO), 48, 50, 60 backhaul, 3, 302, 306, 313 BC, see broadcast channel BCJR algorithm, 80, 86, 89, 90 beamforming, 4 best-effort resource allocation, 261 broadcast channel, 110, 302, 309 capacity achieving code low-density parity-check code, 163, 266 turbo codes, 266 carrier aggregation, 428 cell clustering, 497, 498 cell grouping, 138 cell-specific reference signal (CSR), 457 cellular network, 233 multicell network, 244 relay network, 251 channel capacity, 208, 237 channel state information (CSI), 6, 261 global, 261 local, 281 channel state information reference signal (CSI-RS), 457 classification, 349 clover-leaf-shaped cells, 143 coded cooperation, 205 collaborative power addition, 179, 184 collaborative spatial multiplexing, 9 combinatorial, 276 brute force, 276 common rate, 179, 180, 189–192, 195, 197–199, 201 computation power, 302, 315 convergence, 102 convex optimization, 214, 278 dual decomposition master problem, 279 subproblem, 279

514

duality gap, 243, 254 ellipsoid, 243, 246 first-order condition, 246 gradient method, 280 Hessian matrix, 279; negative semi-definite, 279 Karush–Kuhn–Tucker (KKT) condition, 214, 280 Lagrange dual method, 214 Lagrange multiplier, 210, 279 Lagrangian, 279 Lagrangian duality, 238, 242, 243, 246 subgradient, 243, 246 subgradient method, 214 cooperating jammers, 384 cooperative communication, 205, 259 cooperative network, 233 base station cooperation, 4, 234, 244, 249, 259 cooperative base station, 47 cooperative base station complexity, 61 cooperative transmission algorithm, 60 cooperative transmitter, 49 relay cooperation, 250 relaying, 259 amplify-and-forward (AF), 18, 154, 168, 205, 250, 260 compress-and-forward (CF), 19, 250 decode-and-forward (DF), 18, 154, 162, 205, 260, 470 full-duplex relaying, 259 inband relay, 488, 489 layer 1 relay, 482 layer 2 relay, 483 layer 3 relay, 484 one-way half-duplex relaying, 259 outband relay, 490 relay cooperation, 234, 255 relay selection, 206 selective relaying, 218 two-way half-duplex relaying, 259 type 1 relay, 485 type 2 relay, 485

Index

turbo base station cooperation, 110 user cooperation, 259 coordinated beamforming, 433, 440, 496, 497 coordinated multipoint transmission (CoMP), 426, 431, 495 CoMP feedback, 502 CoMP set, 434 direct channel feedback, 502 explicit channel feedback, 503 reference signal, 499 uplink sounding reference signal (SRS), 503 coordinated scheduling, 433, 434, 442, 496, 497 cost–benefit tradeoff, 317 decode-and-forward (DF), 250 decomposed factor graph, 102 defection function, 361 degraded BC, see degraded broadcast channel degraded broadcast channel, 111 diamond-shaped cells, 143 dirty paper coding (DPC), 48, 111, 133, 307, 309, 445 distributed beamforming, 4 distributed optimization, 206 diversity, 160 delay, 154, 171 diversity-multiplexing tradeoff, 328, 336 dynamic cell selection (DCS), 496 ergodic capacity, 259 extreme value distribution, 267 Fréchet distribution, 268 Gumbel distribution, 268 Weibull distribution, 268 factor graph, 82, 83, 85 femto-cells, 313 flow conservation, 253 forward–backward algorithm, see BCJR algorithm fractional frequency reuse (FFR), 128, 136 frequency reuse, 3, 77, 233 frequency reuse partitioning , 435 frequency-division multiple access (FDMA), 49 front-channel interference, 51, 55 game theory, 385 canonical coalitional game, 349 coalition formation game, 349, 350, 411 coalitional value, 348 core, 357

515

merge-and-split, 359 Shapley value, 356 coalitional game model, 408 coalitional game theory, 348 characteristic form, 348 graph form, 348 partition form, 348 coalitional graph game, 350 cooperative eavesdropping game, 412 Pareto order, 414 Stockholder equilibrium, 391 Stockholder game, 398 Gaussian parallel multiple relay network, 399 geometric mean decomposition (GMD), 59, 60 goodput, 274 Han–Kobayashi coding, 308 Etkin–Tse–Wang coding, 309 hexagonal cellular array, 110 hidden Markov model, 85, 89 information-theoretic security, 382 intercell interference, 3, 107, 233 intercell interference coordination (ICIC), 436 interference alignment, 441 interference channel, 87, 114 interference management, 4 intergroup interference (IGI), 130, 134 interlink interference, 51 interstream interference, 51 intracell interference, 3 iterative transmit–receive antenna weights optimization, 53 joint leakage suppression (JLS), 441, 445 joint network channel coding, 331 joint processing, 433, 496, 497 Kalman smoother, 80, 92 learning phase, 188 linear cellular array, see one-dimensional cellular array linear minimum mean squared error filter, 80 linear program (LP), 194 Lloyd–Max algorithm, 284 LMMSE filter, see linear minimum mean squared error filter LQ precoding, 309 LTE, 8, 176, 451 eNodeB, 425 inter-eNodeB coordination scheme, 499 intra-eNodeB coordination scheme, 499 UE, 425

516

Index

LTE-Advanced, 8, 450, 451, 480 Release 10, 450 Manhattan scenario, 304, 312 MAP detector, see maximum a posteriori detector margin adaptive (MA) scheme, 23 matched filter (MF), 59 maximum a posteriori detector, 80, 91 MCP, see multicell processing MIMO broadcast channel, see vector broadcast channel minimum variance distortionless response (MVDR), 56 modulo operation, 52 multicell MIMO transmission, 307 multicell processing, 79–81 multichannel diversity, 338 multilayer superposition coding (MLSC), 462, 466 multinode partial information relaying, 474 multiple access channel, 302, 307 multiple access relay channel, 331 multiple-input multiple-output (MIMO), 8, 205, 259, 351 distributed, 6 virtual, 259 multiple-input single-output (MISO), 47, 48, 55 multiuser diversity, 261, 266, 267, 338 diversity gain, 210 multiuser MIMO system, 49 myopic optimization, 61 myopic policy, 187 Nash bargaining solution (NBS), 29 network coded cooperation, 326 network coding, 324 network formation, 370, 373 network MIMO, 77, 129, 235 network utility maximization, 240 NP-hard problem, 228 one-dimensional cellular array, 78, 79, 88 open system interconnection, 263 media access control layer, 263 physical layer, 263 orthogonal frequency-division multiple access (OFDMA), 14, 49, 236, 260 subcarrier mapping, 272 orthogonal frequency-division multiplexing (OFDM), 235, 426 orthogonal relaying, 200, 202 outage, 187–191, 197–201 information-outage probability, 163 outage probability, 208

P-CPA, 179, 186 pair-wise error probability (PEP), 36, 161 parallel relay channel, 402 parallel relay network, 213 partial information relaying, 463 partner selection, 138 path-loss, 234, 250 PC-CPA, 179, 186, 192 per-antenna superposition coding (PASC), 462, 465 physical-layer network coding, 334 PMI coordination, 434 power allocation, 57, 245, 254 power control, 192, 194, 201 precoding, 501 precoding matrix index (PMI), 431 preference operator, 358 QR decomposition, 55, 56, 309 quality-of-service (QoS), 266 bit error rate (BER), 266 channel outage probability, 276 delay-sensitive, 266 frame error rate (FER), 266 minimum data rate requirement, 266 nondelay-sensitive, 266 R-factor, 372 random linear network coding, 325 rate adaptive (RA) scheme, 23 rate region, 242 rear-channel interference, 51 recommended PMI, 497 rectangular cellular array, 96 regularized channel inversion beamforming, 113 relay channel, 16, 205 relay station, 368 relay-interference channel, 306 remote radio head (RRH), 446, 455 resource allocation, 233, 337 restricted PMI, 497 reuse partition, 136 routing, 254 scheduling, 245 cross-layer scheduling, 265 max–min fairness, 220 maximum throughput scheduler, 265 proportional fair, 241, 282 proportional fair scheduler, 265 round-robin scheduler, 267 weighted-sum fairness, 220 SCP, see single cell processing secrecy capacity, 382 secrecy region, 402

Index

self-interference, 272 signal-to-interference-plus-noise-ratio (SINR), 48, 237 SINR equalization, 48 SINR maximization, 56 SINR gap, 237, 315 single carrier frequency division multiple access (SC-FDMA), 426 single-cell processing, 79 singular value decomposition (SVD), 55 space-division multiple access (SDMA), 9 space-time block codes, 157 Alamouti, 158 distributed, 153 delay tolerant, 171 linear dispersion, 157 orthogonal, 159 quasi-orthogonal, 159 space-time spreading, 172 spatial diversity, 13 spectral/eigenvalue decomposition, 56 state-based factor graph, 98 suboptimal solution, 229 successive decoding, 477 sum-product algorithm, 83 synchronization, 170 time-sharing, 278 Tomlinson–Harashima precoding (THP), 48, 50–53, 445 transferable utility, 348

517

two-dimensional cellular array, 96 two-stage superposition coding, 463, 475 two-way relay channel, 331, 334 uplink–downlink duality, 116, 118 utility function, 265 vector broadcast channel, 110 virtual antenna array (VAA), 14, 20 virtual LMMSE estimation, 117 vulnerability region, 402 water-filling, 215, 238, 239 iterative, 240 modified, 247 multilevel water-filling, 280 wide-area scenario, 303, 310 WiMAX, 7 WINNER system model, 303 wireless relay, 451 XOR-CD, 338 zero-forcing (ZF) transmission, 48, 53, 133 zero-forcing beamforming, 4, 113, 445 zero-forcing decorrelation, 470 zero-forcing dirty paper coding (ZF-DPC), 133 zero-forcing DPC, 309 ZF beamforming, see zero-forcing beamforming

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