Applications of space-time adaptive processing

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Applications of Space-Time Adaptive Processing Edited by Richard Klemm

The Institution of Electrical Engineers

Published by: The Institution of Electrical Engineers, London, United Kingdom © 2004: The Institution of Electrical Engineers This publication is copyright under the Berne Convention and the Universal Copyright Convention. All rights reserved. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act, 1988, this publication may be reproduced, stored or transmitted, in any forms or by any means, only with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Inquiries concerning reproduction outside those terms should be sent to the publishers at the undermentioned address: The Institution of Electrical Engineers, Michael Faraday House, Six Hills Way, Stevenage, Herts., SGl 2AY, United Kingdom While the authors and the publishers believe that the information and guidance given in this work are correct, all parties must rely upon their own skill and judgment when making use of them. Neither the authors nor the publishers assume any liability to anyone for any loss or damage caused by any error or omission in the work, whether such error or omission is the result of negligence or any other cause. Any and all such liability is disclaimed. The moral right of the authors to be identified as authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

British Library Cataloguing in Publication Data Klemm, Richard Applications of space-time adaptive processing 1. Adaptive signal processing 2. Adaptive antennas 3. Radar 4. Sonar I. Title II. Institution of Electrical Engineers 621.3'848 ISBN 0 85296 924 4

Typeset in India by Newgen Imaging Systems (P) Ltd., Chennai, India Printed in the UK by MPG Books Limited, Bodmin, Cornwall

Preface

I have been asked frequently which is the more difficult task, to write a book on your own or to edit a multiauthor book such as the one at hand. I have tried both and found that each of the two kinds of project has its own charming facets. It is a pity that the work is done now - 1 enjoyed so much working on these books. My first book 'Space-time adaptive processing - principles and applications' (IEE, 1998) contains mainly a summary of my own work in this fascinating area, specialising in the most popular application: clutter suppression for airborne radar. The book has been so well received that a second extended edition 'Principles of space-time adaptive processing' appeared in 2002. While working on the second edition it came to my mind that this book contains only a subset of the broad field of space-time adaptive processing (STAP) and, moreover, reflects only my personal view of the subject. In particular, aspects of STAP operation on real clutter data are missing. Therefore, I proposed to the IEE to edit another book on STAP comprising a large variety of contributions by different distinguished authors so as to cover the entire area of space-time processing as much as possible. In contrast to my first book, applications of STAP are emphasised in this volume. The publisher kindly agreed to this ambitious plan, and I approached a large number of scientists well known in the STAP field and asked them for cooperation. I am amazed that almost all individuals I contacted immediately agreed to contribute. The total number of contributors amounts to 45! Waves are by nature functions of space and time. Whoever deals with the interpretation of waves has to apply space-time processing techniques. The fundamental paper by Brennan and Reed 'Theory of adaptive radar' (IEEE Trans. AES, 9, (2), March, 1973, pp. 237-252) has been formulated already in space-time notation, thus addressing the effects of broadband array antennas. In this paper by 'time' the fast (range equivalent) time was meant. Three years later the same authors extended their ideas to the use of array antennas in the space-slow time domain (pulse-to-pulse) for clutter rejection in moving radar systems. This was the first publication on what most people in the radar community understand by STAR The book is subdivided into two main sections: A 'Suppression of clutter in moving radar' and B 'Other space-time processing applications'. Each main section is divided in different parts dedicated to specific aspects of space-time processing.

Section A consists of four parts which deal with various aspects of the traditional STAP in GMTI (ground moving target indication) applications for moving radar platforms such as an aircraft or a satellite. Here the reader may find detailed information on topics such as STAP and SAR, space-based MTI, specific antenna configurations, STAP performance in real, heterogeneous clutter, specific (e.g. non-linear) algorithms and processor architectures, robust signal detection techniques, non-adaptive space-time clutter filters, effect of range ambiguous clutter etc. Section B includes specific applications of space-time techniques in various disciplines such as fast time STAP for broadband radar (jammer cancellation, superresolution), tracking of ground targets with STAP radar, interference reduction in over-the-horizon radar (with reference to terrain scattered jamming). Another part is dedicated to applications in seismics and acoustics. The last part deals with spacetime techniques as proposed for communication systems, including mitigation of mutual interference in cellular phones, reduction of multipath effects in underwater communications, interference suppression for GPS and space-time coding. At the end of each chapter a brief summary is given in which the major insights are highlighted. Moreover, each chapter concludes with a list of references which helps the interested reader to find in-depth background literature. The total number of references amounts to about 900. I hope that the reader will enjoy reading this unique book and will appreciate the effort made by 45 leading experts in the space-time processing field in order to bring their individual expertise to the reader's attention. In particular, by having a look 'over the fence' in other fields I expect some cross-fertilisation between different but somehow related disciplines. It is intended that scientists working in different disciplines may learn from each other, and that new ideas based on the fruit harvested already in a neighbour's garden are stimulated. If this expectation comes true the team of authors has reached its goal. I want to express my gratitude to all the authors who did a tremendous work in contributing to this unique book and encouraging the editor in his ambitious undertaking. It was a real pleasure to work with all of them. I am grateful to K. Kriicker and J. Ender of FGAN for supporting this work. I want to thank the IEE personally and on behalf of all the authors for the excellent job done. Specifically I would like to thank the anonymous reviewers for their revision of the manuscript, the commissioning editor Sarah Kramer and the editorial assistant, Wendy Hiles, for the excellent cooperation and the high quality of the final product. Richard Klemm

Glossary

a a ABF ACP ACE ADC AEP AEW AIC ALQ AMF AoA Ar ARMA ASB ASEP ASFF ATI AWACS AWGN

auxiliary channel vector noise-to-clutter ratio adaptive beamforming auxiliary channel processor adaptive coherence estimator analogue-to-digital conversion auxiliary eigenvector processor airborne early warning akaike information criterion adaptive linear quadratic adaptive matched filter angle of arrival received signal amplitude autoregressive moving average adaptive sidelobe blanker auxiliary sensor/echo processor auxiliary sensor FIR filter processor along-track interferometry Airborne Warning and Control System additive white Gaussian noise

b B B BASS-ALE Bc #D /3 BER BF BICM BK

beamformer vector bandwidth number of beamformer elements broadband signal subspace spatial-spectral estimation clutter bandwidth Doppler bandwidth look angle relative to array axis bit error rate beamforming bit interleaved coded modulation backward method

bk BLAST BLE BS Bs BW

beamformer weights Bell Labs layered space-time transceiver block linear equaliser basestation system bandwidth beamwidth

c C c cF Cr CALC CCD CCI CDMA CE CFAR CGM CIG CMP CMT CNR Coho COMET CPI CRB CRP CRS CSM CSST CW

light velocity number of space-time channels vector of clutter echoes vector of clutter spectral components transformed vector of clutter echoes constrained averaged likelihood ratio concealment, camouflage and deception cochannel interference code division multiple access capacity efficient constant false alarm rate conjugate gradient method common image gathers common midpoint covariance matrix taper clutter-to-noise power ratio coherent oscillator covariance matching estimation techniques coherent processing interval Cramer-Rao bound common reflection point common reflection surface cross spectral metric coherent signal subspace transformation continuous wave

d dimSS D(O) D{(p) ds DSW DUM dx dy dz D3LS AR

sensor spacing dimension of signal subspace vertical sensor directivity pattern horizontal sensor directivity pattern subarray displacement direct subarray weighting direct uniform manifold model sensor spacing in ^-direction sensor spacing in y-direction sensor spacing in z-direction direct data domain least-squares width of range bin

DF DFB DFT DL DMO DoA DoF DPCA DS

decision feedback Doppler filter bank discrete Fourier transform downlink dip moveout direction of arrival degrees of freedom displaced phase centre antenna direct sequence

e/ E{} ESPRIT

unit vector (7-th column of unit matrix) expectation estimation of signal parameters by rotational invariance techniques envelope of transmitted waveform

E(t) f F F (p FAP FB cpc /c /D FD FDFF FDSP FFT FIR O^ FL tan

radial clutter velocity platform velocity (x-direction) radial target velocity velocity SAR target velocity tangential target velocity

WAVES WNSF WSF WVD

weighted average of signal subspaces weighted noise subspace fitting weighted subspace fitting Wigner-Ville distribution

x xp Xt Xx

vector of received echoes spectral vector of received echoes jc-coordinate of /-th sensor transformed vector of received echoes

y yc yi

output signal correction pattern y-coordinate of i-th sensor

ZF H ZO *

zero forcing z-coordinate of/-th sensor zero offset conjugate complex or conjugate complex transpose

* 0 O

convolution Kronecker product zero vector

List of Contributors

Yuri I. Abramovich CSSIP, SPRI Building, Technology Park Adelaide, Mawson Lakes, South Australia 5095

Russell D. Brown Department of Electrical and Computer Engineering, Syracuse University, Syracuse, New York 13244-1240, USA

Stuart J. Anderson CSSIP, SPRI Building, Technology Park Adelaide, Mawson Lakes, South Australia 5095

Jeffrey T. Carlo AFRL/SNRD, 26 Electronic Parkway, Rome, New York 13441-4514, USA. e-mail: [email protected]

Stephan Benen ATLAS ELEKTRONIK GmbH, Sebaldsbriicker Heerstr. 235, D-28305 Bremen, Germany Steffen Bergler Geophysical Institute, University of Karlsruhe, Hertzstr. 16, 76187 Karlsruhe, Germany R. S. Blum ECE Department, Lehigh University, 19 Memorial Drive West, Bethlehem, PA 18015-3084, USA. Tel: (610) 758-3459; Fax: (610) 758-6279; e-mail: [email protected]. Johann F. Bohme Ruhr-Universitat Bochum, Fakultat Fiir Elektrotechnik, 44780 Bochum

Pei-Jung Chung Ruhr-Universitat Bochum, Fakultat Fiir Elektrotechnik, 44780 Bochum Fabiola Colone Dept. INFOCOM, University of Rome 'La Sapienza', Via Eudossiana 18, 00184 Rome, Italy. Tel: +39-06-44585472; Fax: +39-06-4873300 Eric Duveneck Geophysical Institute, University of Karlsruhe, Hertzstr. 16, 76187 Karlsruhe, Germany Alfonso Farina AMS (Alenia Marconi Systems) Chief Technical Office Scientific Director, Via Tiburtina km. 12.400, 00131 Rome, Italy. Tel: +39-6-41502279;

Fax: +39-6-4150-2665; e-mail: [email protected] Christoph H. Gierull Defence R&D Canada, Ottawa (DRDC-O), 3701 Carling Ave., Ottawa, ON, Canada, KlA 0Z4. e-mail: [email protected] Dhananjay Gore Qualcomm Inc., 9940 Barnes Canyon Road, San Diego, CA 92121, USA. e-mail: [email protected] Alexei Y. Gorokhov CSSIP, SPRI Building, Technology Park Adelaide, Mawson Lakes, South Australia 5095 Peter Hubral Geophysical Institute, University of Karlsruhe, Hertzstr. 16, 76187 Karlsruhe, Germany

Yung P. Lee Science Applications International Corporation, 1710 SAIC Drive, McLean, VA 22102, USA. Tel: 703-676-6512; Fax: 703-893-8753; e-mail: [email protected] Chuck Livingstone Defence R&D Canada, Ottawa (DRDC-O), 3701 Carling Ave., Ottawa, ON, Canada, KlA 0Z4 Pierfrancesco Lombardo Dept. INFOCOM, University of Rome 4 La Sapienza', Via Eudossiana 18, 00184 Rome, Italy. Tel: +39-06-44585472; Fax: +39-06-4873300; e-mail: [email protected] .it, [email protected] .it Dirk Maiwald ATLAS ELEKTRONIK GmbH, Sebaldsbrucker Heerstr. 235, D-28305 Bremen, Germany

Richard Klemm FGAN-FHR, Neuenahrer Str. 20, D 53343 Wachtberg, Germany. Tel: ++49 228 9435 377; Fax:++49 228 348 618; e-mail: [email protected]

Jiirgen Mann Geophysical Institute, University of Karlsruhe, Hertzstr. 16, 76187 Karlsruhe, Germany

Wolfgang Koch FGAN-FKIE, Neuenahrer Strasse 20, D 53343 Wachtberg, Germany. Tel: +49-(0)228/9435-529; Fax: -685; e-mail: [email protected]

K. F. McDonald MITRE Corporation, 202 Burlington Road, Bedford, MA 01730-1420, USA. Tel: (781) 271-7739; Fax:(781)271-7045; e-mail: [email protected]

Stephen M. Kogon MIT Lincoln Laboratory, 244 Wood Street, Lexington, MA 02420-9108, USA

William L. Melvin Georgia Institute of Technology, Georgia Tech Research Institute (GTRI), Atlanta, GA, USA

Wilbur L. Myrick SAIC, 4501 Daly Drive, Chantilly, VA 20151,USA. e-mail: [email protected] Rohit Nabar ETF El 19, Sternwartstrasse 7, Zurich CH8092, Switzerland, e-mail: [email protected]

Tapan K. Sarkar Department of Electrical Engineering and Computer Science, Syracuse University, 123 Link Hall, Syracuse, New York 13244-1240, USA. e-mail: [email protected]; http ://web. syr.edu/~tksarkar

Ulrich Nickel FGAN-FHR, Neuenahrer Str. 20, 53343 Wachtberg, Germany

Helmut Schmidt-Schierhorn ATLAS ELEKTRONIK GmbH, Sebaldsbriicker Heerstr. 235, D-28305 Bremen, Germany

Tim J. Nohara Sicom Systems Ltd., 67 Canboro Rd., 2nd Floor, RO. Box 366, Fonthill, Ontorio, LOS IEO

Richard A. Schneible Department of Electrical and Computer Engineering, Syracuse University, Syracuse, New York 13244-1240, USA

Arogyaswami Paulraj Smart Antennas Research Group, Packard 272, Stanford University, Stanford, CA 94305, USA. e-mail: [email protected]

Nicholas K. Spencer CSSIP, SPRI Building, Technology Park Adelaide, Mawson Lakes, South Australia 5095

Peter G. Richardson QinetiQ Malvern, Malvern Technology Centre, St. Andrews Road, Malvern, Worcs., UK, WR14 3PS. Tel/Fax: 01684 894316/01684 894185; e-mail: [email protected] Magdalena Salazar-Palma Dpto. Senales, Sistemas y Radiocomunicaciones, ETSI Telecommunicacion, Universidad Politecnica de Madrid, Ciudada Universitaria, s/n 28040, Madrid, Spain, e-mail: [email protected] Sumeet Sandhu Intel Corporation, M/S RNB 6-49, 2200 Mission College Blvd, Santa Clara, CA 95052, USA. e-mail: [email protected]

L. Timmoneri Technical Directorate, Radar & Technology Division, Alenia Marconi Systems, Via Tiburtina km. 12.400, 00131 Rome, Italy. Tel: +39-6-41502279; Fax: +39-6-41502665; e-mail: [email protected] Christoph M. Walke COHAUSZ & FLORACK, Patent- und Rechtsanwalke, Kanzlerstrasse 8a, 40472 Dusseldorf H. Wang Department of Electrical and Computer Engineering, Syracuse University, Syracuse, New York 13244-1240, USA

R Weber Sicom Systems Ltd., 67 Canboro Rd., 2nd Floor, P.O. Box 366, Fonthill, Ontario, LOS IEO

Rolf Weber Ruhr-Universitat Bochum, Fakultat Fiir Elektrotechnik, 44780 Bochum

Michael C. Wicks AFRL/SN, 26 Electronic Parkway, Rome, New York 13441-4514, USA. e-mail: [email protected]

Michael Zatman MIT Lincoln Laboratory, 244 Wood Street, Lexington, MA 02420-9108, USA Y. Zhang Department of Electrical and Computer Engineering, Syracuse University, Syracuse, New York 13244-1240, USA Michael D. Zoltowski School of Electrical Engineering, Purdue University, West Lafayette, IN 47907-1285, USA. e-mail: [email protected]

Contents

Preface ...............................................................................

xix

Glossary .............................................................................

xxi

List of Contributors ............................................................. xxxi Section A. Suppression of Clutter in Moving Radar Part I. 1.

Space-slow Time Processing for Airborne MTI Radar

Space-time Adaptive Processing for Manoeuvring Airborne Radar ..................................................................................

5

1.1

Introduction .............................................................

5

1.2

STAP Fundamentals ...............................................

6

1.3

Clutter Angle-Doppler Relationships ....................... 1.3.1 Straight and Level Flight ............................ 1.3.2 Effect of Variations in Platform Orientation .................................................

9 9 11

1.4

Clutter Suppression in Forward-looking Radar ....... 1.4.1 Mainlobe Clutter Suppression ................... 1.4.2 Sidelobe Clutter Suppression ....................

12 12 18

1.5

Slow Moving Target Detection under Conditions of Manoeuvre .............................................................. 1.5.1 Effects of Platform Manoeuvre .................. 1.5.2 Motion Compensation ...............................

23 23 24

Jammer Rejection under Conditions of Manoeuvre .............................................................. 1.6.1 Mainlobe Clutter Filtering Requirements ...

27 27

1.6

This page has been reformatted by Knovel to provide easier navigation.

v

vi

Contents 1.6.2

Advantages of Using STAP .......................

27

Summary ................................................................

33

Non-linear and Adaptive Two-dimensional FIR Filters for STAP: Theory and Experimental Results ...........................

37

2.1

Introduction .............................................................

37

2.2

Adaptive Linear Filters ............................................

38

2.3

AR-based FIR Filters ..............................................

45

2.4

Non-linear Combination of Non-adaptive Filters ..... 2.4.1 Filter Bank Design ..................................... 2.4.2 Detection Threshold and Performance ...... 2.4.3 AR-based Non-linear Detector ..................

51 52 55 56

2.5

Non-linear Combination of Adaptive AR-based Two-dimensional FIR Filters ...................................

61

2.6

Conclusions ............................................................

66

2.7

Acknowledgments ...................................................

69

2.8

Appendix: ML Estimation of Two-dimensional AR parameters ..............................................................

69

Space-time Techniques for SAR ........................................

73

3.1

Summary ................................................................

73

3.2

Description of the Problem and State of the Art .....

73

3.3

Model of MSAR Echoes .......................................... 3.3.1 Aberrations Due to Target Motion ............. 3.3.2 Space-time-frequency Representation ......

76 76 77

3.4

Processing Schemes .............................................. 3.4.1 Taxonomy of Processing Schemes for MSAR ........................................................ 3.4.2 MTI + PD ................................................... 3.4.3 DPCA ........................................................ 3.4.4 Along-track Interferometry (ATI)-SAR ....... 3.4.5 Processor in the Space-time-frequency Domain ...................................................... 3.4.6 Optimum Processing for MSAR .................

82

1.7 2.

3.


82 87 94 95 98 107

Contents

4.

3.5

Conclusions ............................................................

119

3.6

Acknowledgments ...................................................

120

Σ∆-STAP: an Efficient, Affordable Approach for Clutter Suppression .......................................................................

123

4.1

Definition of the Difference (∆) Beams ....................

123

4.2

Σ∆-STAP Algorithms ...............................................

125

4.3

Analytical Performance Formulas of Σ∆-STAP ....... 4.3.1 SINR Potential ........................................... 4.3.2 Probabilities of Detection and False Alarm .........................................................

129 129

4.4

A Real-data Demonstration of Σ∆-STAP ................

131

4.5

Desired ∆-beam Characteristics ............................. 4.5.1 Mathematical Equivalence of Subarray and Σ∆-STAP .............................................

135

Summary ................................................................ 4.6.1 Advantages of the Σ∆-STAP Approach ..... 4.6.2 Limitations of Σ∆-STAP ............................. 4.6.3 Potential Applications of Σ∆-STAP ............

143 143 145 146

STAP with Omnidirectional Antenna Arrays .......................

149

5.1

Introduction ............................................................. 5.1.1 Preliminaries on STAP Antennas .............. 5.1.2 The Circular Ring Array Concept ...............

149 149 151

5.2

Array Configurations for 360° Coverage ................. 5.2.1 Four Linear Arrays ..................................... 5.2.2 Displaced Circular Rings ........................... 5.2.3 Circular Planar Array with Randomly Distributed Elements ................................. 5.2.4 Octagonal Planar Array .............................

152 153 156

5.3

Discussion .............................................................. 5.3.1 Directivity Patterns .................................... 5.3.2 Range-ambiguous Clutter .........................

164 164 165

5.4

Effect of Array Tilt ...................................................

167

4.6

5.

vii


130

142

157 160

viii

Contents 5.4.1

Side-looking Linear and Rectangular Arrays ........................................................ Omnidirectional Arrays ..............................

167 168

5.5

Conclusions ............................................................

169

Part II.

Space-slow Time Processing for Space-based MTI Radar

5.4.2

6.

7.

SAR-GMTI Concept for RADARSAT-2 ...............................

177

6.1

177 177

Introduction ............................................................. 6.1.1 Background ............................................... 6.1.2 Addition of MTI Modes to Spaceborne SAR ........................................................... 6.1.3 RADARSAT-2 Moving Object Detection Experiment ................................................

179

6.2

Analysis of SAR-GMTI Modes for RADARSAT-2 ... 6.2.1 Background ............................................... 6.2.2 Statistical Models of Measured Signals ..... 6.2.3 SCNR Optimum Processing ...................... 6.2.4 SAR Displaced Phase Centre Antenna ..... 6.2.5 SAR Along-track Interferometry .................

180 181 184 188 193 194

6.3

SAR-STAP Scheme for RADARSAT-2 ................... 6.3.1 Detection ................................................... 6.3.2 Parameter Estimation ................................

196 196 201

6.4

Conclusions ............................................................

202

6.5

List of Symbols .......................................................

203

STAP Simulation and Processing for Spaceborne Radar ..................................................................................

207

7.1

Introduction .............................................................

207

7.2

Spaceborne Radar Applications and Design .......... 7.2.1 Spaceborne MTI Radar Applications ......... 7.2.2 Spaceborne MTI Radar Design .................

208 208 209

7.3

STAP Processing for SBR ......................................

212


178

Contents 7.3.1 7.3.2 7.3.3

8.

ix

Typical GMTI Signal Processing ............... Extension to Other Modes ......................... Other Issues ..............................................

212 215 216

7.4

Simulation and Processing for SBR ........................ 7.4.1 User Interface ............................................ 7.4.2 Model the Radar ........................................ 7.4.3 Model the Environment ............................. 7.4.4 Generate the Signals ................................. 7.4.5 Model the Processing ................................ 7.4.6 Evaluate the Results .................................

217 218 224 225 227 228 229

7.5

Discussion and Conclusions ...................................

231

Techniques for Range-ambiguous Clutter Mitigation in Space-based Radar Systems .............................................

235

8.1

Introduction .............................................................

235

8.2

Moving Target Detection with SBR ......................... 8.2.1 STAP for SBR Systems .............................

236 238

8.3

Clutter Characteristics of Pulse-Doppler Waveforms in SBR ..................................................................... 8.3.1 Clutter Doppler Ambiguities ....................... 8.3.2 Clutter Range Ambiguities .........................

240 241 242

Impact of Range-ambiguous Clutter on STAP Performance ...........................................................

244

Range-ambiguous Clutter Mitigation Techniques with Pulse-Doppler Waveforms .............................. 8.5.1 PRF Diversity ............................................ 8.5.2 Aperture Trade Offs ...................................

247 247 249

8.4 8.5

8.6

8.7

Long Single Pulse Phase-encoded Waveforms ..... 8.6.1 Properties of Long Single Pulse Phaseencoded Waveform (LSPW) ...................... 8.6.2 Integrated Sidelobe Clutter Levels ............ 8.6.3 STAP Simulations .....................................

250

Summary ................................................................

260


252 254 257

x

Contents

Part III. 9.

Processing Architectures

Parallel Processing Architectures for STAP .......................

265

9.1

Summary and Introduction ......................................

265

9.2

Baseline Systolic Algorithm ....................................

265

9.3

Lattice and Vectorial Lattice Algorithms ..................

269

9.4

Inverse QRD-based Algorithms ..............................

271

9.5

Experiments with General Purpose Parallel Processors ..............................................................

272

9.6

Experiments with VLSI-based CORDIC Board .......

273

9.7

Modern Signal Processing Technology Overview and Its Impact on Real-time STAP .........................

275

9.8

Processing of Recorded Live Data ......................... 9.8.1 Systolic Algorithm for Live Data Processing ................................................. 9.8.2 Data Files Used in the Data Reduction Experiments .............................................. 9.8.3 Performance Evaluation ............................ 9.8.4 Detection of Vehicular Traffic ....................

278 280 284

9.9

Concluding Remarks ..............................................

285

9.10

Appendix A: Givens Rotations and Systolic Implementation of Sidelobe Canceller ....................

286

9.11

Appendix B: Lattice Working Principle ....................

288

9.12

Appendix C: the CORDIC Algorithm .......................

289

9.13

Appendix D: the SLC Implementation via CORDIC Algorithm .................................................................

292

Appendix E: an Example of Existing Processors for STAP .................................................................

293

9.14

Part IV.

277

Clutter Inhomogeneities

10. STAP in Heterogeneous Clutter Environments .................. 10.1

277

Introduction ............................................................. 10.1.1 Adaptivity with Finite Sample Support .......


305 305 307

Contents

xi

10.1.2 STAP Performance Metrics ....................... 10.1.3 Covariance Matrix Errors ...........................

308 311

10.2

Classes of Space-time Clutter Heterogeneity ......... 10.2.1 General Simulation Characteristics ...........

312 315

10.3

Amplitude Heterogeneity ........................................ 10.3.1 Clutter Discretes ........................................ 10.3.2 Range-angle Varying Clutter RCS ............ 10.3.3 Clutter Edges .............................................

315 315 320 322

10.4

Spectral Heterogeneity ...........................................

325

10.5

CNR-induced Spectral Mismatch ............................

327

10.6

Targets in the Secondary Data ...............................

330

10.7

Joint Angle-Doppler Mismatch and Clutter Heterogeneity .........................................................

337

10.8

10.9

Site-specific Examples of Clutter Heterogeneity ..... 10.8.1 Measured Multichannel Airborne Radar Data ........................................................... 10.8.2 Site-specific Simulation .............................

339 339 342

STAP Techniques in Heterogeneous Environments .......................................................... 10.9.1 Data-dependent Training Techniques ....... 10.9.2 Minimal Sample Support STAP ................. 10.9.3 Clutter Discretes ........................................ 10.9.4 Targets in Training Data ............................ 10.9.5 Covariance Matrix Tapers ......................... 10.9.6 Knowledge-aided Space-time Processing .

344 344 348 350 350 351 352

10.10 Summary ................................................................

353

10.11 Acknowledgments ...................................................

353

11. Adaptive Weight Training for Post-Doppler STAP Algorithms in Non-homogeneous Clutter ............................

359

11.1

Introduction .............................................................

359

11.2

Training of STAP Algorithms ..................................

361

11.3

Post-Doppler STAP Algorithms ..............................

364


xii

Contents 11.4

Phase and Power-selected Training for STAP .......

365

11.5

Experimental Results .............................................. 11.5.1 Example of Phase/Power Selection .......... 11.5.2 STAP Results ............................................ 11.5.3 Experimental Versus Theoretical STAP Performance ..............................................

367 368 369

Summary ................................................................

372

12. Application of Deterministic Techniques to STAP ..............

375

11.6 12.1 12.2 12.3 12.4

Introduction .............................................................

372

375

3

Direct Data Domain Least-squares (D LS) Approach, One Dimension ...................................... 3

D LS Approach with Main Beam Constraints .........

379 385

3

A D LS Approach with Main Beam Constraints for Space-time Adaptive Processing ............................ 12.4.1 Space-time D3LS Eigenvalue Processor .................................................. 12.4.2 Space-time D3LS Forward Processor ........ 12.4.3 Space-time D3LS Backward Processor ..... 12.4.4 Space-time D3LS Forward-backward Processor ..................................................

387 389 390 392 393

12.5

Determining the Degrees of Freedom ....................

394

12.6

An Airborne Radar Example ................................... 12.6.1 Simulation Setup ....................................... 12.6.2 Case I: Single Constraint Space-time Example ..................................................... 12.6.3 Case II: Multiple Constraint Space-time Example .....................................................

396 396

12.7

Conclusions ............................................................

408

12.8

List of Variables ......................................................

408

13. Robust Techniques in Space-time Adaptive Processing .... 13.1 Introduction ............................................................. 13.1.1 Initial Development of Space-time Adaptive Processing (STAP) Algorithms ..................

413 413


398 403

414

Contents

xiii

13.1.2 Hypothesis Testing Problem ......................

417

13.2

Real-world Detection Environments .......................

418

13.3

Non-homogeneity – Causes and Impact on Performance ........................................................... 13.3.1 Signal Contamination ................................ 13.3.2 Non-homogeneity Detection ...................... 13.3.3 Knowledge-based Signal Processing ........ 13.3.4 Analysis of Degraded Performance Due to Non-homogeneity ..................................

420 423 425 428 428

13.4

Antenna Array Errors ..............................................

430

13.5

Deviation from Gaussian Assumption .....................

431

13.6

Jamming and Terrain Scattered Interference ......... 13.6.1 Constraining Detection Schemes .............. 13.6.2 Two-stage Processors ............................... 13.6.3 Three-dimensional STAP ..........................

433 434 434 436

13.7

Reduction in Computational Complexity ................. 13.7.1 Reduced-rank Methods and Covariance Matrix Tapers ............................................ 13.7.2 Techniques Implementing Limited Reference Cells ......................................... 13.7.3 Low Complexity Approaches to STAP .......

437

Conclusions ............................................................

443

13.8

437 439 441

Color Plates: Applications of Space-time Adaptive Processing .............................................................. 463a

Section B. Miscellaneous Space-time Processing Applications Part V.

Ground Target Tracking with STAP Radar

14. Ground Target Tracking with STAP Radar: the Sensor .....

467

14.1

Introduction .............................................................

467

14.2

Properties of the STAP Radar Sensor .................... 14.2.1 Processing Techniques .............................

467 468


xiv

Contents 14.2.2 Array Properties ......................................... 14.2.3 Summary of the Data Output Provided by the STAP Radar ........................................

473

14.3

The Scenario .......................................................... 14.3.1 SNIR and Pd of a Moving Target ............... 14.3.2 System Aspects .........................................

474 474 480

14.4

Degrading Effects ................................................... 14.4.1 Bandwidth Effects ...................................... 14.4.2 Doppler Ambiguities .................................. 14.4.3 Range Ambiguities .................................... 14.4.4 STAP Radar under Jamming Conditions ...

486 486 488 489 492

14.5

Issues in Convoy Tracking ...................................... 14.5.1 Convoy Detection by Range-only Information ................................................. 14.5.2 Convoy Detection by Azimuth Variance Analysis .....................................................

494

Summary ................................................................

499

15. Ground Target Tracking with STAP Radar: Selected Tracking Spects ..................................................................

501

14.6

472

495 496

15.1

Introduction ............................................................. 15.1.1 Discussion of an Idealised Scenario .......... 15.1.2 Summary of Observations .........................

501 502 505

15.2

Tracking Preliminaries ............................................ 15.2.1 Coordinate Systems .................................. 15.2.2 Target Dynamics Model ............................

507 507 509

15.3

GMTI Sensor Model ................................................ 15.3.1 GMTI Characteristics ................................. 15.3.2 Convoy Resolution .................................... 15.3.3 Doppler Ambiguities .................................. 15.3.4 Measurements ...........................................

510 510 512 513 513

15.4

GMTI Data Processing ........................................... 15.4.1 Prediction .................................................. 15.4.2 Data Processing ........................................

514 514 515


Contents

xv

Filtering Process ........................................ Realisation Aspects ................................... Discussion ................................................. Retrodiction ............................................... Effect of Doppler Ambiguities ....................

517 518 519 522 524

15.5

Road Map Information ............................................ 15.5.1 Modelling of Roads .................................... 15.5.2 Densities on Roads ...................................

528 529 530

15.6

Quantitative Discussion .......................................... 15.6.1 Simulation Parameters .............................. 15.6.2 Numerical Results .....................................

533 533 534

15.7


537

15.4.3 15.4.4 15.4.5 15.4.6 15.4.7

Part VI.

Space-fast Time Techniques

16. Superresolution and Jammer Suppression with Broadband Arrays for Multifunction Radar ......................... 16.1

Introduction .............................................................

16.2

Broadband Array Signal Model and Beamforming .......................................................... 16.2.1 Received Signal and Notation ................... 16.2.2 Digital Beamforming with Subarray Outputs ...................................................... 16.2.3 Influence of Channel Imperfections ...........

16.3

16.4

543 543 544 545 548 553

Superresolution with Broadband Arrays ................. 16.3.1 Spatial-only Processing of Broadband Data ........................................................... 16.3.2 Space and Time Processing Methods ....... 16.3.3 Conclusions on Broadband Superresolution .........................................

559

Jammer Suppression with Broadband Arrays ........ 16.4.1 General Principles of Adaptive Interference Suppression .......................... 16.4.2 Spatial-only Adaptation .............................

582


561 566 581

583 589

xvi

Contents 16.5

Part VII.

16.4.3 Space and Time Adaptation ......................

590

Final Remarks .........................................................

595

Over-the-horizon Radar Applications

17. Stochastically Constrained Spatial and Spatio-temporal Adaptive Processing for Non-stationary Hot Clutter Cancellation ........................................................................ 17.1

Overview .................................................................

17.2

SC STAP Fundamentals and Supervised Training Applications .............................................. 17.2.1 SC STAP Algorithm: Analytic Solution ...... 17.2.2 SC STAP Algorithm: Operational Routines .................................................... 17.2.3 SC STAP Algorithm: Efficiency Analysis by Simulation Results ................................ 17.2.4 SC STAP Algorithm: Efficiency Analysis by Real Data Processing ........................... 17.2.5 Summary ...................................................

17.3

17.4

603 603 604 611 624 626 638 642

SC STAP Unsupervised Training Applications ....... 17.3.1 Operational Routine for Unsupervised Training ..................................................... 17.3.2 Operational SC STAP Algorithm: Simulation and Real Data Processing Results ...................................................... 17.3.3 Summary ...................................................

647

SC STAP Convergence Analysis ............................ 17.4.1 Introduction ................................................ 17.4.2 Conditional Loss Factor η1 Analysis: LSMI Versus SMI for SC SAP ................... 17.4.3 Conditional Loss Factor η1 Analysis: LSMI for SC STAP .................................... 17.4.4 Conditional Loss Factor η2 Analysis: Exact PDF for a Single Stochastic Constraint .....

665 665


649

656 664

667 678 681

17.5

Part VIII.

Contents

xvii

17.4.5 Conditional Loss Factor η2 Analysis: Approximate PDF for Multiple Stochastic Constraints ................................................

685


690

Applications in Acoustics and Seismics

18. Space-time Adaptive Matched Field Processing (STAMP) .............................................................................

701

18.1

Introduction .............................................................

701

18.2

Adaptive Matched Field Processing (MFP) ............

703

18.3

Wideband-narrowband Feedback Loop Whitenoise-constrained Method (FLWNC) ......................

705

18.4

MFP Examples .......................................................

707

18.5

Space-time Adaptive Matched Field Processing (STAMP) .................................................................

709

Forward Sector Processing Simulation Geometry ................................................................

711

Summary ................................................................

713

19. Space-time Signal Processing for Surface Ship Towed Active Sonar .......................................................................

715

18.6 18.7

19.1

Introduction .............................................................

715

19.2

Narrowband Multiple Ping Processing .................... 19.2.1 Data Model ................................................ 19.2.2 Fully Adaptive CW Processing .................. 19.2.3 Partially Adaptive Processing Techniques ................................................

720 720 721

19.3

FM Processing ........................................................ 19.3.1 Image Processing Background .................. 19.3.2 Echogram Image Enhancement ................ 19.3.3 Automatic Echogram Detection .................

724 726 726 726

19.4

Experimental Results .............................................. 19.4.1 Sonar System Description .........................

727 727


723

xviii

Contents 19.4.2 19.4.3 19.4.4 19.4.5

CW Pulse Sea Data Analysis .................... Echogram Sea Data Analysis (ACTAS) .... Echogram Enhancement ........................... Automatic Echogram Detection .................

728 729 730 730

20. EM and SAGE Algorithms for Towed Array Data ...............

733

20.1

Introduction .............................................................

733

20.2

Signal Model ...........................................................

734

20.3

EM and SAGE Algorithms ...................................... 20.3.1 EM Algorithm ............................................. 20.3.2 SAGE Algorithm ........................................

736 736 739

20.4

Fast EM and SAGE Algorithms ..............................

741

20.5

Recursive EM and SAGE Algorithms ..................... 20.5.1 Recursive EM Algorithm ............................ 20.5.2 Recursive SAGE Algorithm .......................

742 743 745

20.6

Experimental Results .............................................. 20.6.1 EM and SAGE Algorithms ......................... 20.6.2 Recursive EM and SAGE Algorithms ........

746 747 749

20.7

Conclusions ............................................................

751

21. The Common Reflection Surface (CRS) Stack – a Datadriven Space-time Adaptive Seismic Reflection Imaging Procedure ...........................................................................

755

21.1

Introduction .............................................................

755

21.2

Seismic Reflection Imaging .................................... 21.2.1 The Seismic Wavefield .............................. 21.2.2 Acquisition of Reflection Seismic Data ...... 21.2.3 Seismic Reflection Processing ..................

756 756 758 762

21.3

Common Reflection Surface Stack ......................... 21.3.1 Classic Data-driven Approaches ............... 21.3.2 Second-order Traveltime Approximations .. 21.3.3 Physical Interpretation of the Coefficients ... 21.3.4 Implementation .......................................... 21.3.5 Practical Aspects .......................................

766 767 768 769 771 772


Contents

xix

21.3.6 A Synthetic Data Example .........................

773

21.4

CRS Attributes and Velocity Model Estimation .......

775

21.5

Conclusions ............................................................

777

21.6

Glossary .................................................................. 21.6.1 List of Variables ......................................... 21.6.2 Specific Terminology .................................

778 778 779

Part IX.

Space-time Techniques in Communications

22. STAP for Space/Code/Time Division Multiple Access Systems ..............................................................................

785

22.1

Introduction .............................................................

785

22.2

System Model .........................................................

789

22.3

Time Domain Linear Joint Detection ....................... 22.3.1 Zero Forcing Block Linear Equalisation ..... 22.3.2 Minimum Mean Square Error Block Linear Equalisation ....................................

791 792

22.4

Frequency-domain Linear Joint Detection .............. 22.4.1 Block-diagonal FD System Model ............. 22.4.2 FD ZF-BLE and MMSE-BLE ......................

793 793 796

22.5

Performance of FD Joint Detection ......................... 22.5.1 Exploitation of Spatial and Frequency Diversity ..................................................... 22.5.2 Intracell Interference Cancellation ............. 22.5.3 Intra- and Intercell Interference Cancellation ...............................................

797 798 804

22.6

Conclusions ............................................................

821

22.7

List of Variables ...................................................... 22.7.1 Variables with Roman/Calligraphic Letters ....................................................... 22.7.2 Variables with Calligraphic Letters ............ 22.7.3 Variables with Greek Letters .....................

822


793

813

822 823 823

xx

Contents

23. Underwater Communication with Vertical Receiver Arrays .................................................................................

827

23.1

Introduction .............................................................

827

23.2

The Underwater Acoustic Channel ......................... 23.2.1 Transmission Loss and Ambient Noise ..... 23.2.2 Sound Speed Variability ............................ 23.2.3 Multipath Propagation ............................... 23.2.4 Doppler Effect ............................................ 23.2.5 Summary ................................................... Underwater Acoustic Communications – a Brief Overview ................................................................. 23.3.1 Incoherent Digital Receivers ...................... 23.3.2 Coherent Digital Receivers ........................

828 828 829 830 831 832

23.4

Spatial-temporal Receiver Architecture .................. 23.4.1 Communication Over Channels with ISI .... 23.4.2 Multichannel Digital Receiver .................... 23.4.3 Signal Model .............................................. 23.4.4 Multichannel Equalisation ..........................

834 834 835 837 839

23.5

Multichannel Constant Modulus Algorithm ............. 23.5.1 Blind Stochastic Gradient Descent Algorithms .................................................. 23.5.2 The Constant Modulus Algorithm .............. 23.5.3 Experimental Results ................................

841 841 842 844

23.6

Super-exponential Blind Equalisation ..................... 23.6.1 Iterative Shalvi-Weinstein Algorithm .......... 23.6.2 Recursive Shalvi-Weinstein Algorithm ....... 23.6.3 Adaptive Implementation ........................... 23.6.4 Experimental Results ................................

847 847 849 850 853

23.7


853

23.3

24. Reduced-rank Interference Suppression and Equalisation for GPS and Downlink CDMA ............................................. 24.1 Reduced-rank Interference Suppression and Equalisation ............................................................ This page has been reformatted by Knovel to provide easier navigation.

832 832 833

857 857

Contents 24.1.1 Motivation for Reduced-rank MMSE Processing ................................................. 24.1.2 Understanding the Multistage Wiener Filter .......................................................... 24.1.3 Lattice Structure of the MSWF .................. 24.1.4 MSWF Related to Wiener-Hopf Filter Weights .....................................................

xxi 857 858 861 862

24.2

Application of MSWF to CDMA Downlink ............... 24.2.1 Introduction ................................................ 24.2.2 Data and Channel Model ........................... 24.2.3 Edge of Cell/Soft Hand-off ......................... 24.2.4 Chip-level MMSE Estimator ....................... 24.2.5 Performance Examples .............................

24.3

Application of MSWF to GPS Jammer Suppression ............................................................ 24.3.1 Introduction ................................................ 24.3.2 Power Minimisation and Joint Spacetime Preprocessing .................................... 24.3.3 Space-time Filter Characteristics ............... 24.3.4 Data and Channel Model ........................... 24.3.5 Dimensionality Reduction Techniques ...... 24.3.6 Performance Examples .............................

871 872 873 875 876

Summary of Concepts Involving Reduced-rank Filtering ...................................................................

879

25. Introduction to Space-time Coding .....................................

883

24.4

864 864 865 866 866 868 871 871

25.1

Introduction .............................................................

883

25.2

Multiple Antenna Channel Model ............................

885

25.3

Benefits of Smart Antenna Technology .................. 25.3.1 Array Gain ................................................. 25.3.2 Diversity Gain ............................................ 25.3.3 Multiplexing Gain ....................................... 25.3.4 Interference Reduction ..............................

887 887 888 891 893


xxii

Contents 25.4

Background on Space-time Codes ......................... 25.4.1 Space-time Trellis Codes .......................... 25.4.2 Linear Space-time Block Codes ................

894 895 897

25.5

New Design Criteria ................................................ 25.5.1 Error Performance ..................................... 25.5.2 Capacity Performance ............................... 25.5.3 Unified Design ...........................................

898 899 900 901

25.6

Receiver Design ..................................................... 25.6.1 Modulation and Coding for MIMO .............

905 905

25.7


906

Index .................................................................................. 909


Section A

Suppression of clutter in moving radar

Parti

Space-slow time processing for airborne MTI radar

Chapter 1

Space-time adaptive processing for manoeuvring airborne radar Peter G. Richardson

1.1

Introduction

Since the early 1970s, STAP (space-time adaptive processing) methods have been actively considered for look down airborne radar where target signals have to compete with strong ground clutter returns. Most previous STAP research has been devoted to SLAR (sideways looking airborne radar) applications where the plane of the receiving antenna is coaligned with the direction of travel. For this type of antenna configuration, a linear relationship between the angular location and Doppler frequency of the clutter can be exploited to allow clutter rejection and enhanced signal detectability via twodimensional filtering in the spatial and temporal frequency domains. Appropriate filters can be realised via the sampling of a coherent pulse train with a phased array antenna. Non-adaptive filter weight solutions which theoretically achieve full clutter suppression in SLAR correspond to the well known DPCA (displaced phase centre antenna) technique, e.g. see References 1 and 16. STAP offers the advantage over DPCA that the filter weights are calculated adaptively. This leads to robustness in the presence of errors, e.g. amplitude and phase mismatch errors between channels, or drift in the platform velocity. STAP also offers the capability to simultaneously suppress jamming and clutter. Over the last ten years there has been growing interest in applying STAP techniques for clutter suppression in antenna orientations other than sideways looking. These include forward-looking array geometries where the plane of the array is transverse to the direction of travel [2-^], inclined looking array applications [5,6] and circular arrays [7]. In these cases, the plane of the receiving antenna is not coaligned with the direction of travel, and hence there is no longer a linear dependence between the clutter Doppler and spatial frequencies. The implication of this is that STAP cannot provide the full clutter cancellation that is theoretically possible in SLAR. However,

a major advantage of STAP over conventional MTI (moving target indication) and Doppler filtering approaches is that it offers the capability for detecting slow moving targets, i.e. targets lying within the Doppler bandwidth of mainlobe clutter. Analysis and simulations performed in Reference 2 demonstrated that a sideways looking geometry is not a prerequisite to achieving this. Further improvements in detection of targets, that are masked by either mainlobe or sidelobe clutter, can be achieved by adapting in a range-dependent, or Doppler-dependent manner. Examples of rangedependent STAP can be found in References 4 and 7. Examples of Doppler dependent, or post-Doppler, STAP can be found in Reference 7 and Chapter 9 of Reference 8. SLAR related STAP research is often directed at applications where the airborne radar platform is very large and stable, and the effects of platform manoeuvre can be assumed to be small. Typical examples are AEW (airborne early warning) radar [9-11 ] and SAR (synthetic aperture radar) [12]. In contrast, in forward-looking applications the array antenna is likely to be located in the nose of a relatively small and highly manoeuvrable airborne platform, e.g. as in AI (airborne intercept) radar. In these cases, the radar may be required to function while the platform is performing a steep dive or rolling at a significant rate, and any assumption that platform manoeuvre effects are negligible is less easy to justify. In this chapter we will assess the benefits of using STAP for simultaneously suppressing clutter and jamming in forward-looking phased array geometries. We will initially analyse the clutter suppression problem and show how significant rejection of both mainlobe and sidelobe clutter is achievable using appropriate STAP approaches. This will include a brief consideration of the effects of variations in the platform orientation (rather than the array orientation) on clutter suppression and slow moving target detection. The effects of manoeuvre (e.g. platform yaw, pitch or roll) on clutter and jammer suppression will then be examined and the relative merits of various approaches for compensating for platform manoeuvre will be assessed.

1.2

STAP fundamentals

Throughout this chapter we will consider a pulse-Doppler airborne radar where a coherent burst of M pulses are transmitted at a pulse repetition interval r. We will assume a phased array receive antenna consisting of N elements. The data received by the array at a time t can then be represented by the space-time snapshot vector: x(t) = [x\ (t), x2(t), X 3 (O,-.., xM(t)]T = [xi(t),xi(t

- r),xi(t - 2 r ) , . . . 9xx(t - (M - l ) r ) f e CMNxl

(1.1)

where xm(t) e CNxl is used to denote the spatial snapshot of data corresponding to the (M — m + l)th pulse repetition interval (PRI). In large phased array applications, the cost and complexity associated with digital adaptive processing at element level leads to the need to reduce the number of spatial channels. This reduction is commonly achieved by analogue beamforming of subarrays of elements prior to digitisation, e.g. see References 2, 4 and 8, Chapter 6.

For a system with K subarrays, the spatial channel reduction can be described mathematically by the NM by KM transformation matrix T:

(1.2)

where IM is the M by M identity matrix, Ts is the N by K spatial transformation matrix (K < N) and (g) represents the Kronecker matrix product. The transformed (KM by 1) space-time snapshot vector is then: xT(t) = THx(t)

(1.3)

where the superscript H denotes the Hermitian transpose operator. It is well known that the subarray level STAP filter weights that maximise the output signal-to-noise-plus-interference ratio (SNIR) are given by: w = kQ^sT(0,(/>,fD) = k[THQT]-lTHs(6,(f>,fD)

(1.4)

KMxKM

where k is an arbitrary scalar, QT e c is the covariance matrix of the transformed (subarray level) interference plus noise data, Q e cNMxNM is the corresponding covariance matrix for element level data, sj(#, 0, /b) is the subarray level steering vector for the target signal Doppler frequency / D and direction of arrival (0,0), and s(0,0, / b ) is the corresponding element level steering vector for the target signal. The covariance matrix QT must be estimated from the incoming data and this is usually achieved by forming the maximum likelihood estimate: (1.5) where S is the number of weight training data samples employed. It is usual to collect training data from range samples (sometimes referred to as fast time samples) that neighbour the range (or ranges) at which the adaptive weights are applied. Assuming data that are jointly Gaussian, independent and identically distributed, the value of S must exceed 2KM — 3 ~ 2KM to ensure that the expectation of the ratio of the adaptive SNIR to optimum SNIR is greater than 0.5 (i.e. the loss due to covariance matrix estimation is less than 3 dB) [13]. To determine the optimal subarray weights in equation (1.4), we clearly need to collect data from all M pulses. However, for large values of M it is unlikely that there will be sufficient weight training data available to support the adaptive weight calculation. In addition, the estimation and inversion of a KM by KM covariance matrix may not be possible in real time. It is therefore almost always necessary to reduce the number of temporal channels within the STAP architecture. This can be achieved using pre-Doppler STAP, where a space-time adaptive filter with a small number of tap delays is used as a prefilter to conventional Doppler processing, or by using post-Doppler STAP, where STAP with a small number of temporal or Doppler channels is employed after Doppler processing. Further details of these approaches

can be found in References 8 and 14 and will not be repeated here. It should be noted that in Reference 8 the pre-Doppler STAP approach is referred to as 'space-time FIR filtering'. Although pre-Doppler STAP is usually the more computationally efficient of the two methods, the post-Doppler STAP approach is often found to provide the more effective clutter suppression. In this chapter, most consideration will be given to pre-Doppler STAP implemented at subarray level in a large circular planar array in a forward facing geometry. With this architecture, clutter and jamming suppression can be achieved simultaneously by adaptively combining the outputs of the K spatially separated subarrays and L (with L IINS 2 tap STAP 3 tap STAP

roll rate, degs/PRI

Figure 1.19

Loss in SNlR as a function of roll rate, slow moving target scenario (from [17])

motion may typically take the form of rapid yaw, pitch or roll. If there is no motion compensation, the mainlobe clutter extent within the three-dimensional STAP sampling space is increased. The spreading is due to both the movement of the receiving array and the transmit beam. Simulation results showing the effects of platform roll on STAP slow moving target detection have previously been presented in Reference 17. The results, showing the loss in the output SNIR for a forward-looking airborne radar operating at an altitude of 5 km, are summarised in Figure 1.19. The curves shown are forpre-Doppler STAP architectures with two and three taps per subarray channel implemented in the chequerboard subarray scheme shown in Figure 1.10. The scenario geometry and radar waveform parameters were identical to those used to produce Figure 1.6. The adaptation was carried out using all available range samples with the STAP weights updated every PRI in an attempt to compensate for the effects of motion. The SNIR values were estimated directly from the range-Doppler maps using a simple cell averaged CFAR scheme. The curves in Figure 1.19 show the loss in SNIR (relative to the optimal value) as a function of roll rate. The results indicate that roll rates as small as 0.005° per PRI have significantly reduced slow target detection performance in this case, despite the fact that the adaptive weights were updated at the PRI rate. However, it should be noted that the effects of motion have been accentuated here by the simplified quantised transmit beampattern employed within the clutter model.

1.5.2 Motion compensation The effects of the platform motion on mainlobe clutter rejection can be reduced by motion compensating the beam steering to ensure that the same region of ground is illuminated by the radar main beam throughout the coherent processing interval. This ensures that both the transmit and receive beams are motion stabilised. The technique can be applied effectively in both pre-Doppler and post-Doppler STAP approaches.

target

range Doppler

Figure 1.20

Range-Doppler map - 3 tap STAP output, 0.01° /PRI platform yaw, PRI weight updates

Simulation results showing the effectiveness of the approach for a radar platform yawing at a rate of 0.010° per PRI are shown in Figures 1.20 and 1.21. For adaptive suppression of the clutter, a pre-Doppler STAP algorithm with three taps per subarray channel was implemented in the chequerboard subarray scheme shown in Figure 1.10. Figure 1.20 shows the range-Doppler map produced when the adaptive weights were updated every PRI. The effect of adapting to clutter and the platform rotation has significantly reduced the SNIR from the optimal level of 32 dB for this scenario. The output SNIR estimated from the range-Doppler map in this case was 15.4dB. The result obtained using motion-compensated beam steering with the beam resteered at the PRI rate is shown in Figure 1.21, and it is clear that more effective clutter suppression has been achieved. The SNIR estimated from the range-Doppler map shown in Figure 1.21 was 28.9 dB, an improvement of 13.5 dB. It should also be noted that this result was achieved using a single adaptive weight vector, calculated from data collected over the full coherent processing interval, rather than by updating the adaptive weights at the PRI rate. Motion-compensated beam steering is only effective for compensating for the effects of motion on signals within the mainlobe of the radar beam. The motioninduced angle-Doppler spreading of sidelobe clutter is therefore not mitigated with this approach. Another drawback of the method is that very fine control of the beam steer direction may be required. In conventional phased array beamforming, beam steering accuracy to very small fractions of a beamwidth is not usually necessary, and the scanning is typically achieved using analogue phase shifters employing small numbers of bits. The phase settings for the array elements are therefore heavily

target

range Doppler

Figure 1.21 Range-Doppler map - 3 tap STAP output, 0.01°/PRI platform yaw, motion-compensated beam steering quantised. In the simulation results above, the ability to steer the beam to an accuracy of greater that 1/200th of a beamwidth was assumed. For the array size considered, this leads to a requirement of more than 8 bits resolution for the element level phase settings. Time-dependent adaptive weighting methods have previously been suggested for countering motion effects in adaptive arrays [21]. In this approach, motion compensation is achieved by assuming that the optimal adaptive weight vector is a function of time, and expanding the weight vector as a Taylor series. Assuming that (k •+- l)th order terms and above can be neglected, the adaptive weight vector then becomes: w(t) = w(0) + tw(l) + • • • + tkw{k) + L. The effects can be reduced by applying time-dependent weighting [21], but this is at the cost of a significant increase in computation. Confirmation of the validity of the theoretical analysis can be obtained from examination of the eigenvalues of the covariance matrix, Q, used in the adaptive weight calculation. The number of eigenvalues significantly above the thermal noise level gives an indication of the number of adaptive degrees of freedom required to achieve jammer and clutter suppression. If the number of dominant eigenvalues approaches the total number of adaptive channels, then poor SNIR is likely to result. In Figure 1.22, pre-Doppler STAP covariance matrix eigenspectra are plotted for varying numbers of taps for a simulation scenario with the radar platform rolling at a rate of 0.36° per PRI. The receive antenna used in the simulation was the 2029 circular planar array partitioned into 16 subarrays shown in Figure 1.10. The radar was operating in the presence of three strong (60 dB above noise at the element level) sidelobe jammers.

1 tap 2 taps 3 taps 4 taps

eigenvalue no.

Figure 1.22

Pre-Doppler STAP jamming plus thermal noise covariance matrix eigenspectra, roll rate 0.36°/PRI, sidelobe jamming scenario

The eigenspectra in Figure 1.22 were obtained from the covariance matrices of the jamming plus thermal noise (i.e. with clutter excluded). The important point to note is that, as the number of taps is increased, the proportion of the total spectrum affected by jamming remains the same, as predicted by equation (1.17). This implies that the SNIR output should remain relatively unaffected as the number of taps in the processor is increased. In contrast, the eigenspectra shown in Figure 1.23 reveal that for the MTI/ABF covariance matrix the proportion of dominant eigenvalues increases with the number of taps. Simulation results showing the loss in SNIR as a function of the number of clutter rejection filter taps for the sidelobe jamming scenario are summarised in Figure 1.24. The results show the effect of adapting to jamming and thermal noise data alone, and hence spatial adaptive beamforming can potentially provide optimal performance. Exclusion of clutter allows the impact of the MTI filtering on the sidelobe jamming rejection to be examined in isolation. The adaptive weights were calculated from data collected over a PRI and the SNIR values were calculated from the average of ten simulation runs. The loss in SNIR is given as the output SNIR relative to the optimal level. It is evident from Figure 1.24 that there is only a slight loss in SNIR as the number of taps is increased in the STAP approach. This loss is mainly due to the increase in number of adaptive channels relative to the amount of data used in the adaptive weight calculation. In contrast, the MTI/ABF result shows higher losses in SNIR as the number of taps in increased. However, the difference in performance between STAP and MTI/ABF is always small (i.e. always less than 1 dB). This is due to the fact that the total number of spatial degrees of freedom (1.16) is far in excess of the number of jammers (1.3), and hence, when using the MTI/ABF approach, wide nulls can be formed to counter the apparent spatial spread of the jammers. The penalty

ABF 2 tap MTI/ABF 3 tap MTI/ABF 4 tap MTI/ABF

eigenvalue no.

SNIR loss, dB

Figure 1.23 MTI/ABF jamming plus thermal noise covariance matrix eigenspectra - roll rate 0.36° /PRI, sidelobe jamming scenario

STAP MTI/ABF

no. of taps

Figure 1.24

SNIR loss as a function of number of taps - sidelobe jamming scenario, no clutter, roll rate 0.36°/PRI (from [20])

for doing this is an increase in mean sidelobe levels, as shown in the results plotted in Figure 1.25. The sidelobe levels were calculated from the spatial beampattern evaluated at the target Doppler frequency. Manoeuvring adaptive arrays are extremely sensitive to mainlobe interference, e.g. see Reference 23. This is because extended nulls within the mainlobe of the beam are required to account for the relative jammer motion and this can lead to significant loss in gain in the desired signal direction. The relative performance of

mean sidelobe level, dB

STAP MTI/ABF

no. of taps

Mean sidelobe level as function of number of taps - sidelobe jamming scenario, no clutter, roll rate 0.36°/PRI

SNIR loss, dB

Figure 1.25

STAP MTI/ABF

no. of taps

Figure 1.26

SNIR loss as afunction ofnumber of taps - mainlobejamming scenario, roll rate 0.036°/PRI (from [20])

STAP and MTI/ABF architectures in a mainlobe jamming scenario is therefore of particular interest. Figure 1.26 shows the SNIR loss (relative to the optimal value) as a function of the number of clutter rejection filter taps for a mainlobe jamming simulation scenario where the radar platform was rolling at a rate of 0.036° per PRI. The receive array was again the chequerboard subarrayed configuration shown in Figure 1.10. The jammer was initially located at the —3 dB point of a beam steered off at an angle of 60° from broadside to the array. Clutter was not included in the

simulation. Figure 1.26 shows that there is a significant loss in SNIR as the number of taps is increased in the MTI/ABF architecture. In comparison, STAP is relatively robust to the manoeuvre effects, and for four taps the output SNIR is more than 10 dB higher than that achieved with MTI/ABF. The losses when using MTI/ABF are significantly above those obtained in the sidelobe jamming scenario despite the fact that the platform rotation rate is a factor often less. In Section 1.5.2, it was shown that motion compensation of the beam steer direction helps to reduce the effects of platform motion on mainlobe clutter rejection when using STAR In mainlobe jamming scenarios, motion-compensated beam steering also helps to correct for the relative jammer motion, and hence it is clearly of benefit to apply this technique in scenarios containing mainlobe clutter and jamming. The motion-compensated beam steering approach is appropriate to both MTI/ABF and STAP architectures, but does rely on the phase quantisation being fine enough to allow accurate resteering of the beam. It should also be noted that there are cases where the approach will offer little or no benefit in terms of interference rejection. The case where the beam is at broadside to the array and the platform is rolling is an obvious example. Fortunately, the effects of the relative jammer motion are likely to be insignificant in this geometry, as the mainlobe jammer angular displacement from the roll axis is small. In contrast to the mainlobe jamming case, motion-compensated beam steering tends to accentuate the relative motion of sidelobe jammers. In situations where the number of spatial degrees of freedom far exceeds the number of sources of interference, the effects on adapted sidelobe levels and jammer rejection are likely to be small.

1.7

Summary

STAP techniques can provide simultaneous rejection of jamming and clutter in airborne radar. Although, in the past, STAP has been considered mainly for SLAR applications, there has been growing interest in applying the technique to non-side-looking radar geometries. In this chapter we have considered STAP for forward-looking airborne radar where the array of sensors is orientated transversally to the direction of travel. In forward-looking applications (e.g. AI radar), the effects of platform manoeuvre can be of greater significance than in typical SLAR applications (e.g. AEW and SAR). For example, detection and tracking of targets may be required in situations where the radar platform is performing a steep dive or rolling at a rapid rate. One of the greatest advantages of STAP over conventional signal processing methods is the potential it provides for detecting targets which possess the same Doppler as mainlobe clutter returns (i.e. slow moving targets). In this chapter, we have paid particular attention to the effect of variations in platform orientation and manoeuvre on slow target detection performance. In the scenarios involving constant platform velocities, it has been demonstrated that the slow target detection capability is not sensitive to the platform orientation. In particular, it has been shown that slow target detection can be achieved when the radar platform is performing a steep dive.

The effects of platform manoeuvre on STAP slow target detection performance have also been examined. Simulation results indicate that performance can be sensitive to the effects of roll and yaw. The most effective way of countering the effect of the platform motion is to motion compensate the beam steering to ensure that the target and the same region of ground are illuminated by the radar main beam throughout the coherent processing interval. Techniques involving application of time dependent weighting, or rapid updating of the adaptive weights are only partially effective as they cannot fully compensate for the effects of the transmit beam motion. It has been demonstrated that, under conditions of manoeuvre, pre-Doppler STAP techniques can provide better jammer rejection performance than architectures which cascade conventional clutter filtering and spatial adaptive beamforming. In cases where there is no compensation of the beam steer direction, differences in performance are most apparent in the presence of mainlobe jamming. The effects of platform motion on mainlobe clutter and jammer rejection can be reduced by motion compensation of the beam steering direction, but this approach is likely to accentuate the relative motion of sidelobe jammers.

References 1 RICHARDSON, R G.: 'Relationships between DPCA and adaptive space time processing techniques for clutter suppression'. Proceedings of the international conference on Radar, Paris 1994, pp. 295-300 2 RICHARDSON, R G. and HAYWARD, S. D.: 'Adaptive space-time processing for forward looking radar'. Proceedings of IEEE international Radar conference, Alexandria, VA, USA, May 1995, pp. 629-634 3 KLEMM, R.: 'Adaptive airborne MTI: comparison of sideways and forward looking radar'. Proceedings of IEEE international Radar conference, Alexandria, VA, USA, May 1995, pp. 614-618 4 KLEMM, R.: 'Adaptive airborne MTI with tapered antenna arrays', IEE Proc, Radar Sonar Navig, 1998,145, (1), pp. 3-8 5 WANG, Y.-L., PENG, Y-N., and BAO, Z.: 'Space-time adaptive processing for airborne radar with various array orientations', IEE Proc. Radar Sonar Navig., 1997,141, (6), pp. 330-341 6 BOSARI, G. K.: 'Mitigating effects on STAP processing caused by an inclined array'. Proceedings of IEEE national Radar conference, Dallas, TX, 1998, pp. 135-140 7 ZATMAN5M.: 'Circulararray STAP',IEEETrans. Aerosp. Electron. Syst, 2000, 36, (2), pp. 510-517 8 KLEMM, R.: 'Principles of space-time adaptive processing' (The Institution of Electrical Engineers, London, UK, 2002) 9 WANG, H., ZHANG, Y, and ZHANG, Q.: 'A view of the current status of space-time processing algorithm research'. Proceedings of IEEE international Radar conference, Alexandria, VA, USA, May 1995, pp. 635-640

10 BROWN, R. D., WICKS, M. C , ZHANG, Y., ZHANG, Q., and WANG, H.: 'A space-time adaptive processing approach for improved performance and affordability'. Proceedings of IEEE national Radar conference, Ann Arbor, Michigan, 13-16 May 1996, pp. 321-326 11 FARINA, A., SAVERIONE, A., and TIMMONERI, L.: 'MVDR vectorial lattice applied to space-time processing for AEW radar with large instantaneous bandwidth', IEE Proc, Radar Sonar Navig., 1996, 143, (1), pp. 41-46 12 ENDER, J. H. G.: 'Space-time processing for multichannel synthetic aperture radar', Electron. Commun. Eng. J., 1999, February, pp. 29-38 13 REED, I. S., MALLETT, J. D., andBRENNAN, L. E.: 'Rapid convergence rate in adaptive arrays', IEEE Trans. Aerosp. Electron. Syst, 1974,10, (6), pp. 853-863 14 WARD, J.: ' Space-time adaptive processing for airborne radar'. Technical report no. 1015, MIT Lincoln Laboratory, December 1994 15 HERBERT, G. M. and RICHARDSON, P. G.: 'A constrained adaptive pattern synthesis technique for space-time filtering architectures'. Proceedings of the DGON international Radar symposium, 1998, Munich, Germany, pp. 857-866 16 TAM, K. and FAUBERT, D.: 'Displaced phase centre antenna clutter suppression in space-based radar applications'. Proceedings of Radar '87^ IEE Conf. Publ. 281, pp. 385-389 17 RICHARDSON, P. G.: 'Space-time adaptive processing for manoeuvring airborne radar', Electron. Commun. Eng. J., 1999, February, 77, (7), pp. 57-63 18 PAINE, A. S.: 'Comparison of partially adaptive STAP techniques for airborne element digitised phased array radar'. Proceedings of the IEE international Radar conference 2002, Edinburgh, UK, October 2002, IEE Conf. Publ. 490, pp. 181-185 19 REES, H. D. and SKIDMORE, I. D.: 'Adaptive attenuation of clutter and jamming for array radar', IEE Proc, Radar Sonar Navig, 1998, 145, (4), pp. 193-199 20 RICHARDSON, P. G.: 'Effects of manoeuvre on space-time adaptive processing performance'. Proceedings of the Radar '97 conference, Edinburgh, October 1997, IEE Conf. Publ. 449, pp. 285-290 21 HAYWARD, S. D.:' Adaptive beamforming for rapidly moving arrays'. Proceedings of the CIE international conference on Radar (IEEE Press), Beijing, China, October 1996, pp. 480^83 22 MELVIN, W. L., CALLAHAN, M. J., and WICKS, M. C : 'Adaptive clutter cancellation in bistatic radar'. Record of 34th Asilomar conference on Systems, signals and computers, IEEE 2000, pp. 1125-1130 23 BALLANCE, W. P. and MILLER, T. W.: 'Impact of mainlobe interference angular extent on adaptive beamforming'. Conference record of 25th Asilomar conference on Signals, systems and computers, CA, November 1991, pp. 989-993

Chapter 2

Non-linear and adaptive two-dimensional FIR filters for STAP: theory and experimental results Pierfrancesco Lombardo and Fabiola Colone

2.1

Introduction

A significant challenge for the effectiveness of STAP techniques against real data is presented by the operation against severe and non-homogeneous interference environments. In particular, an airborne early warning (AEW) surveillance radar platform, whose mission is to detect low radar cross section targets, must contend with high levels of undesired clutter returns from both land and sea surfaces. This must operate with a large number of degrees of freedom (DoF) to be able to cancel strong clutter echoes accurately. However, it is impossible to use such a large number of degrees of freedom adaptively, since this would yield unacceptable adaptivity losses [I]. Moreover, the real-time implementation requirements demand the use of filters with a low computational cost. The clutter environment also includes returns from clutter of various sea states, terrain types (i.e. desert, hills, mountains) and large discretes and becomes particularly severe in regions encompassing varying ground surfaces such as regions connecting land and sea. This clutter non-homogeneity limits the amount of homogeneous secondary data available for the adaptive algorithms. Moreover, the presence of interfering targets as well as intense, high-power coherent jamming also affects radar system performance, by contaminating the estimations of the clutter characteristics. Thus the techniques to be applied in practice should be robust to their presence. Many reduced DoF techniques have been proposed to achieve at the same time a reduced computational cost and the requirement for a limited set of homogeneous secondary data without suffering very large adaptivity losses. However, when operating in a highly non-homogeneous environment or in the presence of interfering targets, the robustness of most linear approaches can be gained only at the expense of

a large increase in the computational load. In this chapter, we describe three possible solutions for robust and effective STAP of radar data: (i) adaptive two-dimensional FIR filters with small support (ii) non-linear non-adaptive schemes (iii) non-linear combination of adaptive two-dimensional FIR filters. The performances are evaluated and compared both by a theoretical analysis and by application to a set of recorded radar data. In summary, the non-linear adaptive detector promises remarkable detection performance in a non-stationary clutter background containing interfering targets.

2.2

Adaptive linear filters

We consider a radar system with K spatial channels. Each of these receives M echoes from a transmitted train of M coherent pulses with a pulse repetition interval (PRI) of T seconds. Let xmj be the radar echo at the /th spatial channel (/ = 1 , . . . , K) in response to the rath pulse (ra = 1 , . . . , M). The KM echoes can be arranged into the ATM-dimensional column vector x = [x* . . . x^]*, xm being the column vector of the K echoes received at the rath pulse. The corresponding vector for the echoes from a target with Doppler frequency F (normalised to PRF = 1 /PRI), direction of arrival (DoA) (p and complex amplitude A is defined as: sf(F,(p) = As = A[s*(F, 4 are able to maintain a false alarm rate approximately constant (Figure 2.14d); moreover, only the MTO detector with P = 5 yields a high detection performance (Figure 2.14e). This is also confirmed by the probability of correct filter selection in Figure 2.14f. Notice that with this new non-linear adaptive filter, globally P • Q secondary data are used, so that the probability of including interfering targets is P times larger than when using a single block of Q secondary data. However, in the presence of closely spaced target sequences these interferences cannot be avoided and the presented non-linear adaptive filters are effective despite their presence. This can be easily verified from Figures 2.15 and 2.16 which show the results of the nonlinear adaptive AR schemes against the real data set, with the test configuration of Table 2.1. The non-linear adaptive MRP detector with P = 2 blocks of Q = 16 cells and the non-linear adaptive MRP detector with P-A blocks of Q = 8 are shown in Figures 2.15a and 2.15b, respectively. They yield a very similar detection capability except for set G, where all targets are extracted when operating with P = 4, and the central target is lost when operating with P = 2. In fact, in the latter case both adjacent blocks of secondary data are affected by the strong interfering targets, while the central target of set G is small. Figure 2.16a shows the test statistic of the MTO detector with P = 3 and Q = 10. As apparent, all targets are extracted; when setting a threshold to detect all of them, only a single false detection cannot be avoided. Figure 2.16b shows the result obtained using the MTO detector with P = 5 blocks of Q = 4 cells. As apparent, the targets are extracted better from the clutter and they can be very easily detected by setting a threshold, without suffering any false alarm. Finally, Figure 2.16c shows that increasing the size of the individual blocks does not yield any further performance improvement. Figures 2.17a and 17b show the filter selection around target set D, corresponding to the results of Figures 2.15b and 2.16b, respectively. Notice that in this case there are some errors in the filter selection; however, these errors never appear in a cell containing a real target to be detected (cells 360 and 363). Moreover, the test statistic always has a low value in correspondence of such errors, implying that the filter operates correctly and no targets are detected in those range cells. This justifies the good performance of the non-linear adaptive detectors. It is also interesting to observe that both non-linear adaptive MRP and MTO detectors are

test statistic, 10 log 10 (T) test statistic, 101Og10 (T)

range bin

range bin

Figure 2.15

MRP test statistic versus range against recorded data by AAFTE for the targets test configuration of Table 2.1 a P = 2 and Q = 16 b P = 4 and 0 = 8

also able to correctly extract target set I, which was lost by the non-linear non-adaptive schemes. This can easily be explained recalling that this target set is close to a largely non-homogeneous area, containing a river and its banks. Under such conditions, the bank of adaptive filters (MTO with P = 5 blocks of Q = 4 cells) clearly outperforms the bank of non-adaptive filters (AR-based non-linear with median CFAR on P = 5 blocks of Q = 4 cells).

2.6

Conclusions

In the practical application of adaptive STAP filters against real data, one of the main problems is represented by non-homogeneity of the clutter background and the possible presence of interfering targets among the secondary data used to derive the filter parameters. The latter problem was recognised to be critical for the possibility of properly extracting sequences of closely spaced target echoes. Since the probability that interfering targets affect the secondary data is directly proportional to the number of secondary range cells, a first way to mitigate the problem can be to use STAP techniques that are effective even when operating with a very limited amount of secondary data. A two-dimensional FIR filtering scheme, based on the AR model for the disturbance, was considered to this purpose. The filter was shown to perform

test statistic, 101og10(T) test statistic, 101og10(T)

range bin

test statistic, 10 log 10 (T)

range bin

c

Figure 2.16

range bin

MTO test statistic versus range against recorded data by AAFTE for the targets test configuration of Table 2.1 a P = 3 and Q = 10 b P = 5 and Q = 4 c P = 5 and Q = 6

effectively against the real environment. Specifically for our case even with Q = S secondary data such a filter was shown to yield a detection performance very close to the JDL with Q = 32 secondary data. Moreover, the AR-based FIR filter is a pre-Doppler technique, where the optimisation is independent of the subsequent Doppler filter bank. This also requires a largely reduced computational cost, which is especially important for real-time applications. Unfortunately, when using only few secondary data, the possible presence of an interfering target among them produces a much more devastating effect. This is because the undesired contribution in the sample covariance matrix is averaged with

filter selection filter selection

range bin

b

Figure 2.17

range bin

Filter selection versus range against recorded data by AAFTE for targets test configuration of Table 2.1 (zoom around target set D) a MRPP = 4 a n d £ = 8 b MTO for P = 5 and Q = 4

a smaller number of uncontaminated data. Therefore, the use of two-dimensional FIR filters with short temporal support and limited adaptivity losses does not solve all of the problems, and alternative techniques were considered. In particular, a nonlinear non-adaptive scheme was considered, which is based on the selection of the most appropriate non-adaptive filter out of a bank of filters with different cancellation characteristics. The scheme was shown to yield a good clutter cancellation against the real data and to select the most appropriate filter even in the presence of interfering targets in the secondary data. However, the subsequent CA-CFAR normalisation is still largely affected by the presence of the interference. To solve the problem, a new non-linear non-adaptive filter was introduced that first selects the most appropriate non-adaptive two-dimensional cancellation filter and then selects a block of secondary data that is likely to be uncontaminated. This is obtained by splitting the secondary data in P blocks of range cells and applying the median operator to their mean power, based on the assumption that only a few range cells are expected to be contaminated by other targets. Moreover, to reduce the computational cost of the non-linear filter, the Gaussian filters are replaced with AR-based non-adaptive FIR filters and the filter selection is performed using only the output power corresponding to the CUT. This scheme is shown to be effective against the real data even when a few sets of closely spaced targets are injected. The only weakness of this filter consists in the limited capability of such a scheme to adapt to different and changing clutter conditions as well as to mismatches between assumed and real platform motion parameters and to potential calibration errors in the antenna array.

Finally, two new non-linear adaptive STAP schemes have been presented for the target detection against a non-homogeneous environment. These filters are obtained by selecting the most appropriate filter among a set of two-dimensional AR-based adaptive FIR filters, obtained by estimating the AR parameters on P different blocks of secondary data. Their effectiveness against the presence of interfering targets has been shown both by means of simulated analysis and by application to a real data set. The adaptive nature of the individual filters ensures that the non-linear adaptive scheme is able to cope with any mismatch in system and environment conditions. Moreover, the low computational cost of the proposed schemes, together with their robustness to non-homogeneity and interference, makes them appealing for the practical real-time application. 2.7

Acknowledgments

The authors gratefully thank Dr Alfonso Farina (AMS) for many fruitful discussions on these topics and for his encouragement in this work. They also acknowledge the possibility to use the AAFTE data set collected during the work of Dr Fred Staudaher and Dr Fred Lee and their group at the Radar Division of NLR. Finally, they acknowledge the collaboration with FIAR Spa that originated some of the theoretical and simulated results presented in Sections 2.3 and 2.5. 2.8

Appendix: ML estimation of two-dimensional AR parameters

Using the matrix Y, the joint PDF of the secondary data is simply written as:

(2.21) By defining the matrix L so that R it yields:

x

= LL* and M^y (2.22)

where B =

(2.23)

For convenience, we decompose the matrix MLY in blocks of size K(L — 1) and K, respectively:

(2.24)

Using equation (2.24), the value of B that maximises the exponent of equation (2.22), under the constraint of having the last ^-dimensional block equal to the identity matrix, is:

(2.25)

Therefore, we have the ML estimate A = M^00MyOi • Using this value, we have for the trace: tr{K*KMLY} = ?r{-M* y o l M-^ 0 0 M L y 0 i + M L n i } = f r f - L L ^ M ^ 1 ] ^ } (2.26) where [My ]^,L is the last KxK block in the main diagonal of the inverse of My. Therefore, the maximum of the PDF with respect to A can be rewritten as: max{/?0(Y)} =

(TT-K\R\)^M-L+1)

exp[-;r{R~ 1 PV^ 1JZ i l l

A

By maximising equation (2.27) with respect to R, 1/(2(M-L +I))[M"1]^.

(2.27)

'

it yields R

=

References 1 KLEMM, R.: 'Principles of space-time adaptive processing-principles and applications' (IEE, London, 2002, 2nd edn.) 2 KELLY, E. J.: 'An adaptive detection algorithm', IEEE Trans. Aerosp. Electron. Syst., 1986, AES-22, (1), pp. 115-127 3 BRENNAN, L. E., MALLET, J. D., and REED, I. S.: 'Adaptive arrays in airborne MTI radar' IEEE Trans. Antennas and Propagation, 1976, AP-24, (5), pp. 607-615 4 WANG, H. and CAI, L.: 'On adaptive spatial-temporal processing for airborne surveillance radar systems', IEEE Trans. Aerosp. Electron. Syst., 1994, AES-30, (3), pp. 660-670 5 LOMBARDO, P., GRECO, M. V., GINI, R, FARINA, A., and BILLINGSLEY, J. B.: 'Impact clutter spectra on radar performance prediction', IEEE Trans. Aerosp. Electron. Syst., 2001, AES-37, (3), pp. 1022-1038 6 FARINA, A., GRAZIANO, R., LEE, F., and TIMMONERI, L.: 'Adaptive space-time processing with systolic algorithm: experimental results using recorded live data'. Proceedings of international conference on Radar, Radar 95, Washington D.C., 8-11 May 1995, pp. 595-602 7 FARINA, A., LOMBARDO, R, and PIRRI, M.: 'Non-linear space-time processing for airborne early warning radar', IEEProc, Radar Sonar Navig., 1998,145, (1), pp. 9-18 8 FARINA, A., LOMBARDO, P., and PIRRI, M.: 'Non-linear STAP processing', Electron. Commun. Eng. J., 1999, 11, (1), pp. 41-48

9 KAY, S. M. and NAGESHA, V.: 'Maximum likelihood estimation of signals in autoregressive noise', IEEE Trans. Signal Process., 1994, SP-42, (1), pp. 88-101 10 LOMBARDO, P.: 4DPCA processing for SAR moving target detection in the presence of internal clutter motion and velocity mismatch'. Microwave sensing and synthetic aperture radar, EUROPTO, 2958, September 1996, Taormina, Italy, pp. 50-61 11 LOMBARDO, P.: 'Optimum multichannel SAR detection of slowly moving targets in the presence of internal clutter motion'. CIE-ICR'96, international Radar conference, Beijing, China, 8-11 October 1996, pp. 321-325 12 KLEMM, R. and ENDER, J.: 'Multidimensional digital filters for moving sensor arrays'. Proceedings IASTED on Signal processing and digital filtering, June 1990, Lugano, Switzerland, pp. 9-12 13 KLEMM, R. and ENDER, J.: 'Two-dimensional filters for radar and sonar applications'. Signal Processing V EUSIPCO, September 1990, Barcelona, Elsevier Science Publisher, B.V., pp. 2023-2026 14 WICKS, M. C , MELVIN, W. L., and CHEN, P.: 'An efficient architecture for nonhomogeneity detection in space-time adaptive processing airborne early warning radar'. IEE international Radar conference, Radar'97, October 1997, Edinburgh, UK, pp. 295-299 15 ADVE, R. S., HALE, T. B., and WICKS, M. C : 'Practical joint domain localised adaptive processing in homogeneous and nonhomogeneous environments. Part 2: Nonhomogeneous environments', IEEProc, Radar SonarNavig., 2000,147, (2), pp. 66-74 16 FARINA, A.: 'Linear and non-linear filters for clutter cancellation in radar system', Signal Process., 1997, (59), pp.101-112 17 FARINA, A., LOMBARDO, P., and CARAMANICA, F.: 'Non-linear nonadaptive clutter cancellation for airborne early warning radar'. IEE international Radar conference, Radar'97, Edinburgh, October 1997, pp. 420^24 18 KLEMM, R.: 'Adaptive clutter suppression for airborne phased array radar', IEE Proc. F and H, 1983,130, (1), pp. 125-132 19 LOMBARDO, P.: 'Echoes covariance modelling for SAR along-track interferometry'. IEEE international symposium IGARSS '96, Lincoln, Nebraska, USA, May 1996, pp. 347-349 20 LOMBARDO, P. and COLONE, F.: 'Non-linear STAP filters based on adaptive 2D-FIR filters'. IEEE Radar conference, Alabama, USA, May 2003, pp. 51-58

Chapter 3

Space-time techniques for SAR Alfonso Farina and Pierfrancesco Lombardo

3.1

Summary

This contribution describes the application of STAP (space time adaptive processing) to synthetic aperture radar (SAR) systems. SAR is a microwave sensor that allows us to have a high resolution mapping of electromagnetic (EM) backscatter from an observed scene. A two-dimensional image is provided in the radar polar coordinates, i.e. slant range and azimuth. High resolution in slant range is obtained by transmitting a coded waveform, with a large value of the time-bandwidth product, and coherently processing the echoes in a filter matched to the waveform. High resolution along the transversal direction is achieved by forming a synthetic aperture. This requires us to: (i) put the radar on board of a moving platform, e.g. an aircraft or a satellite (ii) record the EM signals from each scatterer which is illuminated by the moving antenna beam in successive instants of time (iii) coherently combine the signals - via a suitable azimuthal matched filter - thus focusing the sliding antenna pattern in a narrower synthetic beam [I]. The advantage of combining SAR and STAP is evident: the detected moving target is shown on top of the SAR image of the sensed scene. This Chapter describes in detail the multichannel SAR (MSAR). 3.2

Description of the problem and state of the art

In many applications (e.g. surveillance) of SAR, it is desirable to detect and possibly produce focused images of moving objects. A moving low RCS object is not easily detectable against strong echoes scattered from an extended fixed scene. When detected, its resulting image is smeared and ill positioned with respect to the stationary background. These shortcomings are a direct consequence of the SAR image

formation process. The cross-range high resolution in an SAR is obtained by taking advantage of the relative motion, supposed known, between the sensor and the scene. If, however, there is an object moving in an unpredictable manner, the image formation process does not function properly. Basically, the main degradations due to the target motion are: (i)

(ii)

The range migration through adjacent resolution cells (due to the radial velocity of target with respect to radar) causes a reduction of the signal-to-clutter power ratio, which can seriously impair the detection capabilities. Furthermore, range migration causes a decrease in the integration time and a consequent loss of resolution. Even in the absence of range migration, or after its correction, the phase shift induced by the motion causes: an ill-positioning (along track) of the target image with respect to ground, mainly owing to the range component of the relative radar-target velocity; a smearing of the image due to the uncompensated cross-range velocity and/or range acceleration.

An initial possibility that has been studied for discriminating the moving target signals from the fixed scene returns is on the basis of their different Doppler frequency spectra; see, for instance, Reference 2 and Reference 37. In fact, the target spectrum has a Doppler centroid approximately linearly proportional to the along-range velocity of target and a spectrum width depending on the azimuthal velocity and the radial acceleration components of target. Assuming that the radar pulse repetition frequency (PRF) is high enough to make available a region in the Doppler frequency domain not occupied by the stationary scene, the method works as follows (see Section 3.4.2 for details). First, transform a sequence of radar target returns to the frequency domain. Second, locate spectral bands, outside the narrowband frequency around the origin corresponding to stationary scene, and determine the centre frequencies of such bands. Third, translate each outlying spectral band to the origin, convert the resulting signal back to the time domain and correlate with the reference function of the conventional SAR. The correlator output will show the peaks in the correct locations of the targets. A refinement of this basic technique aims at the image formation of each target: it is obtained by also matching the width, not only the mean value, of the spectral band outside the stationary scene Doppler spectrum. The method suffers, however, from three shortcomings: (i)

It requires the use of a high PRF which causes a corresponding reduction of the SAR swath width and an increase of the data throughput. (ii) It does not correctly focus the image of a target having a quite arbitrary path. The spectrum of the target echoes alone is not sufficient; we need to know the instantaneous phase law to form the synthetic aperture with respect to the moving target. (iii) It does not succeed with a target whose motion has a small range velocity component, so that its spectrum is superimposed on the clutter (i.e. on the stationary scene) spectrum.

A distinct advantage of this system relates to the possibility of using it with conventional, non-multichannel phased array radar antennas. More powerful methods have been conceived to overcome these drawbacks; they are based on the use of more than one antenna, on board the moving platform, to cancel the clutter and detect the slowly moving targets. The radar system uses an array of antennas, mounted on the platform along the flight direction, and corresponding receiving channels. This makes available a certain number of space samples (echoes received from different antenna elements) and time samples (echoes collected at different time instants). These echoes are coherently combined, with proper weights, in a space-time processor to cancel the echo backscattered from the ground and enhance the target echo. Space-time effectively reduces the lower bound on the minimum detectable target velocity that would be established by using only frequency filtering. It measures the relative phase between two or more coherent signals, received from different antennas, rather than the Doppler frequency shift within a single receiving channel. Instead of using mono-dimensional filtering, clutter cancellation is the result of a powerful two-dimensional (in the temporal frequency, i.e. Doppler, and in the spatial frequency, i.e. azimuth angle) filtering. Furthermore, this method does not require necessarily to work with high PRF values. This is the STAP approach: see References 3, 4 and 5 for details. However, the conventional STAP techniques have to be extended to be made compatible with the MSAR case, which is intrinsically characterised by a long integration time, during which both target and clutter Doppler and direction of arrival (DoA) change. These characteristics are reviewed in Section 3.3, and Section 3.4.1 presents a taxonomy of a number of MSAR processing techniques proposed in the literature to jointly exploit the effectiveness of SAR and STAP techniques. The way to fully-fledged STAP wasn't immediate: after leaving the single-channel approach (Section 3.4.2) it passed through ATI applied to SAR (described in Section 3.4.4) and DPCA (see Section 3.4.3); both techniques being essentially based on the use of the echoes captured by two antennas. A refinement of ATI-SAR was the VSAR (velocity SAR) method [6]. In a way similar to the progression from a two-pulse canceller to a bank of Doppler filters to reject clutter and detect moving targets in a conventional search radar, the technique can be generalised to a linear array of identical antennas. For each channel a complex SAR image is focused. A Fourier transform along the physical aperture (i.e. the channel number) is applied to each pixel, and this corresponds to a multiple beam former. For each Fourier cell the related image shows the scene for a certain range of radial velocities (velocity SAR image [6]). This method wasn't, however, originally designed to suppress clutter, since no attempt is made to subtract signals. The requirement to cancel the echoes from stationary scatterers leads directly to adaptive space-time filtering. Two classes of advanced STAP techniques are considered in particular for the MSAR case: (i) time-domain reduced DoF (degrees of freedom) adaptive two-dimensional finite impulse response (FIR) filters (Sections 3.4.5.2, [7-11] and Section 3.4.6) (ii) frequency-domain reduced DoF adaptive processing [12].

Finally, Section 3.4.6 considers the optimum MSAR approach in a special case for the clutter characteristics, to gain insight into the properties of the optimum filter and its effectiveness. This can be used for comparison of the different filters and yields the upper bound for achievable performance. Once the presence of a moving target has been detected, we have to estimate its phase modulation law to be able to form a high resolution image of it. A method for providing the estimate is by means of time-frequency analysis of the received signal (Section 3.4.5.1). This, combined with STAP, brings us to the joint spacetime-frequency processing presented in detail in Section 3.4.5.2. The time-frequency representation is obtained by evaluating the Wigner-Ville distribution (WVD) of the signal. This distribution is a signal representation consisting in the mapping of the signal onto a plane whose coordinates are time and frequency. The WVD, in particular, produces a mapping such that the signal energy is concentrated along the curve of the instantaneous frequency. This frequency is obtained as the centre of gravity of the WVD; the instantaneous phase is derived by integration of the instantaneous frequency. The clutter echoes are cancelled by the adaptive space-time processor, where the space-time covariance matrix of clutter is estimated online and used to evaluate the optimal weights of the two-dimensional filter. The time-frequency analysis provides an estimation of the instantaneous frequency of the possibly present moving target, and - by integration - the original instantaneous phase. The phase is used to compensate for the shift due to the relative target-radar motion.

33

Model of MSAR echoes

3.3.1 Aberrations due to target motion There are some interesting effects that occur with moving targets. A moving target with a radial component of velocity vr results in a Doppler shift on each echo of: /o = ^

(3.1) C

where /o is the radar carrier frequency and c is the velocity of propagation. Thus the Doppler history of the sequence of echoes is shifted in frequency (solid line of Figure 3.1), and is matched filtered with a reference chirp (dashed line of Figure 3.1). This produces a shift in the azimuth position, which is given by the product of the target Doppler shift and the slope of the Doppler history

yb-£ = ^

0.2)

where v is the platform speed, r is the platform-target range and d is the along-track dimension of the antenna (the real aperture). It is well known that an image from an aircraftborne SAR of a moving train having a component of velocity in the range direction appears shifted, so it appears to be travelling not along the railway track, but displaced to the side! As another example, a ship in a satellite SAR image with a radial velocity of 10 m/s at a range of 1200 km would experience an azimuth shift of

5 CN

Il ^S

JO

I I ex

a O

1 synthetic aperture length = rl/d

Figure 3.1 A target with a radial velocity (solid line) is matched filtered with the SAR azimuthal reference chirp (dashed line) 1.7 km. On the other hand, the ship wake (which is stationary) appears in the correct position. Thus the ship appears not at the tip of the wake, but displaced in azimuth. This effect is visible in a number of spaceborne SAR images. From knowledge of the geometry, and of the azimuth shift, it is possible to estimate the target velocity.

3.3.2 Space-time-frequency representation The MSAR allows Doppler and angular information to be decoupled by means of the along-track interferometric processing. The derivation of optimum clutter cancellation schemes for moving target detection requires the definition of a model for the covariance of the MSAR space-time clutter echoes to take full advantage of this potentiality. Moreover, a proper representation space for the resulting MSAR space-time model is required to adequately interpret the results. Both models and representations are available separately for single-channel SAR, where the long observation time and the consequent non-linear phase history of the echoes are the main issues, and for multichannel systems [4, Chapters 2 and 3], which assume, on the contrary, a short integration time and focus on the angular characteristics. In this section, a simplified closed-form model for the MSAR echoes is described, which takes into account both non-linear phase modulation and angular position at the same time and defines a proper representation space for it. Even though simple to handle, the model encodes all the main characteristics of the scattering from the observed scene [13]. 3.3.2.1 Echoes from homogeneous correlated clutter A simplified condition is assumed in the following, for which the radiation patterns of transmitting and receiving antennas have the same width. This allows us to reduce again the analytical complexity of the analysis, while considering the effect of parameters. The simplified model is used in the present section to include the effect

TX/RX array antenna

Figure 3.2

The multichannel SAR observation geometry (PRT:pulse repetition time)

of the terrain reflectivity correlation. With reference to the slant plane geometry in Figure 3.2, assume that the radar transmitting antenna moves, with constant velocity v, along a straight trajectory at a fixed distance Ro from the g-axis (crossing the r-axis at time t = 0) and has a fixed pointing, orthogonal to the flight path. The sequence of echoes relative to the TV pulses, transmitted with pulse repetition time PRT, is received by a uniform linear array of K antennas, parallel to the radar trajectory. The K receiving antennas have separate receiving channels and phase centres at distance Sk = (k — (K — l)/2) A, k = 0 , . . . , K — 1 from the transmitter. A pointlike scatterer T is assumed to be for t = 0 on the g-axis at the position xq and to move with velocity components vq and vr along the two axes q and r, named along-track and cross-track. It is further assumed that: (i) the range cell migration is negligible or has been corrected for (ii) the two-way antenna pattern, for the channel k, has the Gaussian shape gk [y] = \/{y/nXq) exp[— (y — sk/2)2/X^\, Xqy being the along-track position of the scatterer relative to the phase centre of the transmitter (iii) quadratic terms in the receiving antennas displacements can be neglected and the Fresnel approximation is valid for the distance of the scatterer from the transmitter (narrow antenna pattern). Thus the echo received by the &th receiving antenna at time tn = (n — (N — l)/2) PRT, n = 0 , . . . , Af — 1 can be modelled as:

(3.3)

where Ao and O are constant amplitude and phase terms and fy = 2vr/X, the Doppler frequency due to the cross-track velocity for the wavelength X. Equation (3.3) takes into account the central Doppler frequency and DoA of the scatterer, which are the usual model for space-time processing techniques based on a short integration time. Moreover, the quadratic term encodes the time varying Doppler and DoA, observed in the long SAR integration time. The clutter echo Ck (t), received at time t and receiving element Jc, is obtained by integrating the echoes from the infinitesimal clutter patches of dimension dxq, modelled as equation (3.3) with instantaneous reflectivity Ao = IJi(xq, t)dxq. The correlation of the clutter echoes received at times tn x = t,tn2 = t+r and receivers in Sk1, Sk2 = Sk1 + 2rj is:

(3.4) the symbol (•) standing for the statistical expectation. The model for homogeneous correlated clutter is obtained in the hypothesis of factorisation of the spatial and temporal correlations, px(x) and pt(t), of the clutter reflectivity: (3.5) Using a Gaussian spatial correlation, with variance o2,px(x) = (\f2nGc)~x 2 exp[—x /(2 a*)], the double integration in equation (3.4) becomes a Gaussian function of the space-time displacement, z = (v — vq)r + rj9 of the two-way phase centre and is thus stationary in both space and time:

(3.6) where E 2 = 1/[1/X2 + (2nXq/(XRo))2] is the square of the maximum SAR resolution. By taking the bidimensional Fourier transform of equation (3.6) with respect to time: t —> f, and space: r\ —> sin(0)/X ^ 6/X, we obtain the clutter power spectral density (PSD) as a function of frequency / and angle 0: (3.7) where Ft [/], is the Fourier transform of pt(r). In the absence of temporal decorrelation (pt (r) = 1), P(f, 0) reduces to a sheet for / = fd + (v — vq)0/X, whose Gaussian shaped amplitude is controlled by the variance £ 2 + o2. This reduces to the square of the SAR resolution for uncorrelated reflectivity and grows with the spatial correlation a2 otherwise. This can be especially important for the new generation of VHF SAR systems, to which the reflectivity of a natural scene can appear more correlated than

to microwave sensors. It applies also in a number of remote sensing applications over smooth surfaces, such as sea or ice covered regions and in some planet exploration missions, where the correlation of the surface scattering is not negligible and also a coherent contribution can be present in the echo. This is evident from the behaviour of the PSD that for a\ —> oo behaves as a Dirac delta for 0 = 0. As expected, the mean cross-track velocity of the observed surface (as, for instance, the sea surface) produces a constant frequency shift, whereas a mean along-track velocity changes the slope of the clutter ridge. The presence of temporal decorrelation spreads the PSD around the straight line above, according to the function FVf/], and Xq controls its amplitude, affecting the angle over which the transmitted power is spread.

3.3.2.2 Representation of MSAR echoes Adequate representation strategies are available separately for single-channel SAR, where the long coherent integration interval (CPI) and the consequent non-linear phase history of the echoes are the main issues, and for multichannel MTI systems, which assume, on the contrary, a short CPI and focus on the angular characteristics. In the present section it is shown that the representation planes used for the systems above are inadequate to fully represent the MSAR echoes. The need for a proper representation space for the MSAR echoes is thus illustrated, which takes into account both non-linear phase modulation and angular position at the same time. The angle-frequency plane (O9 f) in Figure 3.3 is the preferred representation space for the clutter covariance in multichannel systems [4, Chapters 2 and 3]. A short observation time is assumed, so that Doppler frequency and DoA of the single scatterer are constant and the array of receivers is used to exploit the scatterers' angle. The PSD in equation (3.7) is directly mapped into this plane, which seems thus appropriate for homogeneous clutter. However, when the observation time is long, both DoA and Doppler frequency of the clutter echo from the single surface scatterer depend on time (equation (3.3)). This can't be represented in the (O, f) plane, where the contribution from each patch of an homogeneous clutter moves in time along a line with constant slope (see arrows in Figure 3.3). Since the scatterers that quit the antenna beam are replaced by new ones entering, on average, the same PSD is observed. Moreover, since the time-varying characteristic of the echo's DoA and Doppler spreads its power over a line in the (O9 / ) plane, the gain of the SAR coherent integration over the noise can't be related directly to Doppler or angular filtering in this plane. This applies also for the detection of targets, with a motion different from that of the clutter patches. The time-frequency plane (t, / ) in Figure 3.4 is the preferred representation space for single channel SAR, where a long observation time is considered. It allows the correct representation of the time-varying characteristic of the Doppler frequency but doesn't contain angular information. Thus the Doppler frequency / of the generic scatterer, shown in this plane, relates to a combination of cross-track velocity and angular position: this ambiguity cannot be resolved. This is shown in Figure 3.4, where solid and dashed lines represent the echo from the same homogeneous clutter

Figure 3.3 Frequency angle plane: typical of STAP (PRT: pulse repetition time)

Figure 3.4

Frequency-time plane: typical of SAR (PRT: pulse repetition time)

patch, received by different channels. The clutter edge is localised in time in the (t9 / ) plane and the SAR coherent integration gain is now clear. From the analysis above it can be seen that, to interpret the MSAR echoes properly, a higher dimensional space is required, which allows both Doppler frequency

Figure 3.5

Space-frequency-time volume: typical of MSAR (PRT: pulse repetition time)

and DoA to be represented as functions of time [13]. The space-time-frequency space (0, t, / ) , in Figure 3.5, is thus introduced. Its integration over the temporal axis collapses it back into the (O, f) plane, and integration over the angular axis collapses it into the (t, / ) plane. In this space the motion of the scatterer echoes in the Doppler angle limits of the antenna beam are correctly represented for both homogeneous and non-homogeneous scene: ( ). Moreover, the generic target echo: (_._), with velocity components different from the clutter background can be effectively represented in the volume of Figure 3.5 and discriminated from the clutter echoes. This representation can be used to get inside the characteristics of the different processing schemes for the processing of MSAR data and fully understand the effect of their application.

3.4

Processing schemes

In the following several processing schemes for the detection and imaging of moving targets are described.

3.4.1

Taxonomy of processing schemes for MSAR

A wide range of processing architectures has been derived in the last few years to detect and focus moving targets using SAR systems with K antennas, based on the digitised echoes received during the long sequence of N PRI from the Q range cells under analysis. The above mentioned architectures are characterised by different approaches to deal with the three main parameters of the received echo signals: alongtrack velocity (Doppler rate), cross-track velocity (Doppler), and DoA. A brief review of the different processing architectures is reported below.

3.4.1.1

1st processing architecture: optimum filter with very long integration time (due to the extended synthetic aperture required to achieve high spatial resolution) With respect to the conventional optimum STAP filter [4, Chapter 4], this optimum filter (see Figure 3.6) is characterised by a target steering vector with Doppler frequency and DoA that cannot be taken constant during CPI. As apparent from Section 3.3.2, with MSAR these quantities might change considerably during long CPI. This filter has the obvious advantage of yielding an optimum approach, however, it has the full computational complexity due to the three-dimensional filter bank (Doppler rate, Doppler, DoA). Only in special cases can this optimal solution be easily derived and interpreted [10, H]. Moreover, the adaptivity of the filters (ideally the filter weight vector is w = s^R" 1 where H stands for complex conjugate transpose) requires very many taps for each filter of the bank and a very large training area with homogeneous clutter, to estimate the clutter covariance matrix R.

3.4.1.2

2nd processing architecture: STAP filtering + coherent integration for SAR processing [9] This suboptimum scheme (see Figure 3.7) is obtained by using a STAP cancellation filter which performs the clutter cancellation and collapses the K channels into a single ideally clutter-free channel. A two-dimensional filter bank (Doppler rate, Doppler) follows to detect the target. This is based on the consideration that cross-track and speed both contribute to modify the linear phase term (Section 3.3.1). Moreover, the filter effect of STAP is related independently to cross-track speed and DoA. The effect of the STAP filter on the second stage is also analysed in Reference 14. This architecture is less computationally demanding and yields a reasonable suboptimum processing scheme.

K channels

Figure 3.6

target detection & imaging

Optimum processing scheme of MSAR

K channels

Figure 3.7

STAP: 3D filter bank: •DoA •Doppler •Doppler rate

STAP Cancellation filter

1 channel

2D filter bank: •Doppler •Doppler rate via Wigner-Ville

Space-time-frequency processing

target detection & imaging

3.4.1.3

3rd processing architecture: formation of SAR image & detection of moving targets This processing scheme requires the application of a conventional MTI clutter canceller on each channel separately. Then the formation of K SAR images is performed (see Figure 3.8), with the corresponding phase compensation (as it happens for Interfermetic SAR (InSAR)). This is followed by a one-dimensional (Doppler) filter bank for the final target detection. The reduced computational cost of this processing architecture yields largely degraded performance. It is especially difficult to compensate for the along-track speed of the target different from the clutter. This technique does not exploit the spatial processing dimension of the multichannel antenna for clutter cancellation. It is therefore (except for the signal to noise power ratio (SNR)) equivalent to a single-channel MTI SAR. 3.4.1.4

4th processing architecture: joint domain localised (JDL) for MSAR [15] The scheme is depicted in Figure 3.9. First a time-varying transformation is applied to the space-time data to compensate for the time-varying Doppler frequency of the clutter echoes. Therefore, a large reduction of degrees of freedom is performed in the Doppler-DoA plane, after two-dimensional FFT. This is followed by an adaptive optimum generalised likelihood ratio test applied in the reduced domain [16]. This

MTI

SAR

MTI

SAR

MTI

SAR

ID filter bank: •Doppler

K channels

Figure 3.8

Channelised MTI&SAR processing time-varying transformation

NK samples

Figure 3.9

2DFFT

discard data

Yes target GLRT

No target

to compensate for cluster of 2D beams adaptivity on generalised Doppler frequency in Doppler & spatial a reduced number likelihood and DoA variation frequencies domain OfDoF ratio test during CPI

Joint domain localised (JDL) on MSAR

RX-K

SAR processor 1

SAR processor 2

TX

SAR processor K

velocity processor

Figure 3.10

Velocity SAR

scheme has low computational complexity, close to optimum detection performance, and reduced size of required homogeneous clutter area. However, it requires a proper time-varying transformation and is less intuitive for targets with non-negligible alongtrack velocity component. 3.4.1.5 5th processing architecture: velocity SAR (VSAR) [6] As sketched in Figure 3.10, the set of complex video signals is processed by SAR processors to produce complex images: Yk(x, y), k = 0 , . . . , K — 1 with x, y azimuth, range coordinates. Phase of formed images is preserved. The post-processing of complex images brings out the velocity dimension. This step involves processing of each pixel for all images. Consider the whole set of images as a single threedimensional image: Yk(x9 y, k); the velocity processing applies along the rc-axis and provides the resulting three-dimensional image: Z(;t, y, v) in azimuth, range and velocity of the observed scene. Velocity processing in its simple form involves Fourier transformation of K points along the A>axis. Finally, each velocity plane is shifted by an amount proportional to its velocity to correct the motion-induced azimuth displacement. All the planes are summed to produce the final undistorted VSAR. The method is not designed to suppress clutter, since no attempt is made to subtract signals. The requirement to cancel the echoes from stationary scatterers leads directly to adaptive space-time filtering. 3.4.1.6 6th processing architecture: processing in the frequency domain This method finds its mathematical foundation in the stochastic stationary characteristic of the clutter processes that have natural description in the Fourier domain via the spectral density matrix. The Fourier transforms (FT) of the process for fixed

FFT

FFT

FFT receiving channels

spatial null for each frequency bin target match in space

target match in frequency Threshold

Figure 3.11 Frequency domain processing for MSAR [12] frequencies are asymptotically independent when the time base tends to infinity. Thus cross-correlations between frequency channels are negligible. Therefore, frequency processing is valid asymptotically, since the spectral representation provides a time signal extending from — to + infinity. For SAR we have in the limit an infinite sequence of equispaced samples along the pulse-to-pulse time (slow time). This is in contrast to the finite pulse train of airborne early warning (AEW) search radar. For azimuth and range compressions the FT is performed in any case. Moderate time base (= synthetic aperture length) is sufficient to make negligible the cross-terms between the frequency channels. In Doppler domain processing, the clutter energy is collected in one-dimensional subspace. This is the key to using projection methods (see Figure 3.11) with the advantage that the clutter is cancelled perfectly without sensitivity to its amplitude variations. A good estimate of the covariance matrix is achievable since there is a large number of range bins. Even though clutter to noise power ratio (CNR) varies with range, the structure of underlying clutter subspace remains unchanged. The computational load is affordable if only a few spatial channels (three is the minimum) are used for long sample sequences. SMI (sample matrix inverse) and eigendecomposition of 3 by 3 matrices are performed very fast. For details see Reference 12. 3.4.1.7

7th processing architecture: displaced phase centre antenna (DPCA) for SAR The concept of DPCA requires an antenna divided in two subarrays and the transmission of two pulses. Due to the aircraft movement, the transmitting and receiving

antennas form two bistatic configurations for the two pulses. If the subarrays' displacement, the platform speed and the radar PRF are properly selected, the global two-way phase centres of the bistatic antenna configurations are coincident. The stationary clutter is seen at two different time instants from the same radar location and it can be cancelled by subtracting the corresponding echoes. The DPCA corresponds to a kind of spatial MTI: returns from stationary objects cancel, while moving target echoes are maintained. The extreme simplicity of this approach is paid for by very strong constraints on the antenna, PRF and platform speed, which are often unacceptable. Moreover, the technique has no ability to compensate for any mismatch from this idealised condition by means of adaptivity. 3.4.1.8

8th processing architecture: along-track interferometty SAR (ATI-SAR) This operates similarly to DPCA using two displaced antennas connected to two receiving channels. An SAR image is generated for each channel; thereafter, the time delay between the azimuth signals is compensated for using two different azimuth reference signals. By multiplying the first image by the complex conjugate of the second, the remaining phase is zero for stationary objects and non-zero otherwise. Basically this technique is closely related to DPCA and STAR It may suffer from constraints imposed on the processing according to SAR requirements (SAR requires low PRF values to have a wide along-range swath width, and STAP needs large PRF to detect also fast moving targets).

3.4.1.9 9th processing architecture: pulse Doppler and MTI [2] This technique is derived from the well known moving target detector (MTD) processing widely used in conventional ground-based radar. After range compression, an azimuth processor is developed to detect the presence of a moving point-like target in each range cell and to measure its velocity components. The method is straightforward and simple to implement under the conditions that the target velocity is bounded within a minimum detectable value and the unambiguous value, and that range migration is negligible. In the following we will describe in some detail the following processing schemes: MTI + PD (Section 3.4.2), DPCA (Section 3.4.3), ATI-SAR(Section 3.4.4), joint space-time-frequency (Section 3.4.5), optimum filter for a special case (Section 3.4.6). We prefer to follow the historical derivation rather than the optimum approach from which all the suboptimum schemes can be derived.

3.4.2 MTI+ PD The material of this section is derived from Reference 2 which describes the work done by colleagues of the authors. The processing technique, referred to as moving target detection and imaging (MTDI), has been derived by the well known MTD processing widely used in conventional ground-based radars. A range-Doppler SAR processing is adopted; the raw data are first processed along the range direction and then along the azimuth. An azimuth processor is developed to detect the presence of

beam footprint

Figure 3.12

Geometry of SAR and moving target

a moving point-like target in each range cell and to measure its velocity components. The method is valid under the following hypotheses, namely: • •

the target velocity is bounded within minimum detectable and maximum unambiguous values (i.e. PRF/2) the SAR system and the moving target cause a negligible range migration.

It should be noted that with a one-channel antenna no detection of endoclutter targets (i.e. targets with Doppler frequency within the clutter spectrum) is possible. Increasing the PRF may not be desirable because of an increase in range ambiguities, and likewise for SAR applications. The mathematical model of the echo received by the radar antenna during the synthetic aperture time interval is reported in this section. Figure 3.12 sketches the geometry of an SAR system and a moving object of interest. The antenna, on board an aircraft, moves along the azimuth direction x. The antenna beampattern is directed orthogonal to the flight path; 0 (the off-nadir angle) is the angle formed by the normal to the ground and the line from the radar to the central point of the scene; Vx and vy are the velocity components of the target along the reference coordinates. Along the azimuth, the radar transmits pulse trains with repetition frequency PRF, each pulse having a linear frequency modulation (chirp). To account for some unpredictable changes in the environment wherein the transmitter operates, an unknown initial phase 0o» modelled as a random variate uniformly distributed in (0,2n), is assumed in the transmitted signal. At the nth azimuth position of the antenna, the transmitted pulse is expressed as: Tn(t) = A cos(2jtf0t + at2 + 0O),

~

m

+ qt(k\

k = 1,2, . • • ,ft

(6.5)

The composite random vectors x(k) = [x\(k),X2(k)]T are mutually independent identical complex normal distributed with expectation s(fc, #) = ^ Ps(k){\,e^k)Y fork = 1 , . . . , n and covariance matrix Q, i.e. X(A:) ~ Af?r(s(k), Q). In contrast to equation (6.3), the random matrix A = YHc=\ X(A;)X(Zc)* is now non-central complex Wishart distributed, A ~ Vl^p (ft, Q, Q)9 with non-centrality matrix Q = Q - 1 MM*, where: (6.6) The density function of the positive definite A is [32]:

As this density function contains a hypergeometric function of matrix arguments, analytical analysis is exceedingly complicated. However, for two practical cases statistical evaluation becomes possible. First, regarding SAR systems with resolutions of a few metres to submetre range, the assumption of a single moving target within a multilook cell for a reasonable number of looks (MO) seems adequate, i.e. s(k, 0) = S(1O-). This mover can either be a single-point scatterer or an extended target consisting of several scattering centres with approximately the same amplitudes and radial velocities, such as a large truck etc. Under the assumption that the target covers only / < n single-look cells, the matrix of expectation vectors in equation (6.6) is given as:

where the vector e/ has / components equal to one and the rest zeros. In this case the matrix product MM* (and therewith also the non-centrality parameter

Q = Q 1 MM*) has rank one. The non-centrality matrix can be written as £2 = lQ~ls($)s(&)*. The density function of A now involves hypergeometric functions of scalar arguments:

(6.7) The equivalent density function for real variables (when the non-centrality matrix has rank one) was originally derived by Anderson and Girshick [33] where they applied the identity 0F\(a;X) = V(a)/(VX)a~lIa~\(2VX) for the confluent hypergeometric function. / v ( ) denotes the modified Bessel function of order v. Second, when the number of looks becomes sufficiently large, the second moment matrix A can be simplified because the cross terms (of independent random variables with zero mean) tend to zero for increasing n. Hence it can be rewritten as a superposition of the target signal matrix on the clutter covariance matrix: (6.8) Gaussian target model - In the previous moving target model it was assumed that the single mover amplitude was constant from one-look cell to the next one-look cell. In practise this will not be the case because varying propagation conditions, system instabilities and, primarily, variation of the target RCS caused by changing aspect angles are reasons for amplitude fluctuation. If a target consists of many single reflectors, then the backscattered signal is composed of many single contributions with quasi random relative phases. Accordingly, it can be approximated as complex normal distributed. Over short periods of time, e.g. corresponding to the fast time or range direction in SAR, the aspect angle changes only a little and the amplitude can be assumed to be constant. This model is commonly named the Swerling I case. In the flight direction of the SAR, i.e. slow-time or azimuth direction, the pulses may be far enough apart that the amplitudes of the single returns can be considered as stochastically independent. This so-called Swerling II case is investigated in the subsequent sections. Depending on the geometric resolution compared with the target dimensions, two Swerling II applications have to be distinguished. If the mover dimension is of the order of the multilook cell size the resulting covariance matrix for signal plus interference (clutter and noise) can be modelled analogously to equation (6.5), but where the deterministic target signals have to be replaced by the random variables 5/ (k) for / = 1,2. As mentioned above, the composite random vectors S(Jc) = [S\(k)9S2(k)]T are assumed to be mutually independent complex normal distributed S ~ TV^(O, Qs) with expectation zero and covariance matrix:

where ps denotes the coherence of the moving target signals. It is important to note that in the absence of temporal decorrelation, the coherence between the two channel outputs will be exactly identical for the target and the clutter. With temporal decorrelation, the target coherence can either be larger or smaller than the surrounding clutter coherence. A perfectly steady vehicle, for instance, smoothly moving over a terrain of vegetation might have a larger coherence than the vegetation. The contrary, where the vehicle is rolling and bouncing over terrain which is otherwise perfectly stationary, leads to a lower coherence for the target compared with the surrounding terrain. However, this motion-induced decorrelation will not change the principle form of the optimum filter (equation (6.12)). Therefore, by setting ps = 1, one can concentrate on the deterministic signal vector s(#) = ^fP~s[l,exp(—j$)]T. Since the clutter and the target are mutually stochastically independent, the sum of them will still be complex normal distributed, i.e. X ~ A/^ (O9 Qs + Q)- The resulting sample covariance matrix: (6.9)

with \(k) = q(ifc) + s(ifc) is therefore complex Wishart distributed A ~ W*p(n,R) with n degrees of freedom. The composite covariance matrix is given as R = Qs + Q which has the same structure as in equation (6.2). In cases where the moving target dimension is smaller than the multilook cell size, the model in equation (6.9) is no longer adequate. Instead, we get for the sample covariance matrix: (6.10)

when it is assumed that the mover is only contained in the first / G {2,..., n] onelook cells. Therefore, the random matrix A consists of a sum of two independent complex Wishart distributed matrices B ~ W*p(Z,R) and C ~ W ^ (n - /,Q). To the best knowledge of the authors the corresponding density function has not yet been derived in closed form.

6.2.3 SCNR optimum processing 6.2.3.1 Known covariance matrix Let the signal output, i.e. the test statistics on which the actual detection is based, be the magnitude of y = b*X, where b is the filter or beamformer vector and X = [Xi, X2]T is the sensor outputs. Due to one of the most basic facts in detection theory, the probability of detection of a signal in noise depends mainly on the SNR. Therefore, one criterion for adjusting the beamformer vector b could be maximisation of the signal-to-clutter-plus-noise ratio (SCNR) K of the signal output when the processor

is matched to Doppler phase #: (6.11) where s(#) = y^[l,exp(—jtf)] 7 ' is the given target signal vector at this Doppler phase. It is easy to verify that the optimum filter is: bopt(#) = K T 1 / 2 s ( # ) =

YQ~1S(#)

(6.12)

The optimum filter can be interpreted as a two-step process, the decorrelation (whitening) of the clutter with Q" 1 / 2 and a matched filtering with the adapted signal s = Q~1//2s. Applying the optimum filter (e.g. for y = 1) to the measured data vector x, yields for the signal output: y= sWQ-1!

(6.13)

where the data vector x contains only clutter plus thermal noise, i.e. X = Q - A/2 (0, Q), the beamformer output (equation (6.13)) will be a linear combination of normal variables which is also complex normal distributed with zero mean and variance: a 2 = E|v| 2 = S(^) + Q" 1 EXX*Q~1s(#) = s(^)*Q~ 1 sW

(6.14)

Therefore, the magnitude \y\/cry is Rayleigh distributed and the detection threshold can be calculated via the cumulative distribution function of the Rayleigh distribution for any given false alarm rate a. If, for instance, a deterministic target signal s(#) is included in x, such that the corresponding random vector X = s(#) + Q, the magnitude \y\/cry will be Rice distributed with parameter s(^)*Q - 1 s(#)/ oo), p tends to p and 0 towards ^, i.e. the phase density function in that case is identical to the original clutter PDF except for the Doppler shift towards the target frequency. This behaviour of the PDF is illustrated in Figure 6.5, where the perfect agreement between theory and simulation can be seen. The target Doppler phase was chosen to 1.3 rad. Figure 6.6 shows the corresponding probability of detection as a function of target radial velocity for n = 9 and / = 3. It is found that the probability of detection is always less than that of DPCA. Particularly, the example target moving with 18 km/h and possessing a SCR of 10 dB can only be detected with 60 per cent chance compared with 93 per cent for multilook DPCA. However, even though the performance of DPCA seems to be significantly better than that for ATI, one has to bear in mind that this is only true for homogeneous

ATI phase, rad

Figure 6.5

Histograms and theoretical PDFs ofinterferometricphase over varying SCR with Gaussian random target model True phase \jr = 1.3 rad, n = 1

terrain. It was shown in numerous publications (e.g. References 27 and 40) that the interferometric phase is invariant against inhomogeneity of the clutter, hence preserving its detection capability in fairly heterogeneous composite terrain. In contrast, the PDF for DPCA will show larger tails in such cases, i.e. a higher probability of larger amplitudes. In order to keep the false alarm rate constant, the detection threshold must inevitably be increased which in turn decreases the probability of detection. A quantitative comparison of the performance loss caused by extremely heterogeneous terrain, such as urban areas, is currently under way, e.g. Reference 41.

6.3

SAR-STAP scheme for RADARSAT-2

6.3.1 Detection This section gives a brief summary of the theoretical background and the resulting algorithms for adaptive space-time (or more precisely space-frequency) processing in conjunction with SAR for RADARSAT-2. An elaboration of this topic and its successful application to experimental airborne SAR data can be found in References 13 and 14 and also in Chapter 3 in this book.

SCR = 0 [dB] SCR = 5 [dB] S C R - 1 0 [dB] SCR= 15 [dB] SCR = 20 [dB] SCR = 25 [dB]

v rad , m/s

Figure 6.6

Probability of detection of ATI for the Gaussian target model versus radial velocity for varying SCR (dB) after 9-look averaging, Pf = 10~4

Although for the statistical performance analysis in Section 6.2.3 it was sufficient to look at the problem in a static way, such as using two processed SAR images, STAP working on the raw data requires consideration of the time history of the received clutter and moving target echoes. Let x(/,S) be the received echo consisting of a moving target signal s(t,%) superimposed upon the stationary clutter qO) and the unavoidable thermal receiver noise n(t). The parameters describing the moving target, such as velocity in the along-track direction va, velocity in across-track or range direction vr and its location xo at time t = 0 are combined in the vector S = [va,vr,xo]T. In the following, the Fourier transform of the signal will be denoted as X(&>,§) = .^{x^S)}. Even though the correlation time r c of the clutter q(t) in the time domain is rc = l/BC9 where Bc = 2up@3dBA is the clutter bandwidth constrained by the antenna beamwidth @3dB> the frequency bins in the Doppler domain are asymptotically mutually independent. For a sufficiently long time base of the Fourier transform, the receiver output vector can be considered as being stochastically independent and complex normal distributed, i.e. X(O)9 S) - Np(S(CQ9 S), Q((o)), where S(ty, S) is the Fourier transform of s(t, S) and Q(co) the so-called spectral power density matrix of the clutter plus noise. Under this premise, the SCNR optimum filter for a particular frequency is given, analogously

to equation (6.14), y(oo) = S(co, ^TQ'1 (co)X((o) with the optimum SCNR: /CoPt(Co) = S(co, §)*Q~1 (a>)S(G>, §)

(6.26)

Figure 6.7 shows an experimental data example of this SCNR optimum processing in the Doppler range domain for an airborne two-channel side-looking SAR system [11], with S (co, £) = S chosen as fixed to S = [ 1, — 1 ] T . The left-hand image shows y before any clutter cancellation, i.e. y(co) = S*X(co) (the clutter energy spread over the entire clutter bandwidth can be clearly recognised) and the right-hand one after suppression with SMI, y(co) = S*Q~1X(ct>). The clutter covariance matrix was estimated over all the range bins and hence possesses a very low variance. In the right-hand image, one can clearly recognise the enhanced moving target signals which were partly or fully covered by the clutter. The fast moving cars on the highway (upper part) are at least partly outside of the clutter bandwidth, whereas the slow moving vehicle in the bottom part was completely covered. Since the target energy in S(&>, £) spreads over a certain bandwidth, depending on the parameter vector £, the optimum filter is modified as an integration over the target bandwidth:

range bins

range bins

(6.27)

Doppler frequency, Hz

Figure 6.7


Doppler range image of two-channel SAR data before (left) and after STAP processing (right)

To analyse the potential performance of SAR-STAP it is advantageous to have a closer look at the model for the received target signal: Si(t,$)

= Di(ute))e*PU2PRite))

(6-28)

where R(t) denotes the slant range distance and ui(t) the direction history (directional cosine) from the /th antenna to the moving target on the ground. D1-(M) describes the two-way antenna pattern of the /th channel. In the far-field assumption, u\ (t) = u \ (t) and the distances can be written as R((t) = 2R(t) + u\(t)d, where d is the spacing between the receivers and R(t) the slant range distance from any reference channel to the scatterer. The two-dimensional signal vector becomes: (6.29) In array processing terminology the vector a(w) is called the steering or direction of arrival (DoA) vector. Using a special property of chirp signal possessing a large time bandwidth product, the Fourier transform of equation (6.29) can be written in analytical form to: S(CD,!;) = y(coMu(co,i;))

(6.30)

[13], i.e. as a multiple of the DoA vector in direction:

(6.31)

For non-moving objects this dependency tends to a straight line u(co) — —co/(2fivp) where the slope is determined by the platform velocity vp. For spaceborne systems with vp ^$> va, equation (6.31) can further be simplified to u(co, £) = —co/(2fivp) + vr/Vp for any ground moving vehicle. Inserting the normalised vector of equation (6.30) into the optimum SCNR of equation (6.26) leads to the so-called space-time characteristics (STC) or transfer function: (6.32) which is an excellent tool for the examination of moving array systems for GMTI [13]. Figure 6.8 shows the anticipated STC of the two-channel RADARSAT-2 antenna when the signal is transmitted from one half of the antenna and received on both halves, resulting in a phase centre separation of about 3.75 m. For simplicity, the single-element pattern was chosen of exponential form with a beamwidth 0 3 dB = 0.42° (horizontal dashed lines) corresponding to the 7.5 m subaperture.

directional azimuth, deg


Figure 6.8

Space-time characteristics of the two-channel RADARSAT-2 antenna, d= 7.5m

The vertical dashed lines represent RADARSAT-2's maximum PRF of 3.8 kHz and combined with the horizontal lines indicate the GMTI-relevant Doppler direction plane. Bright white indicates perfect clutter suppression, i.e. a detection capability as it would be without any clutter present. Obviously, a fully white plane would be desirable. The adaptive filter (even though it is only of dimension two) forms a sharp notch along the clutter trajectory u(co) = —co/(2pvp) (white solid line). Target motion will create a deviation from this straight line, see equation (6.31), i.e. will more or less fall in the white area and hence become detectable. Most significantly, two ambiguity zones (notches) caused by the spatial undersampling of the array at either side of the plane are visible. Targets with a Doppler direction trajectory getting close to these notches will be partly suppressed as well and will be less detectable. However, the first ambiguous target velocity Vy can be seen to be at the corresponding direction u(v^) = 0.42°, resulting in vay = 0.007vp = 200km/h, which might, at least for ground moving vehicles, only create problems in rare circumstances such as fast traffic on a German autobahn. If, in contrast, the signals are transmitted from the entire aperture of 15 m and received on both halves, the effective two-way antenna beamwidth decreases to 03 ^B = 0.27° (the phase centre separation remains the same)

and the ambiguity notches are (although still existing) less pronounced. However, the clutter-free Doppler zone significantly increases (target detection is straightforward in this area) because of the narrower clutter bandwidth caused by the smaller antenna beamwidth.

6.3.2 Parameter estimation The entire slow-time range of the scene under consideration can be divided into segments of equal duration which are individually transformed in the Doppler domain. The detection and parameter estimation is then done in the Doppler range domain separately for each segment, for instance, by comparing the clutter-suppressed pixels with a predefined CFAR threshold. The duration (length) of the time segments can be chosen as the maximum time stationary targets stay in one Doppler cell. Under the assumption of statistical independency between the Doppler bins, the clutter suppression can be done individually for each frequency bin. For a side-looking SAR, the sample covariance matrix can be averaged over the entire range dimension, usually providing a very low variance of the estimate. Applying the inverse (or eigenvector projection) to the data in this Doppler bin means clutter suppression (with a performance specified by the STC of the moving array), leaving only the moving targets in the data. Having the Doppler frequency ft and the slant-range position Rt determined at this stage, the only remaining unknown parameter is the azimuth location xt or equivalently the target direction ut = xt/Rt. For a multichannel SAR system with N > 2, Ender [42] has proposed a very elegant way to estimate that direction. He used the measured array manifold (estimated via the first eigenvector of the sample covariance matrix) to yield high resolution azimuth spectra for DoA estimation. Unfortunately, this approach cannot be applied to a two-channel system like RADARSAT-2 which has only one spatial degree of freedom (DoF). This DoF is spent suppressing the clutter and hence there is none left to retrieve the direction information. One possible way to overcome this dilemma is the use of several space-time (or frequency) samples to increase the dimensionality. For instance, taking M subsequent time segments, i.e. time segments of same length but staggered by 1 , . . . , M PRIs, transformed into the Fourier domain will all cover exactly the same Doppler frequencies.1 For each Doppler bin the M, Af-element vectors are concatenated to form the NM-dimensional space-time vector X(&>) = [Xi (&>),... ,XM(CO)]T. The estimation of the corresponding space-time covariance matrix is done analogously along the entire range direction. As a main difference, the clutter will not be compressed into one large eigenvalue but spread over N + /3(M — 1) eigenvalues, where /3 denotes the number of half interelement spacing traversed by the platform during one PRI [25,26,37]. For example, if we chose M = 3, and recalling N = 2 and p = 0.52 (PRF = 3.8 kHz) for RADARSAT-2, the clutter rank will be roughly three, i.e. another three DoF would theoretically be available to estimate 1

In classical terminology for airborne MTI this technique is known as PRI-staggered STAP

the target direction. One disadvantage is that many slower targets (which are close to the clutter subspace) will have significant power distributions in the second and third eigenvalues. Hence, adapting and suppressing two or three eigenvalues would also suppress target energy. In other words, there is a trade off between improved DoA estimation and reduced detectability. However, as a compromise the detection could preferably be done without staggering (keeping also the computational load smaller) and the enlarged dimensionality only be used to estimate the location of the target. A drawback of this approach is the increased computational complexity due to the order of the space-time covariance matrix. The inversion or decomposition of such matrices is numerically very intensive. However, many fast methods which avoid these intensive operations but possess almost optimum fidelity are known from classical radar array applications such as jammer suppression or superresolution [26,37,43].

6.4

Conclusions

RADARSAT-2 is a two-aperture SAR interferometer. When used for GMTI measurements, RADARSAT-2 will use beams in the 40° to 50° incidence angle range to maximise the radial velocity component of vehicle motion. The airborne experimental SAR reported here was designed to replicate the RADARSAT-2 GMTI mode resolution and observation geometry as closely as possible and to test data processing algorithms that will be migrated to the RADARSAT-2 GMTI processor. The greatest difference between the airborne and space-based SAR/GMTI capabilities arises from the relationship between the platform velocity and the along-track velocities of moving targets. In the airborne case, the target speeds are a significant fraction of the radar speed and reasonably accurate azimuthal target speed estimates can be made. This is not true for space-based radars. The RADARSAT-2-GMTI processor, which is currently under development, will likely be composed of all presented techniques, i.e. ATI, DPCA and STAR Each technique has strengths and weaknesses. For instance, ATI and DPCA are computationally simple and robust but, because they are based on the processed SAR images, are strongly dependent on the stationary world processing fidelity. On the other hand STAP, working in the raw data domain, circumvents the processing problem, but is computationally much more demanding, particularly for SAR where often several thousands of pulses are used to form the image. Another essential criterion is the robustness against varying degrees of heterogeneity of the underlying terrain in order to provide similar GMTI performance even in challenging environments such as sea surface or urban areas. Feeding the received echoes into parallel GMTI processing chains will result in an estimated target parameter pool, where the redundant information can be used to reject doubtful hits and enhance stable detections and estimates. Last but not least, RADARSAT-2 Modex is designed as an experimental rather than operational/commercial mode with the goal of identifying the potential and weaknesses of single-pass spaceborne SAR-GMTI.

6.5

List of symbols

a b ft d Di K k n N PCi Pn Pri Ps \/r q Q Q Qs pe-i9 R(t) R s S ft u va Vp vr frad jco x X £ y

direction of arrival (DoA) vector beamformer weights wave number sensor spacing horizontal sensor antenna pattern signal-to-clutter-plus-noise ratio wavelength number of independent samples (looks) number of sensors (N = 2 for RAD ARS AT-2) clutter power at /th sensor noise power received echo power at ith sensor signal power interferometric phase clutter-plus-noise vector, clutter-plus-noise covariance matrix estimated clutter-plus-noise covariance matrix signal covariance matrix complex correlation coefficient between sensors range signal-plus-clutter-plus-noise covariance matrix signal vector signal spectrum vector Doppler phase directional cosine along-track component of target velocity platform velocity across-track (range) component of target velocity radial target velocity along-track target location at t = 0 received echo vector spectrum of received echo vector signal parameter vector beamformer output, output signal

References 1 STONE, M. L. and INCE, W. J.: 'Air-to-ground MTI radar using a displaced phase center phased array'. Proceedings of IEEE international Radar conference, 1980, pp. 225-230 2 BROADBENT, S.: 'Joint-stars: force multiplier for Europe', Janes Defense Weekly, April 1987, (19), pp. 729-731

3 COVAULT, C.: 'Joint-stars patrols Bosnia', Aviation Week and Space Technology, February 1996, (9), pp. 4 4 ^ 9 4 TSANDOULAS, G.: 'Space based radar', ScL, 1987, (237), pp. 257-262 5 BIRD, J. and BRIDGEWATER, A.: 'Performance of space-based radar in the presence of earth clutter', IEE Proc. F, Commun. Radar Signal Process., 1984, 131, (5), pp. 491-501 6 CANTAFIO, L. J.: 'Space-based radar handbook', (Artech House, Dedham MA, 1989) 7 CURRY, G. R.: 'A low-cost space-based radar system concept', IEEE Aerosp. Electron. Syst. Mag, September 1996, pp. 21-24 8 Canadian Space Agency and MacDonald Detwiler & Associates: 'RADARSAT-2 programme', http://www.space.gc.ca/radarsat-2, http://radarsat.mda.ca, 2002 9 THOMPSON, A. A. and LIVINGSTONE, C. E.: 'Moving target performance for RADARSAT-2'. Proceedings of IGARSS, July 2000 10 CHIU, S. and LIVINGSTONE, C : 'A simulation study of RADARSAT-2 GMTI performance'. Proceedings of IGARSS, Sydney, Australia, 2001 11 LIVINGSTONE, C , SIKANETA, L, GIERULL, C. H., CHIU, S., BEAUDOIN, A., CAMPBELL, J., BEAUDOIN, J., GONG, S., and KNIGHT, T.A.: 'An airborne SAR experiment to support RADARSAT-2 GMTI', Can. J. Remote Sens., December 2002, 28, (6), pp. 1-20 12 GIERULL, C. H. and SIKANETA, I. C : 'Raw data based two-aperture SAR ground moving target indication'. Proceedings of IGARSS, Toulouse, France, 2003 13 ENDER, J. H. G.:' The airborne experimental multi-channel SAR system AER-II'. Proceedings of EUSAR '96 conference, Konigswinter, Germany, 1996, pp. 49-52 14 ENDER, J. H. G.: 'Space-time processing for multichannel synthetic aperture radar', Electron. Commun. Eng. J., February 1999, pp. 29-38 15 BARBAROSSA, S.: 'Detection and estimation of moving objects with synthetic aperture radar; part 1: optimal detection and parameter estimation theory', IEE Proc. Ff Radar Signal Process., 1992,1, (139), pp. 79-88 16 SUN, H., SU, W., GU, H., LIU, G., and NI, J.: 'Performance analysis of several clutter cancellation techniques by multi-channel SAR'. Proceedings of EUSAR conference, Munich, Germany, 2000, pp. 549-552 17 YADIN, E.: 'Evaluation of noise and clutter induced relocation errors in SAR-MTI'. Proceedings of IEEE international Radar conference, 1995, pp. 650-655 18 YADIN, E.: 'A performance evaluation model for a two port interferometer SAR-MTI'. Proceedings of IEEE national Radar conference, 1996, pp. 261-266 19 STOCKBURGER, E. F. and HELD, D. N.: 'Interferometric moving ground target imaging'. Proceedings of IEEE international Radar conference, 1995, pp. 438^43 20 SIKANETA, I. C , GIERULL, C. H., and CHOUINARD, J. -Y: 'Metrics for SAR-GMTI based on eigen-decomposition of the sample covariance matrix'. Proceedings of international Radar 2003, Adelaide, South Australia, 2003

21 FRANCESCHETTI, G. and LANARI, R.: 'Synthetic aperture radar processing' (CRC Press, 1999) 22 RANEY, R. K.: 'Synthetic aperture imaging radar and moving targets'. IEEE Trans. Aerosp. Electron. Syst., 1971, 7, (3), pp. 499-505 23 FREEMAN, A.: 'Simple MTI using synthetic aperture radar'. Proceedings of IGARSS, 1984, pp. SP-215 24 ENDER, J. H. G.: 'MTI-SARprocessing'. Carl-Cranz-Gesellschaft, course notes SE 2.06 on SAR-principles and applications, 1997 25 WARD, J.:'Space-time adaptive processing for airborne radar'. Technical report TR-1015, MIT Lincoln Laboratory, December 1994 26 KLEMM, R.:' Space-time adaptive processing' (IEE Publishing, Stevenage, UK, 1998) 27 GIERULL, C H . : ' Statistical analysis of multilook SAR interferograms for CFAR detection of ground moving targets: IEEE Trans. Geosci. Remote Sens., April 2004,42, (4), pp. 691-701 28 CONTE, E., LONGO, M., and LOPS, M.: 'Modelling and simulation of nonRayleigh radar clutter'. IEE Proc. F, Radar Sonar Navig., April 1991, 138, (2), pp. 121-130 29 GOODMAN, N. R.: 'Statistical analysis based on a certain multivariate complex Gaussian distribution (an introduction)', Ann. Math. Stat, 1963 (152), pp. 152-180 30 JOUGHIN, I. R. and WINEBRENNER, D. P.: 'Effective number of looks for a multilook interferometric phase distribution'. Proceedings of IGARSS9 Pasadena, CA, 1994, pp. 2276-2278 31 GIERULL, C. H. and SIKANETA, L: 'Estimating the effective number of looks in interferometric SAR data', IEEE Trans. Geosci. Remote Sens., August 2002, 40, (8), pp. 1733-1742 32 GIERULL, C. H.: 'Moving target detection with along-track SAR interferometry - a theoretical analysis'. Technical report TR 2002-084, Defence R&D Canada, Ottawa, Canada, 2002 33 ANDERSON, T. W. and GIRSHICK, M. A.: 'Some extensions of the Wishart distribution', Annals of Mathematical Statistics, December 1944, 15, (4), pp. 345-357 34 REED, L. S., MALLETT, J. D., and BRENNAN, L. E.: 'Rapid convergence rate in adaptive arrays', IEEE Trans. Aerosp. Electron. Syst, 1974, AES-10, (6), pp. 853-863 35 CHEREMISIN, O. P.: 'Efficiency of adaptive algorithms with regulized sample covariance matrix (in Russian)', Radiotechnology and Electronics (Russia), 1982, 2, (10), pp. 1933-1941 36 KREYENKAMP, O. and KLEMM, R.: 'Doppler compensation in forwardlooking STAP radar', IEE Proc. F, Radar Sonar Navig., 2001, 148, (5), pp. 253-258 37 GIERULL, C. H. and BALAJI, B.: 'Minimal sample support space-time adaptive processing with fast subspace techniques', IEE Proc. F, Radar Sonar Navig., October 2002,149, (5), pp. 209-220

38 NICKEL, U.: 'On the application of subspace methods for small sample size', AEUInt. J. Electron. Commun., 1997, 51, (6), pp. 279-289 39 LEE, J.-S., HOPPEL, K. W., MANGO, S. A., and MILLER, A. R.: 'Intensity and phase statistics of multilook polarimetric and interferometric SAR imagery', IEEE Trans. Geosci. Remote Sens., September 1994, 32, (5), pp. 1017-1028 40 JOUGHIN, I. R., WINEBRENNER, D. R, and PERCIVAL, D. B.: 'Probability density functions for multilook polarimetric signatures', IEEE Trans. Geosci. Remote Sens., May 1994, 32, (3), pp. 562-574 41 SIKANETA,I. C. andGIERULL, C. H.: 'Parameterestimationforphase statistics in interferometric SAR'. Proceedings of IGARSS, Toronto, ON, Canada, 2002 42 ENDER, J. H. G.:' Signal processing for multi-channel SAR applied to the experimental SAR system AER'. Proceedings of international Radar conference, Paris, 1994 43 WIRTH, W.: 'Radar techniques using array antennas' (IEE Publishing, Stevenage,UK,2001)

Chapter 7

STAP simulation and processing for spaceborne radar Tim J. Nohara and Peter Weber

7.1

Introduction

Spaceborne radar (SBR) has been proposed for various military and civilian applications [I]. Military applications include wide-area surveillance (WAS), theatre defence and disarmament functions. Civilian ones include remote sensing, air-traffic control, space exploration and law enforcement. The 1970s saw the first spaceborne synthetic aperture radars (SAR) with GEOS-C launched in 1975 and SEASAT in 1978 [2]. These provided remote sensing of the earth, including data such as high-resolution topography and ocean dynamics. Spaceborne SAR has matured and today includes RADARSAT-2, which is due to launch in 2005. SBR for WAS and theatre defence, however, is still in the experimental domain. In the 1980s and early 1990s, research focused on WAS and airborne moving target indication (AMTI) designs [ 1,3-6]. More recently, focus has shifted to theatre defence applications where ground moving target indication (GMTI), and combined SARGMTI modes are of interest [7]. MTI (i.e. GMTI and AMTI) radars exploit space-time adaptive processing (STAP) techniques to detect targets that would otherwise be buried in clutter. In Canada, an experimental GMTI mode is being developed for RADARSAT-2. This programme, along with earlier programmes such as the United States' Discoverer-II programme, are intended to provide much needed design and performance data, which are necessary to take spaceborne MTI and SAR-MTI radars from experimental to operational systems in the next ten years. To help mitigate the exorbitant cost of fielding and testing spaceborne radar prototypes, engineers have come to appreciate the key role that simulation technologies can play in the development process. Recently, many texts have been published that are dedicated to simulating electronic systems such as radars [8-10], and there are now organisations dedicated to promoting the use of simulation technologies through

the development of standards and other support [H]. In addition, there are technical conferences focused entirely on modelling and simulation [12]. Today, good mathematical models are available to represent the entire spaceborne radar, along with sufficient, general-purpose computing power to implement and exercise these models in reasonable times. As a result, spaceborne MTI radar designs can be accurately modelled, their performance evaluated and trade-offs can be carried out over a wide range of design parameters and operating conditions, all before a prototype is built and launched for experimental validation. The principal objective of this chapter is to discuss the design of computer simulation tools suitable for modelling and evaluating the performance of spaceborne MTI radars employing STAP techniques. This objective is met by first reviewing spaceborne MTI radar applications and radar design. This is followed by a review of the STAP techniques typically considered for spaceborne MTI radar. With this background, the design of spaceborne radar (SBR) simulation tools is examined in detail.

7.2

Spaceborne radar applications and design

Reviews of both spaceborne radar MTI applications and typical MTI radar designs are presented. These allow the extraction of modelling and processing requirements for computer simulation tools that can be used for design trade-offs and performance assessments of an SBR.

7.2.1

Spaceborne MTI radar applications

Two key advantages of SBR are a greatly increased field of view (FoV), and global coverage without the political, strategic or geographic issues associated with surfacebased and airborne radars. The portion of the earth visible to a spaceborne platform is referred to as the FoV. As much as one third of the earth's surface can be within the FoV at one time. As a result, large search rates can be achieved and a constellation of SBRs can be designed to meet coverage requirements. WAS is used to protect nations with large geographical areas from threats such as ICBMs or enemy aircraft. Such nations would create search fences surrounding their territories wherein threats are detected. The fence acts as a tripwire when crossed. SBR would detect the intrusion, and report the location to friendly forces to respond. WAS requires radars with airborne moving target indication (AMTI) capability. Theatre defence is used when conflict occurs in some region, and timely intelligence concerning ground-troop movement is needed. During the Persian Gulf War (1990-91), the Joint-STARS and AWACS airborne radars were able to provide long-range air-to-ground and air-to-air surveillance. Such intelligence is only available while assets are deployed in the region. An SBR constellation can provide continuous surveillance in several regions, and can also be quickly deployed to new trouble spots. Theatre defence requires radars with ground moving target indication (GMTI) capability. Spaceborne MTI radar applications are illustrated in Figure 7.1. A radar waveform is transmitted from a transmit antenna whose beam is steered towards the desired

transmit waveform characteristics

receiver front-end SBR motion

external noise antenna characteristics: • main • auxiliaries

ionospheric effects Faraday rotation scintillation attenuation

tropospheric effects: volumetric clutter attenuation refraction

target characteristics

jammers

ianu

sea discrete earth's rotation

Figure 7.1 Spaceborne MTI radar applications footprint on the ground. The signal interacts with the ionosphere and is affected to some degree by Faraday rotation, scintillation and attenuation. The signal then interacts with the troposphere and is affected by volumetric clutter (e.g. rain), further attenuation and refraction. In an AMTI application, the signal of interest reflects off airborne targets, and in a GMTI application, the signal of interest reflects off ground targets, before propagating back towards the receive antennas. Only a single receive antenna is shown, but in practice at least two are needed for MTI operation using STAP techniques. Auxiliary antennas may be available for other functions such as electronic counter counter measures (ECCM), to deal with sidelobe jammers, for example. The receive antennas have moved with respect to the transmit location due to the high speed of the orbiting satellite (typically several km/s) and the long distance to the ground. The clutter signals reflected off the earth's surface and the signals transmitted by jammers towards the SBR are interference signals, which must be suppressed by the radar signal processor, so that the desired targets can be reliably detected. The large FoV is evident in the Figure.

7.2.2

Spaceborne MTI radar design

Several radar and system elements are designed and traded-off in order to meet particular mission requirements. The SBR orbit altitude and inclination are two key design considerations. Circular orbits are preferred for SBR because of the uniform coverage

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Electronic steering geometries for SBR

provided and because an elliptic orbit has large variations in power-aperture requirements. Circular orbits also minimise the constellation size for global coverage. For weight and cost reasons, altitude is constrained by the Van-Allen belts. Higher radiation levels need more (heavier) shielding to protect onboard electronics and thus have higher launch costs. Altitudes of interest are thus limited to approximately 2800 km. Spacecraft at higher altitudes provide a larger field of view, and require fewer satellites for efficient global coverage. Below 800 km, the number of satellites needed to provide a given level of global coverage increases rapidly. However, coverage of limited regions can be accommodated at lower altitudes. Lower altitude SBRs are cheaper because of reduced power-aperture and shielding requirements. For a given altitude, the orbit inclination determines the geographical coverage provided. An equatorial orbit will only cover regions within a band on either side of the equator; a highly inclined orbit will cover all of the earth's surface. Antenna design is one of the key elements that influences radar performance. Whereas rotating antennas have been proposed for some MTI radars, electronicallysteerable antennas are preferred (see Figure 7.2 for illustrations of the features described below). Conventional SAR systems (e.g. RADARSAT-I) usually only provide elevation beam steering. With this type of antenna, stripmap SAR imaging can be performed. The antenna beams can be electronically scanned in elevation to move the beam inward or outward from the satellite track. However, azimuth scanning, which would allow the beams to move (almost) instantly forward and backward, is not supported. Combined azimuth and elevation scanning is needed for MTI SBRs and represents a significant engineering challenge. In surveillance applications, scanning a specified volume, where beams are steered and tiled on the ground to interrogate the specified region, is often required (rather than a stripmap). Certain look directions may be revisited for confirmation or tracking dwells. Information from other sensors may be used to cue the radar to look at a given area at a certain time. If the dwell time

for a given look is long enough, the antenna may require spotlighting, which involves steering the antenna during the dwell so that its boresight remains fixed on the area of interest. All of these scanning features require electronic steering to work well. Active phased-array antennas provide the ability to quickly look to arbitrary directions, and to reconfigure the aperture for STAP operation (i.e. forming multiple simultaneous subapertures on receive). Usually the array is aligned with its face either down (nadir-pointing) or inclined to the side (side-looking) and with its longer dimension parallel to the flight direction. In this case, phase shifts that vary across the length of the array cause the beam to steer forward and backwards (i.e. azimuth steering), while phase shifts varying across the width of the array cause the beam to shift up and down (i.e. elevation steering). In practice, the FoV available for surveillance is between the grazing angles 3° and 50°. The lower limit is due to atmospheric effects such as attenuation, whereas the higher limit is due to stronger clutter returns and lower target Doppler. Furthermore, the small antenna footprint at higher grazing angles makes surveillance inefficient. The circular region bounded by 50° grazing angle is referred to as the nadir hole (in surveillance coverage). WAS applications often favour the lower grazing angles due to the longer footprint and higher search rates achievable, whereas theatre defence applications usually work with the higher grazing angles (lower incidence angles). For SBR, the choice of RF is one of the most complex and important design decisions. Low-frequency systems are generally simpler and cheaper, but some hardware is bulkier and heavier. Higher frequencies offer better angular resolution and thus lower minimum detectable velocity (MDV) (which is important for MTI) for a given aperture size. Low frequencies suffer less atmospheric and rain attenuation, but have more problems with the ionosphere. Clutter CTQ tends to increase with RF. Proposed SBRs have varied from UHF to X-band. A typical WAS AMTI system provides long-range surveillance, where high power is needed, which is cheaper at lower frequencies. Since AMTIMDV requirements are not too stringent, L-band provides a reasonable overall compromise. Theatre defence GMTI systems, on the other hand, require more stringent MDV, which is more easily attainable at X-band. Rain is less problematic because of the higher grazing angles. STAP techniques are needed to provide suitable MDV with SBRs. Consider the mainbeam clutter bandwidth, which is nominally 2vp/L Hz, where vp is the spacecraft velocity in m/s and L is the antenna length in m. Given a typical low-earth orbit satellite speed of 7350 m/s and an antenna length of say 10 m, the mainbeam clutter will occupy a Doppler bandwidth of 1470Hz. This translates to mainbeam clutter velocities spreading ± 110 m/s at L-band and ± 11 m/s at X-band. Sidelobe clutter can easily fill the remaining spectrum as illustrated in Figure 7.3. As a result, subclutter visibility is needed for all small targets, and for large targets that are not fast enough (in radial velocity) to shift in Doppler out of the mainbeam clutter. STAP techniques filter or cancel the clutter in two dimensions (space and time) in order to provide the required MDV for targets of interest. In Reference 6, a simple expression for the MDV achievable is derived, which is given by MDV = 0.23 * Vp * X/L. This expression says that an MDV of 5 m/s (for a GMTI application) can be achieved with a 10 m antenna at X-band using STAR STAP

jammer mainbeam clutter

jammer interference sidelobe clutter SBR antenna pattern

small target large slow target

large fast target

SBR direction of motion Doppler

Figure 7.3

Typical SBR clutter spectrum

requires a radar system with a minimum of two receive antennas, suitably spaced, each with dedicated and well matched receivers.

7.3 7.3.1

STAP processing for SBR Typical GMTI signal processing

A review of signal processing techniques typically considered for spaceborne MTI radars is presented next. In this section, both adaptive and non-adaptive MTI signal processing algorithms will be briefly examined. Although this examination is not exhaustive, it illustrates the kinds of signal processing typically considered. Later in this chapter, signal processing requirements for computer simulation tools will be derived, based on this discussion. Space-time adaptive processing techniques are effective for cancelling clutter viewed from fast-moving platforms. STAP techniques operate adaptively on time samples collected from several spatially distinct receive antennas, in order to suppress unwanted clutter. An MTI filter that operates in only one dimension (time) does reduce the mainbeam clutter power. Unfortunately, with moving platforms, it also annihilates targets. STAP filters that operate in both dimensions (time and space) attenuate mainbeam clutter while not overly harming moving targets. Possible STAP domains are time and aperture (space), time and angle, Doppler and aperture, and Doppler and angle. In all cases, STAP is applied quasi-independently over the range dimension. In the time and aperture domain, adaptive clutter cancellation weights are computed from and applied to the pulsed (slow-time) signals from each aperture. MASR (multiple antenna surveillance radar) DPCA [16] and subCPI STAP

are algorithms in this domain. In the Doppler and aperture domain, pulsed-Doppler processing is performed before STAP, which works on the Doppler signals from each aperture. ASAR (arrested synthetic aperture radar) DPCA [5], PRI-staggered STAP and factored STAP [17] are examples of Doppler aperture domain algorithms. A variety of two-dimensional STAP processors that operate simultaneously in time and space are described in Reference 18. Non-adaptive space-time processing can also be applied successfully, using the displaced phase centre antenna (DPCA) technique. The DPCA technique is a form of STAP that works well with only two receive apertures. The whole antenna aperture is used on transmit. On receive, the aperture is divided into halves, each of which feeds its own receiver. The DPCA condition assumes that the phase-centre separation between the two is twice the distance that the platform moves in one PRI. If the condition holds, then on any pulse, the ranges to clutter scatterers for the leading aperture are the same as those for the trailing aperture one pulse later. Therefore, clutter can be cancelled by a conventional (non-adaptive) MTI filter operating on the pulse streams from the two subapertures (shifted by one pulse with respect to each other). Since a target moves over the PRI, its range changes, and it is not cancelled by the filter. The DPCA technique works for clutter from any look direction, and can be generalised to three or more receive apertures. Adaptive cancellation can also be performed effectively with DPCA. A candidate signal processing baseline suitable for GMTI operation is shown in Figure 7.4. If DPCA operation is desired, then the delays shown must correspond to one pulse repetition interval (T) or a multiple thereof. If an algorithm such as PRI-staggered STAP is employed, then a few delays (not shown) would have to be provided for each antenna channel. If a factored STAP algorithm is employed, then the delays are not needed. A minimum of two antenna channels is needed for MTI operation; three channels are shown in Figure 7.4, which allows monopulse estimation to be carried out concurrently with MTI operation. Pulse Doppler (PD) and pulse compression (PC) operations are performed on each channel; these provide the required coherent integration against noise. (Often, PC precedes PD; however, the ordering shown in Figure 7.4 supports the use of non-Doppler tolerant waveforms.) Each STAP filter combines its set of input channels into a single clutter-cancelled signal. The signals from multiple bursts are integrated noncoherently by the NCI function. The detection function thresholds the data and assembles a detection list, which includes position and velocity information, to complete the processing. Adaptive nulling (ECCM) is also shown in Figure 7.4. This function suppresses sidelobe and mainbeam jammers. Sidelobe nulling uses signals from the auxiliary antennas to cancel the jammer signals in the main antenna channels. To illustrate typical processing steps associated with the STAP filtering, the PRIstaggered STAP technique is described in some detail. For each antenna channel, PRI-staggered STAP uses the signals from a number of temporal taps. All temporal taps consist of the same number of pulses, but they differ in their starting pulse. For example, tap 1 's signal consists of pulses 1 to ND, while tap 2 has pulses 2 to No -f-1. A particular tap from a particular antenna is referred to as a space-time channel,

Bogpfef

STAP

auxiliaries

Figure 7.4

Typical MTIprocessor architecture

and corresponds to an adaptive degree of freedom in the STAP algorithm. With PRIstaggered STAP, the number of degrees of freedom is KN, where K is the number of taps and N is the number of channels. The total number of pulses range-compressed is M = No + K — 1, in order to handle all of the taps. Each space-time channel is Doppler processed after range compression. The input to the STAP processing is ^Vrange-Doppler arrays, each with NR range gates and ND Doppler bins, or NRNO resolution cells. For each range-Doppler cell, which has a length KN vector of samples spanning the space-time channels, STAP processing is applied. This involves collecting the vector of samples from the given cell (x) and a size KN by Ns matrix of snapshot vectors from neighbouring cells (X). The snapshot vectors are from the same Doppler bin as the current cell, at ranges surrounding it. The snapshot region specifications (Ns, guard region) are algorithm design parameters. Outer products of the snapshot vectors are averaged to form a covariance matrix:

which is an estimate of the clutter covariance across the space-time channels. R is then inverted. Two options are available for forming the weight vector used to cancel clutter: STAP without steering vectors and STAP with steering vectors. STAP without steering vectors forms the product xHR~ 1X, which cancels the clutter while taking the power of the target plus residual noise. The product, arranged as a range-Doppler array, is the STAP output signal, and is the input to the CFAR detection processing. Optimal detection matches the received vector to all possible steering vectors, and then picks the best one. A steering vector is the response across the space-time channels to an ideal target with a specified position and velocity. To generate the STAP output signal in each range-Doppler cell, the statistic xHR~ls is computed for all steering angles, and the one with maximum amplitude is kept. This is maximum likelihood (ML) processing. The operation, like STAP without steering vectors, uses R~l to cancel the clutter components in x. The advantage with steering is in the suppression of the noise components in x by matching with s. The steering vectors may be scaled by (sHR~ls)~1/2 as described in Reference 13; this is required for proper angle estimation.

7.3.2 Extension to other modes It is unlikely that an SBR would only provide a single mode of operation such as GMTI. Other modes, such as AMTI, pulse Doppler (PD), SAR and SAR-MTI, would also be considered. Trade-offs concerning the performance of any given mode against the other modes is necessary. Therefore, simulation tools used to assist in these trade-offs would need to support a variety of modes. AMTI operation, for example, requires similar processing to that shown in Figure 7.4, but would typically use a waveform optimised for faster targets and greater search rates (i.e. lower resolution). Additional processing considerations, such as range ambiguity removal, would be required. The pulse Doppler mode is suitable for fast targets that are clear of clutter, as well as for the detection of very large targets such as ships. Only a single antenna channel is needed. PC and PD operations are performed, followed by NCI and detection. SAR operation is similar to pulse Doppler in that a single antenna channel is required. PC and PD operations are replaced by an SAR algorithm, which includes range processing similar to PC, range cell migration correction to account for range walk due to the longer dwells and azimuth processing to form the synthetic apertures. NCI is replaced with multilook processing to reduce image speckle, and automated detection, if present, is usually image based. SAR-MTI operation combines features of MTI and SAR to allow moving targets to be detected and overlaid onto an SAR image. At least two channels are needed to support the MTI operation. In a conceptually simple case, SAR processing is performed first on each channel, followed by MTI processing and automated detection. Delay taps can be used as illustrated in Figure 7.4 to implement a DPCA condition, or to support MTI algorithms such as PRI-staggered STAR

7.3.3 Other issues There are a few system and environment issues that impact STAP performance and hence require special modelling considerations. The following issues are discussed below before leaving this section: (i) (ii) (iii) (iv)

effect effect effect effect

of internal motion of random sidelobes of the earth's rotation of jammers and rain.

Clutter internal motion is an inherent characteristic of clutter that fundamentally limits the ability of STAP algorithms to cancel clutter. Sea scatterers are moved about by sea swell, waves and wind, and sea clutter can have a spectral spread of the order of 1 m/s. Land clutter (e.g. vegetation and trees) vibrates due to the wind to a lesser degree, and can have a spectral width of the order of 0.1 m/s. This random motion introduces random phase shifts that limit the amount of cancellation otherwise achievable. Other system elements also impact cancellation (e.g. how well matched and calibrated the antennas and receivers are). Therefore, clutter internal motion effects should be considered when evaluating STAP performance. As alluded to above, the level of matching associated with the receive antennas impacts STAP performance. Consider an active phased array that is an ideal candidate for an SBR antenna. The beam pattern is formed by summing the element responses, suitably weighted and phase shifted. Due to imperfections in manufacturing, there are random variations in the spacing and gains associated with the elements. These variations have two effects. First, they result in the presence of random sidelobes in the beam pattern of a given antenna. Second, the patterns (main beam and sidelobes) of different antennas will be different. As a result, perfect clutter cancellation will not be possible due to these imperfections. In order to mitigate STAP performance degradations that would otherwise result due to random sidelobes, STAP algorithms adaptively compute separate weights for each Doppler bin, which has the effect of making piecewise gain corrections to the antenna patterns. Random sidelobe effects should be considered when evaluating SBR designs or trading-off STAP performance. Since an SBR orbits around it, the earth's rotation imparts different radial velocities on clutter scatterers, depending on their look directions to the radar. As a result, earth's rotation causes clutter spectral spreading in addition to that caused by the motion of the radar platform. To mitigate the effects of earth's rotation, the radar antenna can be mechanically slewed so that the receive antennas align with a certain vector: the sum of the satellite orbital motion vector and the earth's rotational vector (which varies with latitude). Alternatively, if a programmable active phased array is used, receive antennas can be properly aligned electrically, by controlling their aperture shading functions. Earth's rotation and slewing (mechanically or electrically) should be taken into account when modelling and evaluating the performance of STAP radars. The presence ofjammers or rain has the effect of requiring more adaptive degrees of freedom to maintain the same STAP performance. In the case of rain, this is because

the total clutter spectrum becomes more complex in the Doppler dimension. Rather than a simple notch, a more elaborate filter response is needed. Thus extra temporal degrees of freedom (e.g. more taps from each subaperture) may be needed to mitigate rain clutter. Dealing with jammers requires spatial diversity in the radar antennas, so that angular nulls (regions of low gain) can be steered toward the jammer. By varying multiplicative weights on the antenna signals before summing their signals, interferometric nulls can be moved to arbitrary directions. Differing strategies are needed for dealing with either mainbeam or sidelobe jammers. Because the gain towards a sidelobe jammer is low, the interferometer can be set up with a low gain auxiliary antenna and the main aperture. Main beam jammers are more problematic. Nulling them requires similar procedures as for clutter cancellation, namely dividing the main aperture into a small number of large subapertures. Then the interferometer is set up with apertures having similar gains towards the jammer. Combining clutter cancellation with main beam jammer nulling requires more spatio-temporal degrees of freedom than for either individually. It also requires a STAP algorithm designed to handle both forms of interferes

7.4

Simulation and processing for SBR

SBR simulators are used to estimate the performance of space-based radar systems and their signal processing algorithms. They are also used to design space-based radar systems by trading-off and optimising design parameters to achieve a specified performance. In the previous sections, it is seen that GMTI radar detection concepts rely on the cancellation of strong clutter signals, in order to allow the detection of weak target returns. The clutter signals that are combined for cancellation by the STAP filter originate from different apertures at different times. To draw meaningful conclusions, it is imperative that proper correlation (in space and time) of both clutter and target signals be modelled. It is also important to model the effects of real hardware because, as discussed earlier, it impacts radar performance. A simulator must properly model platform motion, range and Doppler ambiguities, clutter internal motion, antenna patterns (differing between apertures) and earth's rotation. It should support a myriad of design choices, with selectable radar, antenna, platform and signal processing parameters so that different radar designs can be traded-off or optimised. It should also be able to simulate arbitrary scenarios, with selectable targets, clutter, and jamming so that particular applications or scenarios of interest can be evaluated. All of these requirements point to a baseband signal simulation, where the radar return signal is generated as samples in range for each pulse. The simulator models the full, expanded, transmit pulse, and then implements pulse compression, rather than modelling an effective compressed pulse. This approach results in greater fidelity and also provides the mechanism for efficiently implementing receiver response mismatch. Also, by starting off with an expanded pulse, imperfections in pulse compression operation can be embedded naturally. The full signal path must be modelled, including the environment, the antennas, the radar analogue and digital parts (for both

transmit and receive) and the signal processor. All of the effects in Figure 7.1 (motion, atmosphere, large FoV etc.) must be dealt with. As return signals are convolutions of the transmitted pulse with each scatterer's response function, range equation terms are needed for each scatterer (gains, range, Doppler, RCS) so that its sampled return signal can be generated. The difficulty with baseband signal simulation is in generating the returns from the many scatterers contributing to the return signal. Although the mathematics for computing their returns is (relatively) straightforward, the sheer volume of computations can easily render a simulator unable to generate the signals in an acceptable time frame. Clutter generation is the single most computationally intensive operation, and care must be taken to optimise its speed and fidelity. Efficiency in generation is a key requirement in radar simulator design. A well designed graphical user interface (GUI) is important to the user, who is the person using the tool to carry out design studies or performance evaluations. It eases the entry of parameters that describe the radar system and scenario, and the subsequent running of simulation experiments. The GUI also permits the quick derivation and cataloguing of results from the experiments, including the plotting of images and curves. The user should be able to specify the design of a radar system and scenario of interest, generate the corresponding complex baseband signals, and then process them with algorithms and parameters that he/she selects. In this section, the aforementioned high-level simulator requirements are broken down into a set of design elements, which describe a candidate baseband signal simulator of space-based radars. Quantities that are described as being modelled, computed, converted, transformed etc. are operations internal to the simulator code. The presentation below organises the design elements into functional areas, beginning with the GUI and followed by discussion of the models needed for the radar, the environment, the baseband signal generation, the GMTI signal processing, and tools needed for evaluation of the results. Radarsim™ SBR [15] is a space-based radar simulator codeveloped by the authors that satisfies the requirements described herein. Selected screen-captures taken from this tool will be used to illustrate design concepts, where appropriate.

7.4.1

User interface

For convenient use of a simulator, a properly designed graphical user interface (GUI) is important, since radar systems and engagement scenarios have so many variables. GUI designs that intuitively manage related groups of parameters make the user's job easier. Below is sampling of logical parameter groupings needed to specify a typical space-based radar, followed by a description of how the environment might be conveniently defined via a GUI. 7.4.1.1 Simulation parameters Reference to the spaceborne radar section yields several logical groupings of radar system parameters that need to be specified by the user: orbit, waveform, receiver,

Table 7.1 Orbit parameters Parameter

Typical value

Altitude Inclination Subsatellite point

800 km 80° latitude less than inclination; any longitude north or south

Direction

Table 7.2

Waveform parameters

Parameter

Typical value

Peak power Carrier frequency Expanded pulse width Pulse bandwidth Burst length Nominal PRF Pulse modulation Fill pulse duration PRI compensation? ZRT compensation? Spotlighting?

5 kW 10 GHz 50 |xs 200 MHz 100 ms 2000Hz linear FM 5 ms yes yes yes

antenna, generation and environment parameters. These are summarised in the following series of tables. Circular orbits are preferred for GMTI radars. A parameter set suitable for specifying a circular orbit is shown in Table 7.1. The subsatellite point and direction relate the SBR to the environment scenario. Pulse Doppler waveforms are appropriate for space-based GMTI (and other modes). Such waveforms can be modelled using the parameters shown in Table 7.2. The pulse compression ratio is defined by the product of its expanded width and its bandwidth. Other forms of modulation include phase coding, non-linear FM and none. The fill pulse duration should be long enough to fill the footprint with ambiguous pulses. The effects of non-ideal receivers are important because of their impact on clutter cancellation. The receivers can be modelled according to the noise added, their frequency responses (including differences between channels) and their non-linearities. The IF filter parameters in Table 7.3 allow the nominal response for each channel

Table 7.3 Receiver parameters Parameter

Typical value

Noise temperature Radar system loss IF bandwidth IF filter type and order IF centre frequency Channel to channel mismatch Number of mismatch ripples A/D sampling rate A/D quantisation level Number of A/D bits Phase noise spectrum

10000K 3 dB 200MHz Chebyshev, 8 1500 MHz —40 dB 8 200 MHz — 120 dB m 8 levels (dB c) at a discrete set of frequencies

Table 7.4 Antenna parameters Parameter

Typical value

Receive aperture locations

+0.5 m azimuth +0 m elevation 4 m azimuth by 1 m elevation Taylor —45 dB azimuth; —30dB elevation to place footprint at desired location 30° elevation tilt; auto-yaw for minimum clutter spread — 50 dB 1.5 cm

Aperture sizes Aperture shadings Electronic steering Mechanical positioning Random sidelobe levels Element spacing

to be computed; the mismatch parameters are used to compute each error response. Additional parameters are used to model the A/D and phase noise characteristics. A phased array antenna system, with multiple subapertures on receive, is a part of most high-performance GMTI designs. Parameters to describe such a system are listed in Table 7.4. Aperture sizes and shadings are specified for the transmit and all receive apertures. Locations are of the given receive aperture's centre, relative to the transmit aperture centre. Random sidelobes are due to aperture errors, whose level can be derived from the entered sidelobe level. An auto-yaw capability is provided, which sets the positioning to minimise the effects of earth's rotation on clutter.

Table 7.5 Generation parameters Parameter

Typical value

Noise seed Clutter seed Aperture error seed Jammer seed

large large large large

integer integer integer integer

Table 7.6 Clutter patch parameters Parameter

Typical value

Position Size Scatterer spacing Backscatter statistics a0 Spectral width Mean radial velocity Height Rain rate

within range swath and main beam 5 km by 5 km 1 m range; 10 m cross-range log-normal, with 10 dB spread -20dBm 2 /m 2 0.1 m/s 2 m/s 3 km 5 mm/hr

Random number seeds (such as those in Table 7.5) for all statistical processes modelled should be user-set parameters, so that simulations can be repeated, and so Monte-Carlo experiments can be performed. Modelling realistic clutter returns is required in order to properly assess the target detection capability of SBR. Parameters to describe clutter patches and rain cells are listed in Table 7.6. (Land clutter should have zero mean radial velocity.) Height and rain rate are only appropriate for rain cells. Rain cells are modelled as sources of clutter as well as in terms of the attenuation they impart on propagating signals. Typical target and jammer parameters of interest are shown in Tables 7.7 and 7.8. These parameters are most easily obtained from the user using a dialogue window. Figure 7.5 shows one such window for some of the receive aperture parameters. 7.4.1.2 Environment GUI Although dialogue windows are good for obtaining parameters such as those discussed in Tables 7.1 to 7.8, they are not well suited to placement of targets and clutter.

Table 7.7 Target parameters Parameter

Typical value

Position Velocity Mean RCS Spectral width

within range swath and main beam 10 m/s; heading towards radar 10 m 2 0.1 m/s

Table 7.8 Jammer parameters Parameter

Typical value

Position Velocity ERP Centre frequency Bandwidth Type Modulation Start and end times

anywhere in FoV stationary 500W 9.5 GHz 1 GHz barrage not pulsed extends over duration of radar waveform

Editing parameters for receive subaperture 1 Select subaperture: | Rx aperture 1 Azimuth (X) taper: | taylor Az. sidelobe level (dB): | X width (m): [ X position (m): [

jjj

jjjt| Elevation (Y) taper: j taylor El. sidelobe level (dB): |

jf|

-40

j

T

|

Y width (m): [

-30 T

^3

]

Y position (m): ["""

0

Figure 7.5 Parameter window A graphical display tool for specifying the locations of clutter patches, rain cells, targets and jammers is a better design. It also allows the placement of the antenna beam and the range swath. The display can provide a map of the earth with latitude/longitude grid lines. Zoom and pan capability can also be provided. The display can also have km rulers as a guide to the distortions introduced by the projections and zooming. Objects can be placed in the environment using controls on the side of the display. After selecting the object to place, the mouse can be used to click and place the object

(or to click and drag out the region occupied by a patch). Once placed on the display, objects can be edited by first selecting them, and then raising a window for their parameters. The subsatellite point can be indicated on the display to assist the user in locating objects. Other useful indicators that can be shown on the display include the orbit ground track, a world map and the azimuth, ground range and slant range to any selected object. In addition, isodop and isorange contours (including the horizon) can be drawn. Surface scatterers on a given isorange line (circle) have the same range to the radar. Stationary scatterers on a given isodop line (hyperbola) have the same radial velocity with respect to the radar. Having these contours helps the user to design good test experiments by allowing him/her to easily place objects so that they appear at desired locations within the radar images. Land and sea patches can be indicated in the display by rectangles of a specified size at the indicated centre location. Targets can be indicated by an appropriate symbol placed at the location of the target, with an attached arrow denoting the direction of motion at that location. Figure 7.6 shows a sample environment display (zoomed in) for an example scenario. Targets are denoted by T symbols, and the solid square is a land patch. The range swath is between the dotted lines (the O symbol is the userdefined swath centre). Solid lines are isodops. The dashed curves are the antenna beam contours (the + symbol is the electronic scanned boresight).

environment editing area (axes in degrees) to add objects select object and press define

!attitude, degrees

Land Patch

axes dimensions (km): x-top: 16.3021 x-middle: 16.3954 x-bottom: 16.4886 y: 40.3316 instructions:

longitude, degrees object geometry from SSP (deg/km): azimuth, slant range, ground range zoom: state: 88.196 817.564 415.123

Figure 7.6

Environment display

zoom:

pan:

7.4.2

Model the radar

In the next two subsections (model radar and environment), suitable models for the platform, antenna, radar and environment are described which form the basis of a simulator for SBR applications. Model-related operations computed as initialisations before core generation operations are also discussed. 7.4.2.1 Platform geometry Standard circular orbits are modelled, and Kepler's laws are used to determine the orbital speed, given the altitude. The satellite orbit is computed in its plane given its inclination, altitude and subsatellite point at time zero. Orbiting platforms are first computed in an ECI (earth-centred inertial) frame, within which the earth rotates. Orbit positions are then transformed into the ECR (earth-centred rotating) frame, where the target and clutter scatterers are represented, by applying earth's rotation. The positions of the transmit and receive antennas are computed at time instants spanning the duration of the waveform. The antenna orientation is computed at the same instants; it consists of the three-dimensional rotation matrices required to convert scatterer ECR coordinates to antenna coordinates (which are azimuth (w), elevation (t>) and boresight (w)). Coordinate transformations are a fundamental aspect of the simulation of radar return signals. Since these transformations are executed many times, they are designed and implemented as efficiently as possible. The positions of the radar and the environment are both described in the ECR coordinate system, in order to difference them for range and bearing computations. They are then converted to antenna coordinates for gain computations. The conversion between the coordinate systems uses time-varying rotation matrices. The user enters the antenna boresight at the beginning of the waveform. It is entered either as its intersection with the earth's surface or as angles in the satellite FRD (forward-right-down) frame. The antenna is assumed to have the same FRD orientation throughout the waveform. The boresight orientation and the aperture positions are combined to determine the rotation matrices. 7.4.2.2 Antenna patterns The antennas are modelled according to the voltage distribution across their apertures. Aperture shadings are computed on two-dimensional x-y grids. Antenna errors (deviations from ideal in amplitude and phase for each element) lead to increased antenna sidelobes. The shadings include aperture errors that, for active phased arrays, are correlated for overlapping subapertures. (STAP processing needs the formation of multiple simultaneous subapertures on receive.) The errors cause the patterns to differ between otherwise identical subapertures. These pattern differences lead to reduced clutter cancellation (relative to ideally matched patterns) and therefore must be modelled. Antenna patterns (in azimuth and elevation) are computed as Fourier transforms of the shading functions. Electronic steering is modelled by applying phase shifts to the element shadings.

7.4.2.3 Receiver responses The receiver frequency responses are modelled as standard (Chebyshev, Butterworth) filter responses. Real receivers have imperfections in their responses that differ between channels. Channel-to-channel mismatch is introduced by multiplying each channel's nominal response with a different error response. The user specifies the level of error and mismatch. The channel responses are later applied to return signals (as filtering operations). 7.4.2.4 Waveform Pulse Doppler waveforms (identical pulses transmitted at an approximately constant repetition interval) are used for SBR. The pulse parameters (duration, bandwidth, RF, PRF etc.) are user-selectable. If selected, motion compensation (ZRT) attempts to keep a desired spot or track at the middle of the range swath. This is done by first computing the range to the spot/track for each pulse, and then delaying the start of sampling (i.e. zero range) appropriately. PRI compensation (if selected) has the pulses transmitted at constant azimuth separation, rather than at a constant time interval. The radar only samples and processes the signal returned from within a userdefined range swath. The swath width must be less than the PRI. The swath's position on the earth varies with time as the platform moves. The swath has range ambiguities, where returns from ranges within the swath plus or minus an integer number of PRIs are received. Range-ambiguous clutter returns can be more troublesome to cancel, thus modelling them is needed for a true assessment of performance. Fill pulses can be transmitted, to ensure that ambiguities of the swath have the same number of pulses returned to the radar. The transmit and receive times for each pulse are computed. Note that these times must be separated by the two-way delay to the swath. 7.4.2.5 Errors All forms of amplitude and phase mismatch between channels reduce the achievable cancellation of strong clutter signals. These include mismatches between antenna gains as a function of angle, those between receiver channels as a function of frequency and those between the I and Q channels of digitisers. All can be helped (but not eliminated) by various calibration and equalisation schemes. Short-term transmitter stability is also important for cancellation, which operates over different pulses. Each of these forms of error is modelled by applying the appropriate distortions to the received signals.

7.4.3

Model the environment

The environment includes models for targets, clutter, jammers and noise. 7.4.3.1 Positions of scatterers In order to properly model their returns across range and Doppler, distributed clutter patches are described as two-dimensional arrays of scatterers, located at the centres

of nominal resolution cells. A position is computed for each scatterer within a patch. Scatterer positions are laid out on a range/cross-range grid. This allows the scatterer spacing to account for the resolution available in each dimension. Target positions are computed as they move over the duration of the waveform, and are not represented on any grid. The atmospheric and rain attenuation are computed at each scatterer location. 7.4.3.2 Reflectivity of scatterers Land and sea clutter amplitude distributions (over area) are in general non-Rayleigh, especially with high range resolution. The distributions one should model include log-normal, K, Rayleigh and fixed. Consider a log-normally distributed patch as an example. Log-normally distributed variates are generated, and these become the mean powers of the scatterers within the patch. However, each scatterer is temporally Rayleigh amplitude distributed. That is, as time evolves, its amplitude will vary according to a Rayleigh distribution, with a user-specified spectral width. This is a realistic model, since a given ground scatterer is unlikely to be log-normal temporally. The target models can be chosen from the same distribution families, and also include a spectral width for their scintillation. The temporal variation models clutter internal motion; doing so properly is critical to deriving performance in realistic clutter. The scattering time sequences, which are their radar cross sections (RCS) described as a (complex) voltage for each pulse, are computed for each scatterer. This can be done in either of two ways. The first is to generate a random spectral sequence shaped by the amplitude spectrum, and then inverse Fourier transform. The second is to generate a white time sequence and then FIR filter with a response shaped by the correlation. The choice depends on the scatterer bandwidth relative to the PRF. These techniques are described in Mitchell [14].

7.4.3.3 Noise For each channel, a white noise signal is first computed, and then the receiver response is applied. This approach works for receiver channels originating from independent apertures. To implement proper receiver noise modelling, its channelto-channel correlation across overlapping subapertures of phased arrays must be included. This is important because adaptive algorithms can be impeded by this correlation. A selectable noise temperature completes the model. 7.4.3.4 Jammers Jammer generation is performed in a manner similar to noise generation. Extra steps include applying antenna gains, propagation loss (radar equation terms) and jammer modulation. When aperture separations and receiver bandwidths are both large, it is important to model jammer decorrelation between channels, since it leads to degradations in achievable cancellation.

7.4.4

Generate the signals

This part of the simulation generates the return signals from the scatterers. The received signal is the sum of scatterer returns, noise and jamming. It is of dimensions (number of receivers) by (number of pulses) by (number of samples in range swath), typically 2 by 128 by 4 K. The objective of STAP processing is to cancel the strong clutter return that originates from a large number of scatterers. It is thus important that the amplitudes and phases for all contributing range equation terms for each scatterer at each time instant be consistent. Any discontinuities in the models can lead to spurious clutter residue that really does not exist. In particular, the following terms must be simulated with high fidelity: • • • •

range and bearing (as functions of time) from each aperture to each scatterer cross section (as function of time) for each scatterer gain (as function of angle) for each aperture towards each scatterer distortions (as functions of time or frequency) for each channel.

7.4.4.1 Range equation terms On each pulse, the range, azimuth (w), elevation (i>), Doppler, transmit and receive gains, carrier phase and cross section are computed for each scatterer. These are obtained by differencing scatterer and satellite positions, rotating to antenna coordinates, differencing ranges at the two time instants, looking up and interpolating the antenna pattern grids, respectively. Ranges to each aperture are computed using their respective positions at the receive time. Accurate range computations are important to get the correct carrier phase relation between apertures, which is needed to accurately model the achieved cancellation. Doppler is needed for interpolations in the scatterer summation/convolution. Bistatic range computations are necessary for high fidelity modelling of spacebased radars. These account for motion between the transmission and reception of the radar pulses. The algorithm interpolates backwards from receive times to find reflection and then transmit times for each scatterer, and then interpolating the satellite position to the transmit time. For moving targets, their range computations also include interpolation of the target position to the reflection time. The range, transmit power, system loss, RCS, antenna gains etc. are combined together as range equation terms into a (complex) return signal voltage for each aperture. The return from each scatterer now conceptually consists of a delta function at its range delay, weighted with this voltage. The sum of delta functions is next convolved with the transmit pulse. The result of the convolution is the received reflected signal. Depending on whether there was a transmit pulse for a given scatterer's range ambiguity (i.e. if there were enough fill pulses), its returns may be suppressed for the first or last few pulses. 7.4.4.2 Scatterer summation The purpose of the scatterer summation is to generate the complex voltage signal that is the superposition of the pulse returns from all scatterers. For all of the scatterers, the

range delays t;(0), received voltages Vix and Doppler frequencies Di(O) have been computed (/ denotes scatterer and t denotes continuous time starting at the zero-range return for the given pulse):

T[ is the range to the /th scatterer and fc is the carrier frequency. The total voltage is the sum of the individual scatterer voltages convolved with the expanded pulse response p(t): VcumiO = J2

Vix

P(f ~ T 'W) exp(-j27r/ c r/(0)

i

Each scatterer pulse return requires a complex exponential (representing the expanded pulse) to be evaluated at every receiver sampling time, which is very expensive if done by brute force. The process of optimising this computation is most challenging in terms of maintaining both high fidelity and high execution rates. 7.4.4.3 Receiver responses Receiver responses and models for the non-linearities (including the A/D), phase noise and eclipsing are applied to received signals. Receiver responses are implemented as filtering operations, while the other effects are single-point functions applied to each received sample.

7.4.5

Model the processing

Simulating the processing is more straightforward, since most algorithms can be simulated exactly as they would be implemented. The challenge is in simulating most of the many potentially viable algorithmic alternatives. The user first selects one out of a number of candidate baselines, and then chooses a set of appropriate parameters. The baselines of interest for SBR in general consist of coherent integration followed by STAP and then by detection. 7.4.5.1 Coherent integration Range and Doppler processing form a bank of matched filters to the waveform over the span of resolvable target ranges and velocities. The user specifies which channels and how many pulses are required as part of the processing parameters, as well as window parameters to control range and Doppler sidelobes. Each pulse from each spatial channel is range compressed. Range compression produces NR range gates for each pulse. Doppler processing immediately follows range compression, and produces No Doppler bins from Np pulses, and is performed on each space-time channel.

7.4.5.2 Clutter cancellation STAP processing then filters across the space-time channels. Covariance matrix estimates are formed for each range-Doppler cell, and these are used to compute a weight vector. The reference cell parameters should be user entered. The weight vector is used for summing the signals over the channels, resulting in a single cluttercancelled matrix of ND by NR resolution cells. With this part of the processing, the numerical precision of the SBR target computer should be modelled, since it has important effects on adaptive algorithms that are attempting to cancel interference that is considerably stronger than target returns. 7.4.5.3 Non-coherent processing After clutter has been cancelled, detection, estimation and imaging operations are typically performed. CFAR processing typically includes either the cell-averaging (CA) or the ordered statistic (OS) algorithm in order to produce a list of target detections. The user selects the threshold and the CFAR reference cell region (including guard bins) spanning both the range and Doppler dimensions.

7.4.6

Evaluate the results

Important performance measures for a radar system relate to the detectability of targets: how small? how slow? at what range? in what clutter? A simulator needs tools to measure the detection (and estimation) performance of the radar system being modelled. It also needs the ability to analyse the signals after various processing steps, in order to determine their effectiveness. 7.4.6.1 Intermediate products During processing, intermediate products (the signals coming out of each processing stage) should be stored in data structures so that the user can analyse them. The twodimensional signal after each stage can be displayed as an image depicting amplitude as a function of range and Doppler (or pulse). Intensity/colour denotes amplitude and each signal dimension takes a Cartesian axis. The following images can be displayed, depending on the processing baseline and options: 1 2 3 4 5

input signal: amplitude versus fast-time and pulse range-compressed signal; amplitude versus range and pulse post PC/PD signal: amplitude versus range and Doppler clutter-cancelled signal: amplitude versus range and Doppler CFAR normalised signal: amplitude versus range and Doppler

For each image, the user selects the two-dimensional region to display and the dynamic range. For images 1 to 3, the channel number is also selected. Target positions can be overlaid with symbols at their true (known a priori) locations; this helps greatly in determining the effectiveness of various processing steps. Figures 7.7 and 7.8 show images of the post-PC/PD and of the clutter-cancelled signals for an example scenario.

Doppler, Hz

ASAR post PC-PD signal, channel 1

range, m

Figure 7.7 Signal before STAP processing

Doppler, Hz

ASAR post-STAP signal

range, m

Figure 7.8 Signal after STAP processing

In the second image, notice that the clutter has been significantly cancelled, and that targets now appear as bright regions surrounding their true locations. 7.4.6.2 Analysis products Target statistics can be extracted from (small) range-Doppler regions surrounding their true positions. Each target's level, SES[R and improvement factor is computed as the maximum over its respective region. Clutter statistics (level, cancellation ratio)

can be extracted from a larger range-Doppler region. All target regions are excluded from the clutter statistics. Statistics are extracted from the signals both before and after STAP processing. This allows improvement factors to be computed. Target statistics can be displayed versus target number, Doppler, range, RCS or ground velocity to provide additional information. The detection process also creates a detection list (Doppler bin, range bin and power). Clutter statistics can be displayed as histograms, or as scatter plots versus Doppler or range.

7.5

Discussion and conclusions

Computer simulation tools for modelling space-based radars employing STAP have been presented. Using these tools, the performance of SBR designs can be evaluated, and design parameters can be optimised. Spaceborne radar applications and design were reviewed. SBR has a large FoV and is capable of global coverage and large search rates. WAS is used to protect large geographical areas from airborne threats and requires AMTI. Theatre defence is used for monitoring a localised region and requires GMTI. STAP techniques for space-based radar were reviewed. Clutter signals must be suppressed, so that targets can be detected. With fast-moving platforms, STAP filters the clutter in space and time in order to cancel it. This provides the required MDV for targets. STAP requires a minimum of two displaced receive antennas with well matched receivers. Pulse compression and pulse Doppler provide the coherent integration. The STAP algorithm combines the channels into a single clutter-cancelled signal, where targets can be detected. Active phased array antennas with electronic steering are preferred for SBR, because they provide beam agility, spotlighting and the ability to form multiple subapertures on receive. Clutter internal motion, ambiguities, pattern and receiver mismatches, earth's rotation, rain clutter and jammers all limit the ability of STAP to cancel clutter with SBR. To mitigate, STAP algorithms adaptively compute weights, have extra degrees of freedom and have their antennas slewed. SBR simulators are used to estimate performance and to help design systems. STAP cancels large clutter signals in order to detect small target returns. To ensure accuracy, proper correlation of signals must be modelled, as must the above limiting factors. Thus baseband signal simulation is recommended, where the radar return signal is generated as samples in range for each pulse. The implementation of a baseband simulator is difficult because of the large number of scatterer returns that must be included. The simulator should also support many design options, parameters and scenarios. Because of the many parameters needed to describe SBR, a well designed GUI is important. It eases parameter entry and allows the running of experiments. To generate the return signals, there are many details to be modelled: positions and orientation of antennas, ranges and bearings of scatterers, aperture shadings with errors, antenna patterns, pulse Doppler waveforms, the range swath with its ambiguities, clutter patches, scatterer distributions over area, and scatterer temporal variation. These are

all used to derive range equation terms that are convolved with the transmit pulse and combined to form the return signal voltage. It is important that the amplitudes and phases of modelled functions be accurate and consistent. It is also important to optimise the signal generation routines, in order to run in reasonable time. Optimising the convolution with the expanded pulse is typically the most difficult of the speed-fidelity trade-offs. A simulator needs tools to measure performance. It also needs the ability to analyse the signals after various processing steps, in order to determine their effectiveness. The two-dimensional signals after each stage can be displayed as images. Target and clutter statistics can be extracted both before and after STAP processing, and be displayed as histograms, curves or scatter plots. The statistics from a series of experiments can be extrapolated to determine whether the SBR design can meet mission requirements. SBR simulators should become increasingly more useful to radar designers in the future, as long as the models within them are accurate and flexible, with appropriate care taken so that both fidelity and speed are achieved. Their implementation on general-purpose office computers, making them widely available, should result in future SBRs being designed and launched with significantly reduced development costs. Finally, it is worth noting that the simulation requirements for SBR are common to other applications such as airborne MTI radars; hence, simulators for them can be designed using similar strategies to those described herein.

References 1 CANTAFIO, L. J. (Ed.): 'Space-based radar handbook' (Artech House 1989) 2 SKOLNIK, M.: 'Radar handbook' (McGraw-Hill, 1990, 2nd edn.) 3 BIRD, J. S. and BRIDGEWATER, A. W. 'Performance of space-based radar in the presence of earth clutter' IEE Proc. F, Radar Sonar Navig., August 1984, 131, (5), pp 491-500 4 BROOKNER, E. and MAHONEY, T. F.: 'Derivation of a satellite radar architecture for air surveillance', Microw. J., February 1986, pp 173-191 5 NOHARA, T. J.: 'Design of a space-based radar signal processor', IEEE Trans. Aerosp. Electron. Syst, April 1998, 34, (2), pp 366-377 6 NOHARA, T. J., WEBER, P., and PREMJI, A.: 'Space-based radar signal processing baselines for air, land, and sea applications', Electron. Commun. Eng. J., October 2000, pp 229-239 7 NOHARA, T. J., WEBER, P., PREMJI, A., and LIVINGSTONE, C : 'SARGMTI processing with Canada's Radarsat 2 satellite'. Proceedings of the IEEE symposium 2000 on Adaptive systems for signal processing, communications, and control, Lake Louise, Alberta, Canada, October 1^4, 2000 8 YAKOV D. SHIRMAN: 'Computer simulation of aerial target radar scattering, recognition, detection and tracking' (Kharkov Military University, Editor, Artech House Publishers, 2002)

9 SERGEY A. LEONOV: 'Handbook of computer simulation in radio engineering, communications and radar' (Artech House Publishers, 2001) 10 BASSEM R. MAHAFZA: 'Radar systems analysis and design using MATLAB' (Chapman & HALL/CRC, 2000) 11 U.S. Defense Modeling and Simulation Office (DMSO), http://www.dmso.mil 12 Modeling and simulation conference, Association of Old Crows, U.S.A., Orlando, FL, July 17-18, 2002 13 KELLY, E. J.: 'An Adaptive Detection Algorithm', IEEE Trans. Aerosp. Electron. Syst, AES-22, (1), March 1986, pp. 115-127 14 MITCHELL, R. L.: 'Radar signal simulation' (Artech House, Dedham, MA, 1976) 15 Radarsim®SBR Space-based radar design and performance evaluation tool, Sicom Systems Ltd., www.sicomsystems.com 16 KELLY, E. J., and TSANDOULAS, G. N.: 'A displaced phase center antenna concept for space-based radar applications'. IEEE Eascon, Washington, 1983, pp.141-148 17 TIM J. NOHARA: 'Comparison of DPCA and STAP for space-based radar.' Proceedings of the 1995 IEEE international Radar conference, Arlington, VA, USA, May 8-11, 1995, pp. 113-119 18 KLEMM, R. and ENDER, J.: 'New aspects of airborne MTF. Proceedings of the 1990 IEEE international Radar conference, Arlington VA, USA, May 7-10, 1990, pp. 335-340

Chapter 8

Techniques for range-ambiguous clutter mitigation in space-based radar systems1 Stephen M. Kogon and Michael Zatman

8.1

Introduction

Space-based radar (SBR) systems provide several important capabilities for the detection of moving targets that are not possible from an airborne platform. These advantages include continuous access to important tactical areas as well as rapid surveillance of large regions on the ground [I]. Although SBR systems have been studied for some time now, it is only recently with the rapid development of computational and antenna array technology that these systems have come closer to realisation. As a result, a large research investment has been made into the development of future SBR systems [2]. SBR systems show great promise for the detection of ground moving targets, a mode commonly referred to as ground moving target indication (GMTI) which is enabled by ground clutter cancellation using space-time adaptive processing (STAP). A GMTI mode typically utilises a pulse-Doppler waveform, consisting of a series of pulses transmitted at a constant rate known as the pulse repetition frequency (PRF). The advantage of these waveforms is the approximate decoupling of range and Doppler that allows for efficient processing with fast Fourier transforms (FFTs). However, these pulse-Doppler waveforms are plagued by ambiguities in both Doppler and range [3, Chapter 17]. In SBR geometries, these ambiguities intercept clutter and cause problems for GMTI detection [I]. Doppler ambiguities arise due to the high platform velocity in an SBR but can be effectively managed through sidelobe control and STAP algorithm design. Range ambiguities, on the other hand, are a problem

1

This work was supported by the U.S. Air Force under Air Force Contract # F19628-00-C-0002. Opinions, interpretations, conclusions and recommendations are those of the authors and are not necessarily endorsed by the United States Government

radar pulses

Figure 8.1 Range-ambiguity problem for an SBR at low grazing angles or long ranges for an SBR at low grazing angles or equivalently long ranges when the area on the ground illuminated by the radar exceeds the radar receive window of each pulse. An illustration of this problem is shown in Figure 8.1. These ambiguities are much more difficult to handle. Mechanical steering of the SBR array to maintain boresight on an area of interest produces a variation in clutter angle-Doppler characteristics with range. This non-stationarity leads to multiple Doppler frequencies with SINR loss holes from range-ambiguous clutter and can severely compromise detection performance. The use of STAP in the presence of range ambiguities and strategies for coping with these ambiguities are the topics of this chapter. For this chapter, we focus on a notional SBR platform in low-earth orbit (LEO) at 1000 km altitude with an antenna 20 m in length (azimuth) and 2 m in height (elevation). First, notation and metrics are established for moving target detection from an SBR with STAP followed by a discussion of the unique characteristics of ground clutter returns in SBR. In particular, the problem of range-ambiguous clutter is described. Next, we demonstrate the impact of range-ambiguous clutter on STAP performance and describe two means of overcoming the range-ambiguous clutter problem for pulse-Doppler waveforms: PRF diversity and an increase in elevation aperture. Last, the use of an alternative new waveform, namely a long single pulse waveform, that eliminates ambiguities both in range and Doppler, is considered for an SBR system.

8.2

Moving target detection with SBR

An SBR is a very powerful asset for surveillance applications since it can observe a large area on the ground below due to its high platform altitude. This large observable area gives an SBR a great deal of flexibility in where it looks and offers the capability of rapid search rates. The difficulty that arises from a large observable area is the management of all the returns. A large azimuthal aperture or array length focuses the SBR to a particular azimuth or cross-range area. In addition, aperture in the azimuth dimension limits mainbeam clutter Doppler spread which in turn determines performance against slow moving targets. The other dimension of range has an extent starting at the subsatellite point out to the horizon. This large range extent can present problems for a pulse-Doppler waveform. Unlike airborne applications which have

platform velocity

aimpoint

mechanical steering angle

Figure 8.2

Mechanical steering of SBR with angles with respect to array
is used as the cone angle with respect to the array and ^ is the cone angle with respect to the velocity vector. The difference in these two angles: #mech=0-^

(8-1)

For example, at an altitude of 1000 km the PRF to remain range unambiguous to the horizon would be 55.5 Hz

is the mechanical steering angle. The angle between the array axis and the velocity heading is often referred to as the crab angle in certain airborne systems [4, 5]. This mismatch of the array axis with velocity heading leads to a range dependence of clutter Doppler and has certain consequences on STAP both in terms of training adaptive weights [6, 7] and range-ambiguous clutter. Although electronic steering can also be employed,3 for the analysis in this chapter we will restrict ourselves to a mechanically steered array without any electronic steering, i.e. array broadside 0 = 90°.

8.2.1 STAP for SBR systems Space-time adaptive processing (STAP) has become a well established research area, in large part due to a heavy research effort over the past 15 years, most of which has been well documented [4, 5]. Although the cancellation of ground clutter in radar systems using STAP had been introduced back in the 1970s [8], STAP has matured to the point that a recent textbook has been devoted to the topic [5]. Although most STAP work to date has focused on airborne platforms, space-based platforms have been considered more recently [9, 10]. STAP is the two-dimensional adaptive filtering for ground clutter cancellation used in radar applications with a moving platform, airborne or space-based, for the detection of moving targets. The principle that STAP exploits is that clutter returns constitute interference from the non-moving ground. These returns have a unique spatial and Doppler structure determined by the platform velocity and the orientation of the array. Moving targets, on the other hand, have a different Doppler than ground clutter due to the additional Doppler shift from their own radial velocity i>t relative to the radar. The Doppler frequency of a moving target is given by: ft = -r1 + - ^ c o s V t A

(8.2)

A

where up is the radar platform velocity, A is the radar wavelength and i/rt is the cone angle between the platform velocity vector and the direction to the target.4 The Doppler frequency of clutter coming from the same angle as the target is: 2 Un

/ c = - ^ cos Vt

(8.3)

A

Hence, the use of the two dimensions of space and time makes it possible to separate moving targets from clutter that is not possible in either angle or Doppler alone. Although most STAP analyses assume an TV element uniform linear array with A/2 spacing, SBRs typically use a two-dimensional array that is so large that forming digital channels on each element is not practical. Thus, we consider an SBR twodimensional array with subarrays formed in two-dimensional panels to create an array of TV spatial channels, i.e. subarrays, with a uniform spacing of D metres. Note that the spatial channels are formed in one dimension along the azimuthal axis as the 3

Electronic steering is used to alleviate mechanical steering requirements or to simultaneously cover multiple areas on the ground 4 V = 0° is forward, \Jr = 180° is aft and f = 90° is broadside

entire elevation dimension has been beamformed to the aimpoint for each subarray.5 Consider the problem of detecting a moving target at a Doppler frequency / t and an angle with respect to the array 0t- The pulsed waveform uses M coherent pulses transmitted at the pulse repetition frequency (PRF) /PR. The time between pulses, known as the pulse repetition interval (PRI), is simply the reciprocal of the PRF. The returns from these M pulses make up a coherent processing interval (CPI). The space and time response vectors of this target are given by: (8.4) (8.5) respectively. The combined space-time response vector of the target is then simply the Kronecker product: v(0t,/t) = b ( / t ) ® a ( 0 t )

(8.6)

Let us consider a space-time snapshot containing a target signal and given by: x ( / i ) = a t v ( 0 t , / t ) + Xi+n(n)

(8.7)

where oft, 4>u and / t are the target amplitude, angle with respect to the array, and Doppler frequency, respectively. Xi+n is the interference-plus-noise signal and n is the snapshot index. Here, we only consider interference consisting of ground clutter returns from the transmitted radar signal. The optimum space-time weight vector6 steered to 0o a t Doppler frequency /o is given by [8]: (8.8) where Qi+n = E{xi +n (n)xj +n (n) // } is the interference-plus-noise covariance matrix due to clutter coming from all angles. This version of the optimum STAP weights has been normalised for unit gain in the look direction. The performance of the optimum space-time processor from equation (8.8) is measured via the output signalto-interference-plus-noise ratio (SINR). As the name implies, SINR is simply the ratio of output target signal and interference-plus-noise powers: (8.9) where orf is the target signal power in a subarray channel. Many times, we want to compare the SINR to the maximum SINR that could possibly be achieved. This upper limit is determined by the ideal matched filter for the interference-free case, i.e. thermal noise only. Normalising the SINR by the SNR of the ideal (interference-free) The use of two-dimensional array channels is not considered in this chapter; adaptation for threedimensional STAP with two-dimensional degrees of freedom requires more complicated algorithms and training due to the range-dependent nature of clutter in the elevation dimension ^ STAP weights are optimum when (pQ = (pt and /o = ft

matched filter SNRo yields: (8.10) which is known as SINR loss [4]. Many times SINR loss is computed across angles and/or Doppler frequencies. An SINR loss of unity (0 dB) indicates perfect interference cancellation. Although the SINR loss metric indicates the losses associated with the presence of clutter, a more meaningful metric for a GMTI radar is the slowest velocity it is able to reliably detect, known as the minimum detectable velocity (MDV). A common measure of MDV is the minimum velocity for an acceptable SINR loss, e.g. LSINR = - 5 dB.

8.3

Clutter characteristics of pulse-Doppler waveforms in SBR

In this section, we examine the characteristics of clutter in an SBR system using pulse-Doppler waveforms that lead to some unique issues for STAP ground clutter cancellation. These characteristics arise from the range-Doppler ambiguity function for a pulse-Doppler waveform shown in Figure 8.3. Doppler ambiguities occur at regular spacings of the PRF /PR, and range ambiguities occur at integer multiples of the PRI, i.e. inversely proportional to the PRF. Control of these two ambiguity types is clearly at odds with one another. As we will see, requirements on a minimum PRF for Doppler considerations can lead to range ambiguities and degraded STAP performance. In addition, the Doppler resolution is determined by the coherent integration time (CPI length) and the range resolution by the radar bandwidth as shown in Figure 8.3. The implications of this pulse-Doppler ambiguity surface for an SBR arise from some unique aspects of the SBR platform. These aspects include:

azimuth beamwidth

Doppler

1 large platform velocity 2 high altitude 3 full mechanical steering (360°).

elevation beamwidth 2*bandwidth

integration time

range

Figure 8.3 Range-Doppler ambiguity surface for a pulse-Doppler waveform

The high platform velocity of an SBR leads to large Doppler frequencies for clutter and a large Doppler spread of mainbeam clutter. As a result, the radar has a minimum PRF that must be maintained for effective clutter mitigation and MDV performance. On the other hand, a high platform altitude leads to a large range to the ground and therefore a large illuminated area on the ground. To remain range unambiguous over the illuminated area, the radar must operate at a maximum PRF corresponding to the range extent of this illuminated area. Finally, range-ambiguous clutter is complicated by the mechanical steering of the array which leads to misalignment with the platform motion. The clutter has range-dependent angle-Doppler characteristics resulting in non-stationary behaviour in range complicating the clutter mitigation problem. We detail these characteristics and their implications on STAP in the following section.

8.3.1

Clutter Doppler ambiguities

SBR systems, unlike airborne radars, have such a high platform velocity that it is not possible to operate at a PRF that does not result in ambiguities in Doppler. Recall that the Doppler frequency of clutter from any point on the ground is given by: /c = ^COSi/rc A

(8.11)

where \j/c is the angle to the clutter with respect to platform velocity. The total Doppler extent of clutter is then the difference between forward ^c = 0° and ^c = 180° and is given by: 4v A/c = - 1

(8.12)

A

Since the PRF is essentially the Doppler sampling frequency, it must be greater than the total clutter Doppler extent in equation (8.12) to avoid any aliasing, i.e. to be unambiguous. For example, for a low-earth orbit SBR with an altitude of 1000 km and a platform velocity of 7000 m/s operating at / = 10 GHz, the total Doppler extent is 933.3 kHz. Choosing a PRF to be Doppler unambiguous in this case is clearly not practical.7 The fact that can be exploited in order to manage Doppler ambiguous clutter is that clutter has a unique angle-Doppler correspondence. As a result, Doppler ambiguous clutter can be rejected spatially either with low two-way transmit/receive (Tx/Rx) azimuth sidelobes or with STAP spatial degrees of freedom. For low grazing angles, i.e. shorter range, received clutter power is stronger and spatial DoFs can be used to handle clutter that leaks through azimuth sidelobes. At smaller grazing angles (long ranges), clutter power is weaker and azimuth sidelobes should be used to suppress Doppler ambiguities. Since we can rely on sidelobes and STAP to handle Doppler ambiguities, the key requirement is that we do not allow any Doppler ambiguities 7

A PRP this high would yield an extremely low range extent and would be highly range-ambiguous. In addition, this PRF would be severely oversampled and therefore redundant in terms of potential target velocities placing an unnecessary processing burden on the SBR

to exist within the receive azimuth mainbeam. Satisfying this condition allows for effective nulling of the clutter Doppler ambiguity and maintains acceptable SINR loss and MDV performance.8 For an array with an azimuthal aperture L az , the PRF must be chosen to be larger than the mainbeam clutter extent to avoid mainbeam Doppler ambiguities. Clutter within the mainbeam already requires STAP to perform mainbeam nulling to detect targets within the mainbeam clutter spread. For an array of length L32, the nulls for an untapered beam fall at COs^11 ^ = A/L az and the null-to-null beamwidth is: Acos

(mb)^|i

(8.13)

Therefore, the mainbeam clutter spread measured from null to null of the beamwidth is found by substituting equation (8.13) into equation (8.11) and is given by:

A/ffi = ^

(8-14)

L az

Note that this Doppler spread is independent of frequency or wavelength. As a result, the minimum PRF for effective STAP clutter suppression and to maintain good MDV performance is:

/PR > ~ L

(8.15)

az

This PRF is commonly referred to as the displaced phase centre array (DPCA) PRF which is the PRF that has a pulse-to-pulse delay T equal to the time for equivalent monostatic phase centres from the front and back halves of the array to spatially align from consecutive pulses [4]. Using a time delay between pulses that spatially aligns the front and back half apertures results in matching clutter characteristics for the two spatial channels. In theory, this condition allows for the perfect cancellation of clutter by subtracting consecutive pulses from the two half-aperture phase centres.

8.3.2

Clutter range ambiguities

The amount of unambiguous time associated with a pulse in a pulse-Doppler waveform is the pulse repetition interval (PRI) given by: ^P = y -

( 8 - 16 )

/PR

and the amount of time associated with a range extent AR on the ground is: At=™*

(8.17)

C

Provided the coherent integration time is long enough to give sufficient Doppler resolution and to ensure STAP performance is aperture limited, e.g. r c o h > ^r 2 -

Therefore, the amount of unambiguous range associated with a PRI, considering two-way propagation from the radar to the ground, is:

A*=-f-

(8.18)

2/PR

We will strictly concern ourselves with elevation mainbeam clutter since remaining range unambiguous out to the radar horizon is not practical for SBR. Instead, we will rely on the elevation Tx/Rx sidelobes and proper radar management of clutter power to ensure that ambiguities in the elevation sidelobes can be ignored. The amount of range illuminated by an SBR antenna array is determined by the elevation aperture Lei and the range to the ground. Although, for a flat earth assumption the illuminated range can be approximated by R\\ ~ /?A0ei, SBR applications must account for earth curvature and such a simple expression for illuminated range is generally not possible. However, the illuminated range is easily computed by computing the angles of elevation beamwidth nulls and computing the grazing angle, and therefore range, associated with these elevation angles. From the illuminated range, we can compute the range-unambiguous PRF by substituting for AR in equation (8.18) and solving for /PR. Figure 8.4 shows the range-unambiguous PRF, i.e. the maximum PRF for which the radar does not have any range ambiguities in the elevation mainbeam, as a function of grazing angle for our SBR example at / = 10 GHz with a platform

range-unambiguous PRF, Hz

5 metre 2 metre 1 metre

grazing angle, deg

Figure 8.4

Range-unambiguous PRF versus grazing angle for SBR with platform altitude h = 1000 km, f = 10 GHz and elevation apertures of1 m (solid line), 2 m (dotted line) and 5 m (dashed line)

altitude of 1000 km for elevation apertures of 1, 2, and 5 m. Recall the PRF for effective clutter cancellation from equation (8.15) is a function of the azimuth aperture. Usually, azimuth aperture will be L32 > 10 m for MDV considerations and 1500 > /PR > 3000 Hz. This requirement for range-unambiguous PRF is in clear violation of our minimum PRF requirement to maintain MDV performance from Section 8.3.1, especially for low grazing angles (long range). For these grazing angles, an SBR must simply accept the fact that range-ambiguous clutter exists within the elevation mainbeam. As we also see from Figure 8.4, more elevation aperture allows an SBR to operate range-unambiguously out to lower grazing angles. We explore this option as a tool to combat range-ambiguous clutter in Section 8.5.2.

8.4

Impact of range-ambiguous clutter on STAP performance

In the previous section, we discussed ambiguities in range and Doppler. Doppler ambiguities of clutter can be effectively handled with proper sidelobe control and STAP spatial degrees of freedom. Range-ambiguous clutter, however, is much more difficult to alleviate since STAP does not have a dimension to discriminate ambiguities from one another. Here, we give examples of the impact of range-ambiguous clutter and show the two aspects that affect the impact of range-ambiguous clutter: grazing angle or range to the radar and mechanical steering of the array. As discussed in Section 8.3.2, range ambiguities arise at long ranges due to the range extent of the elevation mainbeam. Mechanical steering of the array, however, is the mechanism which makes range-ambiguous clutter a big problem for GMTI performance. Consider the depiction of range-ambiguous clutter for the cases with and without mechanical steering shown in Figure 8.5. For a mechanically steered array, the misalignment between the velocity vector and the array axis produces isoDoppler and isocone angles that no longer overlay. As a result, clutter will have angle-Doppler characteristics that vary with range. This problem arises for STAP training across range, but its impact is much more severe in the case of range-ambiguous clutter. The result is multiple clutter ridges for all ambiguities which result in multiple Doppler frequencies that have clutter for any given angle, as shown in Figure 8.5. As we will see, the result is multiple SINR loss notches that create several blind velocity zones. To illustrate the impact of range-ambiguous clutter on STAP clutter cancellation performance, we show SINR loss versus target velocity for a few SBR scenarios.9 Throughout this chapter, SINR loss is computed from true covariance matrices and is intended to provide an upper bound on STAP performance that could be achieved in an actual SBR for the given geometry. The results do not reflect any losses arising from estimated covariances or from training STAP weights with range-varying clutter snapshots. In both cases, we look at the performance of a 20 x 2 m array operating 9 SINR loss is plotted versus target velocity and not Doppler frequency. Clearly, for mechanical steering angles other than broadside # mec h = 0°, the Doppler shift at array broadside is /dOpp ¥= 0- These SINR loss curves versus target velocity reflect the Doppler contribution of the target only and can be thought of as having compensated for SBR platform-induced Doppler on the target

isocone isoDoppler ambiguity aimpoint ambiguity

Doppler

no mechanical steering (azimuth = 90°)

angle mechanical steering

Doppler

range ambiguities

angle

Figure 8.5

Non-stationarity ofclutter ridges in angle-Dopplerfor range-ambiguous clutter

at a 1000 km altitude, / = 10 GHz and a PRF of / P R = 2500 Hz at the two ranges of 1300 km and 2700 km (47° and 11° grazing angles). The number of subarray channels is N = 8 and the CPI length is M = 64 pulses. The clutter-to-noise ratio in this case is 25 dB. SINR loss is shown for target velocities between ±100 km/hr (Doppler/velocity unambiguous out to ±67 km/hr for /PR = 2500 Hz), a typical range of velocities to expect for ground moving vehicles.10 First, we examine the performance for the array mechanically steered to broadside of the radar t = 0 km/hr is deeper for the long range case with the range ambiguities. The deeper notch is due to the fact that the clutter range ambiguities aligned in Doppler and angle and therefore just have an additive effect on overall CNR. Since the elevation mainbeam contains three ambiguous ranges at 11° grazing angle, the SINR loss is approximately —4.5 dB deeper. Next we look at SINR loss for the case when the array is mechanically steered forward to #mech = 60° shown in Figure 8.6b. Now clutter range ambiguities no longer align in Doppler and there are multiple SINR loss notches. The effect is that in addition to low velocity targets several other target velocities are undetectable, commonly referred to as blind velocities. *l

10 Note that Doppler frequency of a moving target corresponds to the radial velocity of the target with respect to the radar platform 11 Blind velocities are typically associated with Doppler frequencies separated from the Doppler at array broadside by multiples of the PRF but in this case are due to range ambiguous clutter

target velocity, km/hr

Cl

Figure 8.7

b

target velocity, km/hr

U

SINR loss, dB

SINR loss, dB velocity, km/hr

mechanical steering, deg

SINR loss without range-ambiguous clutter (1300 km range) and with range-ambiguous clutter (2700 km range) for mechanical steering of (p = 0° (broadside to platform) and 0 = 60° (forward scanned) a mechanical steering = 0° b mechanical steering = 60°


Figure 8.6

SINR loss, dB

SINR loss, dB a

velocity, km/hr

SINR loss versus mechanical steering angle without range-ambiguous clutter (1300 km range) and with range-ambiguous clutter (2700 km range) a Range = 1300 km (grazing angle = 47°) b Range = 2700 km (grazing angle =11°)

These complete losses in coverage are clearly undesirable. To get a better feel for the full effect on the coverage of an SBR, we show the SINR loss performance at both ranges for all mechanical steering angles from platform broadside (#mech = 0°) to forward (#mech = 90°) in Figure 8.7. Here, the effect on SBR coverage is quite dramatic. The region 0° < #rnech < 40° is almost completely lost as the range ambiguities have separated in Doppler and are all within the azimuth mainbeam. STAP cannot place multiple mainbeam nulls and as a result performance is clutter

limited rather than noise limited. As the array is steered forward (#mech > 40°), it is able to resolve the clutter range ambiguities and at least restore performance between the resulting blind velocities from the range-ambiguous clutter. In contrast, for the shorter range without clutter range ambiguities, coverage is complete for all mechanical steering angles.

8.5

Range-ambiguous clutter mitigation techniques with pulse-Doppler waveforms

We have now outlined the problem of range-ambiguous clutter for pulse-Doppler waveforms and shown their effect on GMTI performance with STAR Examining the pulse-Doppler ambiguity function from Figure 8.3, we clearly have two means of controlling clutter range ambiguities: lowering the PRF to increase the unambiguous range extent for a PRI from equation (8.16) or reducing the elevation beamwidth of the SBR by increasing the elevation aperture. Since PRF can only be reduced to the limit imposed by mainbeam clutter spread, we instead will consider a scheme of using multiple range-ambiguous PRFs to cover all potential target velocities, referred to as PRF diversity. For increasing the SBR elevation aperture, we will consider the case of maintaining the same azimuth aperture for MDV purposes. The resulting twodimensional array, therefore, has a larger array total area and is more costly in terms of deployment. This analysis may be used to gain insights into the amount of improvement additional elevation aperture provides to determine if the performance gains justify the additional cost. Note that we do not consider a true two-dimensional array with spatial channels in both the azimuthal and elevation dimensions. We assume that the elevation dimension is increased to reduce the elevation mainbeam and do not consider the use of elevation degrees of freedom for clutter cancellation [5, Chapter 10].

8.5.1 PRF diversity As has been shown, range ambiguities have the effect of creating additional blind velocities other than v\ = Okm/hr as illustrated in Figure 8.6b. The location of these blind velocities is determined by the range-ambiguous PRF falling at the Doppler frequencies of the clutter range aliases. By changing the alias ranges, accomplished by changing the PRF, we can alter the Doppler frequencies of the aliases and therefore move the blind velocities. In this section, we explore the use of multiple PRFs, or PRF diversity to cover all target velocities of interest. Note that this technique results in a loss in terms of surveillance rate since now multiple CPIs with different PRFs must be devoted to each area on the ground. We will not attempt to quantify this loss here since its specifics are highly dependent on the radar system parameters. Wereturntothecaselookedatearlierwitha20x2marrayat/z = 1000 km altitude mechanically steered to #mech = 60°. The range of the SBR to the aimpoint is 2700 km (Bp = 11°). Recall the SINR loss for a PRF / P R = 2500 Hz in Figure 8.6b. This plot is repeated in Figure 8.8 as the dash-dot line. Here, we also consider the two other

SINR loss, dB

PRF =1500 Hz PRF = 2000 Hz PRF = 2500 Hz target velocity, km/hr

Figure 8.8

SINR loss for multiple PRFs at 2 700 km range and mechanical steering ofcp = 60°. Solid line is / P R = 1500 Hz, dotted line is / P R = 2000Hz and dash-dot line is /PR = 2500 Hz

PRFs of/PR = 2000 Hz and 1500 Hz shown in the dotted and solid lines, respectively. Note that both of these PRFs are above the minimum PRF for this array which from equation (8.15) is / ^ m ) = 1400Hz. Using all three PRFs, we see that there is no additional blind velocity zone (LSINR < —5 dB) other than the ft = 0 km/hr zone. Clearly, three PRFs are sufficient to accomplish coverage for ±100 km/hr, although with the resulting losses in surveillance rate associated with dwelling on the same area with three different PRFs. Next, we consider full mechanical steering for PRFs of 1800 Hz and 2500 Hz shown in Figure 8.9. The lower PRF has reduced the number of total range ambiguities and therefore has fewer blind velocities, especially noticeable as the array looks forward. Important to note is that the region of mechanical steering angles of 0° < #mech < 40° has very poor performance for both PRFs, lacking detectability for all velocities. The reason for the complete loss of performance is that range ambiguities are now separated in Doppler due to the mechanical steering, yet both ambiguities fall within the azimuth mainbeam. STAP cannot cope with multiple mainbeam nulls and performance therefore becomes clutter limited since clutter cannot be effectively nulled. Once the mechanical steering is beyond #mech > 40°, the clutter range ambiguities fall outside the azimuth mainbeam and only affect the velocity corresponding to their associated Doppler frequency. Again, all the STAP performance results shown here are with true covariance matrices and do not reflect various real-world effects, e.g. estimation/training or nonstationary clutter. The training of the STAP adaptive weights with range-ambiguous clutter is complicated by the non-stationary nature of clutter for any mechanical steering. With multiple clutter points that all vary differently with range, techniques such as

Figure 8.9

SINR loss, dB


SINR loss, dB


velocity, km/hr

velocity, km/hr

SINR loss versus target velocity and mechanical steering angle for 20 x 2m array at range of 2700km a PRF = 2500Hz b P R F = 1800Hz

Doppler warping [6, 7] will not be very effective. The best alternative is to have the weights vary with range and update rapidly in range or to use some technique that accounts for non-stationarity.

8.5.2 Aperture trade offs The complete solution to the range-ambiguous clutter problem for SBR is to increase the elevation aperture to the point where range ambiguities do not exist. Of course, in most cases this increase in aperture comes at a very large cost. We will not attempt to get into this aspect of larger SBR antenna arrays but instead will only attempt to show how the use of larger apertures can enable full coverage for an SBR. We again consider the case of an SBR at an altitude of h = 1000 km operating at / = 10 GHz and a range to the aimpoint of 2700 km (0& = 11°). We look at the STAP performance for the same PRFs (/ PR = 1800 and 2500 Hz) as in Figure 8.9 for the 20 x 2 m aperture. However, in this case, we consider a 20 x 5 m aperture. The larger elevation aperture reduces the range extent illuminated on the ground and therefore the radar can still be range unambiguous at higher PRFs. The performance of the 20 x 5 m aperture is shown in Figure 8.10 for mechanical steering angles from #mech = 0° to #mech = 90°. This aperture can operate range-unambiguously for /PR = 1800 Hz while still having two range ambiguities for /PR = 2500 Hz. Clearly, the /PR = 1800 Hz could operate at this range without any problems. Even the higher PRF /PR = 2500 Hz has much better performance, even for 0° < #mech < 50° when the ambiguities cause multiple mainbeam nulls. Overall, the increased aperture is the most attractive solution for the rangeambiguous clutter problem since it completely eliminates the ambiguities. It should be noted that we demonstrated performance for a 20 x 5m array at #gr = 11° or 2700 km range. Further ranges still have range ambiguity problems and the amount

Figure 8.10

SINR loss, dB


SINR loss, dB


velocity, km/hr

velocity, km/hr

SINR loss versus target velocity and mechanical steering angle for 20 x 5 m array at range of 2700km a PRF = 2500Hz b PRF = 1800Hz

of elevation aperture needed to remain range unambiguous for all ranges depends on the maximum range for the SBR application.

8.6

Long single pulse phase-encoded waveforms

It has already been established that more aperture and multiple coherent processing intervals with different PRFs can be used to overcome the ambiguous nature of the returns from pulse-Doppler waveforms. Another way of handling this problem is to use waveforms which are effectively unambiguous in both range and Doppler. In this section, the use of unambiguous long single pulse waveforms is discussed.12 Examples of appropriate modulation include random binary phase encoding [3, Chapter 10.6] and chaotic modulation [H]. In this section, we consider the binary phase-encoded waveforms for illustration purposes. The Doppler resolution for single pulse waveforms is simply the inverse of the pulse length, i.e. the total coherent integration time. For conventional monostatic radars, which are unable to transmit and receive simultaneously, the pulse length is limited to less than half the propagation time to the target, since there must be enough uneclipsed range samples to fill the pulse-compression filter. We use the following well known relationships of the propagation time Jpuise> Doppler resolution A/dOpP

The objective could be viewed as designing a waveform whose ambiguities, if they exist, do not coincide with clutter returns, i.e. ambiguities are moved in such a way that all returns from the earth are unambiguous. We focus merely on the concept and do not investigate waveform design

resolution, km/hr

range, km

Figure 8.11 Doppler (velocity) resolution versus pulse length for a 10 GHz radar

of the pulse, and Doppler frequency /dopp(8.19) where R is the range to the target, c is the speed of light (propagation velocity), v is velocity and k is the wavelength. From these relations, we can derive the Doppler (velocity) resolution: Aw=^

(8.20)

Figure 8.11 shows the limit on Doppler resolution as a function of range for a radar operating at 10 GHz. The Doppler resolution of a GMTI radar should be significantly better than the specified target MDV for the radar. Airborne GMTI radars typically look for targets at ranges of under 300 km, equating to Doppler resolutions which are worse than 25 km/hr and clearly inadequate for typical GMTI performance requirements. However, SBR systems have considerably longer ranges to the target. For the SBR example explored in this chapter with a 1000 km orbit and a minimum range of 1200 km, the Doppler resolution without simultaneous transmit and receive is better than 7 km/hr, which is adequate for most GMTI applications. Figure 8.12 pictorially summarises the concept of the long single pulse waveform for SBR.

amplitude

phase encoded waveform

time

Concept of long single pulse waveform for SBR

response, dB

velocity, km/hr

Figure 8.12

range (km)

Figure 8.13 Ambiguity surface for a 10 ms 5 MHz chip rate phase-encoded pulse at 10 GHz 8.6.1

Properties of long single pulse phase-encoded

waveform (LSP W)

Except for a few special cases [12-14], phase-encoded waveforms have mean range and Doppler sidelobes levels that are inversely proportional to the time-bandwidth product given by: SLL = — — (8.21) TxB For example, a time-bandwidth product of one million is needed to achieve mean range-Doppler sidelobes of -6OdB. This mean sidelobe level is combined with a point-like ambiguity function as shown in Figure 8.13. These waveforms are

unambiguous in range, and unambiguous in Doppler up to the sample or chip rate of the waveform. As we will discuss below, this mean sidelobe level is a limitation of the phase-encoded LSPW, and care must be used in designing the radar to cope with this limitation. In conventional pulse-Doppler radars that utilise chirp waveforms or short phase-encoded pulses, the large amount of range-Doppler coupling makes the pulsecompression and Doppler filtering operations approximately separable. Since the range-Doppler coupling of the phase-encoded LSPW described here is minimal, the pulse-compression and Doppler filtering operations of the radar are not separable, and a Doppler optimised pulse-compression filter is required for each Doppler bin. There are both pros and cons to having separate pulse-compression filters for each Doppler bin. The pro is that for constant velocity targets there are no range walk losses due to target motion over the length of the single pulse. The Doppler-dependent pulse-compression filters are already tuned to the motion. The con is the amount of computation required. For example, an X-band SBR system with a 3000 km (20 msec) pulse has a Doppler resolution of 2.7km/hr from equation (8.20). To cover target velocities of ±110km/hr, eighty separate pulse-compression filters are needed. For waveforms with large time-bandwidth products, the computational complexity of the pulse-compression and Doppler filtering becomes phenomenal with conventional FIR implementations of the pulse compressor. However, the use of overlap-add FFTs helps ameliorate the computational burden. One example of an LSPW STAP processing chain is shown in Figure 8.14. In this case, the Doppler-dependent pulse-compression filters naturally feed the adjacent bin post-Doppler STAP algorithm [15]. However, this is not the only STAP algorithm which may be applied to the LSPW. Application of an inverse-discrete-Fourier transform to the output of all the pulse-compression filters on a per-range-gate basis (Figure 8.15) converts the output into a pre-Doppler pulse-like space with an apparent

pulse comp. Doppler bin 1 N channels pulse comp. Doppler bin 2 digital receiver pulse comp. Doppler bin...

pulse comp. Doppler bin M

Figure 8.14

Adjacent-bin post-Doppler STAP for a long single-pulse waveform

Af channels pulse comp. Doppler bin 2 digital receiver

pulse comp. Doppler bin...

inverse Fourier transform

pulse comp. Doppler bin 1

M 'Pulses' (nyquist sampled for highest Doppler)

pulse comp. Doppler bin M

Figure 8.15

Pulse-Doppler matched filtering for LPSW radar with an inverse DFT across Doppler frequency allows LPSW radar to emulate a conventional pulse-Doppler radar

PRF of: (8.22) where / ^ a x and /^ 11 I are the Doppler frequencies of the highest and lowest Doppler bins used. With this transformation any STAP algorithm that can be applied to pulseDoppler waveforms may also be used with an LSPW. The LSPW advantages of no Doppler or range ambiguities are still retained.

8.6.2 Integrated sidelobe clutter levels One of the key issues with LSPWs is the integrated sidelobe clutter level. If the integral of all the clutter outside the range-gate and Doppler bin of interest is significant compared with the noise floor, then the radar will be desensitised. Therefore, a fundamental requirement on an LSPW radar is an average range-Doppler sidelobe level that is better than the integrated clutter level. The integrated clutter level is computed by integrating the radar range equation over the illuminated clutter [16]: (8.23) where Pt is the transmit power, G(4>az, R) is the antenna gain as a function of azimuth angle 0 ^ and range R, o~(R) is the clutter reflectivity as a function of range, t the pulse length, X the wavelength, k Boltzman's constant, TQ = 290 K, L the radar system losses and F the noise figure. In determining the integrated clutter level, the radar designer only has control over the first three terms in the equation, transmit power and transmit and receive gain.

By approximating the azimuth distribution of the antenna pattern by the Rayleigh beamwidth b and modelling the clutter reflectivity with the constant Gamma clutter model [17] where #gr represents the grazing angle, equation (8.23) becomes:

(8.24)

CNR, dB

The middle term of equation (8.24) represents the clutter reflectivity multiplied by the area illuminated between the ranges R and R + Rg (Rg is the range resolution of the radar). It is interesting to note that since the area illuminated by the radar is approximately inversely proportional to the antenna's gain, the integrated clutter level is approximately proportional to the power aperture of the radar. Since the received target power is proportional to the power aperture squared of the radar, for the same target SNR, radars with larger apertures (and hence less transmit power) will exhibit smaller integrated clutter levels. For the X-band SBR described earlier, with a peak transmit power of 30 dBw, a 20 x 2m aperture (gain of 57.5 dB), noise figure of 4dB, 1OdB of losses, range resolution of 1 m, pulse length equal to the propagation time and a 50 dB receive taper in elevation, Figure 8.16 depicts the clutter-to-noise ratio as a function of range for a beam illuminating the ground at a range of 2000 km with a clutter y of —12 dB.

range, km

Figure 8.16

Clutter-to-noise ratio versus rangefor an LSP W with the example radar system

level, dB

constant power CNR mean sidelobe level variable power CNR range, km

Figure 8.17

Clutter-to-noise ratios for constant and variable transmit power and mean sidelobe level versus range

The CNR is positive for a range extent of about 150 km, or 150000 range gates. Integrating over range gives an integrated clutter-to-noise ratio of 65.2 dB. Figure 8.17 shows both the integrated clutter level and mean range-Doppler sidelobe level (assuming the LSPW length is the same as the propagation time and a bandwith of 150 MHz) as a function of range. If the transmit power is kept constant irrespective of the range which is being illuminated, then the integrated CNR is larger than the mean sidelobe level at ranges less than 2565 km. This would make the radar's performance clutter limited rather than noise limited. However, it should be noted that the target SNR grows faster with decreasing range than does the unsuppressed clutter, so target detectability still improves. However, if the transmit power is varied so as to keep constant SNR on target, then the ratio of the integrated CNR to the mean sidelobe level drops with decreasing range. The effective transmit power to the target can be adjusted in two ways: either by reducing the gain of the transmit amplifiers, or by broadening the transmit beam and forming multiple high gain receive beams. The latter method has the advantage of maximising the radar's search area rate. If the radar is designed to meet the SNR on target and the integrated CNR requirements at maximum range, then performance will be better at all closer ranges. As an example, consider the design of a radar which needs to attain a target SNR of 7.5 dB per pulse at 3000 km. Figure 8.18 shows how the integrated CNR changes as a function of array area and transmit power at 3000 km for a bandwidth of 150 MHz. The integrated CNR is approximately proportional to the radar's power aperture. Contours

integrated CNR, dB

area, m2

7.5 dB SNR on target 63 dB ICNR contour 66 dB ICNR contour peak power, dBw

Figure 8.18

Integrated CNR as a function of area and peak power

of constant integrated CNR and a constant target SNR of 7.5 dB are also shown in the Figure. To design a 150 MHz bandwidth radar which would achieve 7.5 dB SNR per pulse and have the integrated CNR equal to the mean range-Doppler sidelobes requires an array area of 56 m2 and a peak power of 1.25 kW. A radar with the integrated CNR 3 dB below the mean range-Doppler sidelobes at 3000 km requires an area of 111 m2 and a peak power of 330 W.

8.6.3 STAP simulations Here, we look at STAP simulations using the 40 m2 aperture SBR described earlier, and an LSPW with -7OdB range-Doppler sidelobes. The target range is 2500 km and the mechanical steering angle is 30° from the velocity vector, i.e. #mech = 60°. Two hundred snapshots are selected from between 2490 km and 2510 km to estimate the clutter-plus-noise covariance matrix. There are eight spatial degrees of freedom (subarrays) and the pulse is 16 msec long. Three different processing schemes are considered: 1

Pulse-Doppler with a PRF of 2 kHz, Doppler warping [6] and PRI-staggered STAP [5, Chapters 10, 18 and 19] 2 LSPW with adjacent-bin post-Doppler STAP from Figure 8.14 3 LSPW with transformation back to pulse-space from Figure 8.15, Doppler warping and PRI-staggered STAR In case 1, the /PR = 2000 Hz PRF means that range-ambiguous clutter at ±75 km will also be above the noise floor. Doppler warping is applied in cases 1 and 3 to compensate for the change in the Doppler of the mainbeam clutter as a function of

SINR loss, dB

velocity, km/hr

Figure 8.19

STAP performance for processing case 1

range due to the Doppler. However, in case 1 the Doppler warping is only precisely correct for the clutter around 2500 km, not the range-ambiguous clutter, leading to further degradation of the STAP performance. Since the Doppler warping is applied across the pulses on a range gate by range gate basis prior to the Doppler filtering, it is incompatible with the processing in case 2. The PRI staggered processing is chosen for cases 1 and 3 since this algorithm is known to exhibit better performance than the adjacent bin algorithm. The results are plotted in Figures 8.19 to 8.21. In all cases optimum refers to full dimension STAP with exact knowledge of clutter covariance (impossible in practice). Figure 8.19 shows the SINR performance of processing case 1. The nulls at about —32 km/hr and 27 km/hr are due to the range-ambiguous clutter from 2425 km and 2575 km. In this case, the range-ambiguous clutter nulls are only slightly wider than the correct null at 0 km/hr, since the Doppler warping is close to being correct for these ambiguities. With higher CNR the broadening of these nulls would be more severe. Figure 8.20 shows the STAP performance of processing case 2. In this case there is only a single null, but it is broad. Since processing chain 2 is incompatible with Doppler warping, the change in the Doppler of the mainbeam clutter as a function of range cannot be compensated for in the training data. Figure 8.21 depicts the STAP performance of processing case 3. There is only a single narrow null. The combination of the LSPW with a transformation back into the time domain from the Doppler domain, Doppler warping and PRI staggered STAP combine to give near-optimal performance. The only losses with respect to optimum

SINR loss, dB

optimal adjacent bin

velocity, km/hr

STAP performance of processing case 2

SINR loss, dB

Figure 8.20

optimal PRI stagg.

velocity, km/hr

Figure 8.21

STAP performance of processing case 3

STAP are due to the finite sample support and low sidelobe weighting on the Doppler filters in the PRI staggered algorithm.

8.7

Summary

In this chapter, we have discussed the problem of range-ambiguous clutter and its effect on the performance of an SBR system used for GMTI. Range-ambiguous clutter is a problem that arises at long ranges when the array is mechanically steered forward or aft. The misalignment of the array with the velocity vector creates a change in the angle-Doppler characteristics of range-ambiguous clutter and results in multiple blind velocity regions for GMTI. Pulse-Doppler waveforms can utilise multiple PRFs in order to shift the Doppler of these ambiguities and cover all velocities. The cost of this PRF diversity approach is the loss in search rate associated with using multiple PRFs to cover each spot on the ground. Also, PRF diversity is only effective at overcoming clutter range ambiguities that fall outside the mainbeam. For mechanical steering angles from broadside #mech = 0° to #mech = 40°, the 20 x 2m array considered in this chapter could not place multiple mainbeam nulls and, as a result, suffered large losses for all velocities. A more effective means of mitigating range-ambiguous clutter for pulse-Doppler waveforms was to increase the elevation aperture, completely eliminating or reducing the number of range ambiguities depending on the grazing angle. More aperture is clearly the preferred method of overcoming range-ambiguous clutter, the problem becomes a matter of the large cost of deploying a large aperture for an SBR. Finally, we discussed the new, novel approach to range-ambiguous clutter that uses an alternate waveform consisting of a single, long pulse utilising phase encoding to remain range and Doppler unambiguous. The length of the pulse is determined by the range of the SBR to the aimpoint so that at longer ranges, longer pulses are possible. Recall that the problem of range-ambiguous clutter arises at longer ranges. One of the main issues with a long phase-encoded pulse waveform is integrated sidelobe levels which are a problem due to the range-Doppler sidelobe levels of this waveform. Another issue is the amount of computation associated with the matched filtering in range and Doppler of the phase-encoded waveform. Two efficient architectures for STAP were given along with simulations demonstrating the viability and benefit that a range and Doppler unambiguous waveform could provide. This alternative waveform shows promise for SBR applications and bears further investigation and experimentation. References 1 CANTAFIO, L. J.:' Space-based radar handbook' (Artech House, Norwood, MA, USA, 1989) 2 DAVIS, M. E.: 'Technology challenges in affordable space-based radar'. Proceedings of IEEE international Radar conference. Washington, USA, 2000, pp.18-23

3 SKOLNIK, M.: 'Radar handbook' (McGraw-Hill, New York, USA, 1990) 4 WARD, J.: 'Space-time adaptive processing for airborne radar'. MIT Lincoln Laboratory TR 1015, ESC-TR-94-109, 1994 5 KLEMM, R.: 'Principles of space-time adaptive processing' (IEE, London, England, 2002) 6 BORSARI, G. K.: 'Mitigating effects on STAP processing caused by an inclined array'. Proceedings of IEEE Radar conference, 1998, pp. 135-140 7 KREYENKAMP, O. and KLEMM, R.: 'Doppler compensation in forwardlooking STAP radar', IEE Proc, Radar Sonar Navig., October 2001, 148, (5), pp. 253-258 8 BRENNAN, L. E. and REED, I. S.: 'Theory of adaptive radar', IEEE Trans. Aerosp. Electron. Syst., March 1973, 9, (2), pp. 237-252 9 NOHARA, T. J.: 'Design of a space-based radar signal processor', IEEE Trans. Aerosp. Electron. Syst., 1998, 34, (2), pp. 366-377 10 KOGON, S. M., RABIDEAU, D. J., and BARNES, R. M.: 'Clutter mitigation techniques for space-based radar'. Proceedings of IEEE international conference on Acoustics, speech, and signal processing, 1999, pp. 2323-2326 11 OPPENHEIM, A. V. and CUOMO, K. M.: 'Chaotic signals and signal processing', in MADISETTI, V. and WILLIAMS, D. (Eds.): 'Digital signal processing handbook' (CRC Press, Boca Raton, USA, 1997) pp. 71.1-71.13 12 BARKER, R.H.: 'Group synchronizing of binary digital systems', in 'Communication theory' (Academic Press, 1953) pp. 272-287 13 ZIERLER, N.: 'Linear recurring sequences', /. Industrial Applied Mathematics, 1959, 7, pp. 31-48 14 WELCH, L. R.: 'Lower bounds on the maximum cross correlation of signals', IEEE Trans. Inf. Theory, 1914, 20, pp. 397-399 15 DIPIETRO, R.: 'Extended factored space-time processing for airborne radar systems'. Proceedings of Asimolar conference on Signals and systems, 1992, pp. 425-430 16 VAN TREES, H.: 'Detection, estimation, and modulation theory, part III (John Wiley & Sons, New York, USA, 2001, 2nd edn.) 17 BILLINGSLEY, J. B.: 'Low angle radar land clutter measurements and empirical models' (SciTech Publishing, Norwich, NY, 2002) 18 BRENNAN, L. E. and STAUDAHER, R M.: 'Subclutter visibility demonstration'. Adaptive Sensors Inc. technical report, RL-TR-92-21, 1992 19 WARD, J. and STEINHARDT, A. O.: 'Multiwindow post-Doppler space-time adaptive processing'. Proceedings of 7th workshop on Statistical signal and array processing, 1994, pp. 461-464

Part III

Processing architectures

Chapter 9

Parallel processing architectures for STAP Alfonso Farina and Luca Timmoneri

9.1

Summary and introduction

This chapter describes methodologies for online processing of received radar data by a set of N antennas and M pulse repetition intervals (PRIs) for the calculation of space-time adaptive (STAP) filter output. The numerically robust and computationally efficient QR-decomposition (QRD) is used to derive the so-called MVDR (minimum variance distortionless response) and lattice algorithms; the novel inverse QRD (IQRD) is also applied to the MVDR problem. These algorithms are represented as systolic computational flow graphs. The MVDR is able to produce more than one adapted beams focused along different angular directions and Doppler frequencies in the radar surveillance volume. The lattice algorithm offers a computational saving; in fact, its computational burden is 0(N2M) in lieu of 0(N2M2). An analysis of the numerical robustness of the STAP computational schemes is presented when the CORDIC (coordinate rotation digital computer) algorithm is used to compute the QRD and the IQRD. Benchmarks on general purpose parallel computers and on a VLSI (very large scale integration) CORDIC board are also presented.

9.2

Baseline systolic algorithm

The detection of low flying aircraft and/or surface moving targets, and the standoff surveillance of areas of interest require a radar on an elevated platform like an aircraft. The AEW (airborne early warning) radars pose a number of interesting technical problems especially in the signal processing area. The issue is not new: detect target echoes in an environment crowded with natural (clutter), intentional (jammer) and other unintentional radiofrequency (especially in the low region of microwaves, e.g. VHF/UHF bands) interference. The challenge is related to the large dynamic range of the received signals, the non-homogeneous and non-stationary nature of

the interference, and the need to fulfil the surveillance and detection functions in real time. One technique proposed today to solve the problem is based on STAP [2-4,9,10,14-18]. Essentially, the radar is required to have an array (for instance, a linear array along the aircraft axis) of Af antennas each receiving M echoes from a transmitted train of M coherent pulses. Under the hypothesis of disturbance having a Gaussian probability density function and a Swerling target model, the optimum processor is provided by the linear combination of the NM echoes with weights w = M - 1 S*, envelope detection and comparison with threshold. M is the spacetime interference covariance matrix, i.e. M = E{z*zT} where z (dimension NM x 1) is the collection of the NM disturbance echoes in a range cell, s, the space-time steering vector, is the collection of the NM samples expected by the target and (*) stands for complex conjugate. A direct implementation (via sample matrix inversion, SMI) of the weight equation w = M - 1 S* is not recommended. One reason is related to the poor numerical stability in the inversion of the interference covariance matrix especially when a large dynamic range signal is expected during the operation; another one is the very high computational cost. There is a need of extremely high arithmetic precision during digital calculation. Note that double precision costs four times as much as single precision. The situation would be different if, instead of operating on the covariance matrix M, we would operate directly on the data snapshots z(k), k = 1,2,... ,ft where n is the number of snapshots (i.e. range cells) used to estimate the weights w. It can be shown that the required number of bits to calculate the weights, within a certain accuracy, by inversion of M is two times the number of bits to calculate the weights operating directly on the data snapshots z(k). This is so because the calculation of power values is avoided, and thus the required dynamic range is halved. The algorithms that operate directly on the data are referred to as data domain algorithms in contrast to the power domain algorithms requiring the estimation of M. Figure 9.1 depicts both approaches; in this chapter we will develop the algorithms based on the data domain approach. The QRD is a numerical technique for solving least squares problems, like the one in STAP, that avoids direct computation and inversion of interference covariance matrix [1,5]. Indicate with Z the n x (NM)-dimensional matrix which collects the n data snapshots: (9.1) The weight equation can be written as follows: (9.2) where (m)H stands for the complex conjugate transpose. Taking the data matrix Z and operating on it with unitary (i.e. covariance preserving) matrix Q (with dimension ft x /i) we are able to transform the matrix Z in an upper triangular matrix R (with dimension NM x NM): (9.3)

data cube CUT linear combination of weights and signals from the cell under test (CUT)

antenna elements

adapted output

range cells PRT

covariance matrix estimation

weight calculation

power domain approach

data matrix triangulation data domain approach

Figure 9.1

The power and data domain approaches for STAP

thus equation (9.2) can be rewritten as: R^Rw = s*

(9.4)

which is now easily solved by forward and back-substitution steps as follows. Indicating by a new vector, t, the product Rw, equation (9.4) becomes: R H t = s*

(9.5)

that can be solved in t. Subsequently, the additional equation: Rw = t

(9.6)

is solved in w. A noticeable improvement of the basic technique allows us to calculate the STAP output without extracting the weights, i.e. without performing the two substitutions above (see, for instance Reference 1 at page 147, see also Section 9.10, Appendix A). In summary, either the weight vector w or the output signal of the STAP are obtained without forming and inverting any covariance matrix. By using a large number of bits the data domain algorithm provides the same results as the power domain algorithm which estimates the covariance matrix ZH(n)Z(n) and derives the weight vector by the conventional Cholesky factorisation of that matrix in equation (9.2). The noticeable result is related to the far superior performance of the data domain algorithm when using a limited number of bits; in fact, the data domain algorithm needs half the number of the bits required by the power domain method to reach good interference cancellation and target coherent integration. The triangularisation of the data matrix, see equation (9.3), can be done with the following known methods: Givens rotations, Householder reflections (a generalisation of Givens rotations) and Gram Schmidt [I]. Another method to obtain a sparse (actually a diagonal in lieu of triangular) data matrix is singular value

decomposition (SVD); the Jacobi and Hestenes are recursive parallel algorithms to efficiently obtain the SVD. The Lanczos is another numerically efficient candidate to solve our real-time STAP problem [6]. The preferred approach in this chapter is the one based on Givens rotations (see Section 9.10, Appendix A). All these methods enj oy the possibility of being mapped onto a parallel processor such as a systolic array. This means that the algorithm is readily transformed in a computer architecture; this is not the case for the equation (9.2) where a single processor computer has the task of performing the indicated operations. Today it is possible to implement a systolic array with custom VLSI technology thus providing compact processors requiring limited prime power. An additional advantage is related to the large data throughput of the parallel processor representing a suitable means of reaching real-time operation. A remarkable implementation of a systolic algorithm on VLSI chips is called MUSE; it was developed by C. Rader and colleagues at MIT-Lincoln Laboratory (USA) (see third entry of the table in Section 9.14, Appendix E). The baseline architecture considered for the STAP problem is the trapezoidal one depicted in Figure 9.2 [5]. This constitutes the generalisation of a method, which was originally developed for MVDR beamforming, by QRD. The TVM-dimensional triangular array ABC receives the snapshots of data from a set of range cells and outputs from the right-hand side the matrix R produced as the data descend through the array. The matrix is passed to the right-hand column of cells DE which serves to steer the main beam in the desired angular direction and Doppler frequency. Multiple beams can be formed simply by adding right-hand columns as depicted in Figure 9.2; they are constraint post-processors. The bulk of the computation, i.e. the QRD, is common to all of the separate beamforming tasks, and only needs to be performed once. The MVDR processor in Figure 9.2 is designed to operate in the following manner [5]. The triangular processor, in normal adaptive mode (selected by setting an input binary flag / = 1), is fed with sufficient data snapshots to form a good statistical estimate of the environment. The triangular array is then frozen (by setting the input binary flag / = 0) while a look-direction constraint is input as though it were a data vector z(n) emerging from the multichannel tapped delay line. This serves to calculate the vector a = ( R ^ ) " 1 s* which is captured and stored in the right-hand column (also operating in mode / = 0); this vector is needed to determine the STAP output e(n) = zT(n)R~l (RH)~l s*. Once the vertical columns have been initialised, the adaptive mode of operation ( / = 1) is selected for both the main triangular array and the right-hand columns and more data snapshots are presented to the processor. The processor then updates its estimate of the environment (via the stored quantities R and a) and simultaneously outputs the STAP signals from the bottom of the columns DE. The number of processing elements in the triangular systolic arrays is 0.5(MN + X)-MN. The MVDR algorithm has a noticeable computational advantage with respect to the SMI which requires O(N3 M3) arithmetic operations per sample time. Two types of processing element are needed within the triangular array: one calculates the sine and cosine of an angle between two input data values, the other rotates the remaining data of the same angle. The calculation of the rotation and the application of the rotation is repeated for each row of the triangular array. A third cell type is used in

triangular array

Figure 9.2

detection

detection

no target target present

no target target present

Baseline QRD based MVDR flow graph [5]

in the look-direction constraint columns. Every processing cell of the triangular array should perform on average 24 floating-point operations per data snapshot. Let d be the desired data rate, i.e. the snapshots per second to process, the systolic machine should perform HdM2N2 flops. As an example, let d be 1 MHz and NM = 1 0 0 the corresponding processing power needed is 100 Gflops approximately. By down sampling (see also Section 9.4) the radar data by a factor often, the required processing power is 10 Gflops.

9.3

Lattice and vectorial lattice algorithms

An advanced processing architecture referred to as the MVDR lattice processor requires 0(N2M) arithmetic operations per sample time; it is described in Reference 5. It takes advantage of the time-shift invariance1 associated with STAR 1 This requirement is fulfilled only if the PRI is constant (no PRI staggering) and no platform motion perturbations (e.g. rapid acceleration) occur

trapezoidal array

1st stage

delay 2nd stage

MVDR column final stage

beamformer residual

Figure 9.3 MVDR lattice processor [5]

The data entering the triangular array change very little from one PRI to the next which means that a large part of the computation is being repeated on successive PRIs albeit in different parts of the array. This repetition is eliminated in the lattice algorithm where the big trapezoidal array is decomposed in a lattice of smaller (i.e. of dimension N) trapezoidal arrays; the lattice has M stages (see Figure 9.3). The lattice-based MVDR operates in a similar manner to the big trapezoidal array; details are found in Reference 5 (see also Section 9.11, Appendix B). If M = N = 10 and the update rate is one tenth of 1 MHz, the required computational power is 1 GfIop. The lattice

algorithm has also been designed and tested with simulated data for wideband STAP [12]; this architecture is particularly useful: (i) to deal with wideband radar, (ii) to compensate for amplitude and phase mismatching between the receiving channels, and (iii) to combat the hot clutter. The processing architecture, named the vectorial lattice, operates on an array of Af antennas, M PRIs and P samples taken within the radar range cell. The lattice has again M stages, each having trapezoidal arrays of dimension NP. The computational complexity of the scheme is 0(MN2P2). In the above mentioned processing architectures, namely the MVDR, the lattice and the vectorial lattice, the common processing module is the triangular systolic array. In Sections 9.5 and 9.6 we report the results concerning the mapping of the triangular systolic array onto parallel processors.

9.4

Inverse QRD-based algorithms

A further improvement of the triangular systolic array for STAP processing is called IQRD (inverse QR decomposition) and promises an additional decrease of the required computational power. The need to reduce the computational requirements of the triangular systolic array was discussed in Section 9.2. The possibility of down sampling of a factor ten, say, the update of the triangular array was mentioned. This tacitly requires the extraction of the adaptive weights of the STAP at the low update rate and the application of the weights to the radar echoes at the natural rate of the data. This approach has the following practical problem. The MVDR systolic array of Figure 9.2 could extract the adapted weights via back substitution; however, pipelining the two steps of triangular update and back-substitution seems impossible. There are two possibilities to overcome this problem. The first is to use a triangular array in addition to the main one, the second triangular array being reversed with respect to the array which updates the matrix R [14, p. 332]. This approach requires more hardware to be integrated on the chip. The second approach exploits a recursive equation which updates ( R ^ ) " 1 instead of R. The update of ( R ^ ) " 1 serves the purpose of extracting the weights. This algorithm, referred to as IQRD, can be implemented with just one triangular systolic array, which has a specular orientation of the basic triangular array to update R. Figure 9.4 illustrates the processing scheme for the sidelobe canceller (an adaptive system with a main antenna and a number of auxiliaries); by resorting to the concept of generalised sidelobe canceller, it is possible to show that a slightly modified version of the scheme is applicable to STAR The complex valued set of data x e CN are received by the N auxiliary channels; y is the data collected by the main antenna; x, y are processed to give the set of adapted weights w. The quantity e = y — x r w is the adapted residue; the parameter 8/8* occurs to update the weights as more data are received, during time, by the radar; see Section 3.1 of Reference 14 for details. A limitation of this approach is related to the difficult schedule of the various processing steps. A detailed comparative analysis of the IQRD and QRD-based MVDR algorithms is presented in Reference 14. Also, an implementation of the corresponding systolic architectures, with the use of the CORDIC algorithm as a basic building block, is discussed.

Figure 9.4

9.5

RLS-IQR array [14]

Experiments with general purpose parallel processors

This section summarises the findings described in detail in Reference 8; today this study seems out of date for the advancement in signal processing hardware, nevertheless it is still very instructive. We study the use of parallel processors of MIMD (multiple instruction streams multiple data streams) and SIMD (single instruction stream multiple data streams) types available on the market (early 1990s). This approach is meant to be preliminary to the VLSI solution. In fact, it provides guidelines for the design of the processing architecture to be implemented on silicon. The problems of synchronisation of the whole systolic array by a master clock and the data transfer between processors can also be investigated. Additionally, an estimate of the computational performance of several candidate processing architectures is also possible. With reference to the MIMD machine, a reconfigurable transputer-based architecture (the MEIKO computing surface, using up to 128 T800 INMOS transputers) has been adopted and three solutions have been proposed. The first uses a ring of transputers. Then an improvement of performance is reached by diminishing the amount of communication required; such a result has been achieved by using a linear array of processors. The mapping of the algorithm onto a triangular array of processors has also been studied. This solution allows the use of an arbitrary number B of processors provided that B = p(p + l)/2, p being an integer number. This mapping shows performance better than does linear mapping. The investigation on MIMD computers is concluded with a comparison of the results achieved by using the nCUBE2 with 64 processing elements. With reference to SIMD machine, tests on the Connection Machine CM-200 and the MasPar MP-I have been performed. CM-200 is equipped with 8192 single bit processors, whereas MP-I has 4096 four bit processors. The QRD has been mapped onto a mesh architecture for both machines.

Table 9.1 Pros and cons of COTS Pros

Cons

programmable and flexible

complex infrastructure including I/O control and protocols high speed data buses high speed memory and memory control

robust to technology obsolescence reuse of previously developed software essential in design trajectory of VLSI custom architecture (search for trade-off between flexibility and modularity, parallelisation options)

multi-DSP infrastructure requires extra-overhead which brings to a decline of ideal linear increment of computational power

Without going into the details, which are described in Reference 8, the main conclusions of the work are the following. The experimental work done suggests mapping the systolic array for the QRD algorithm onto an MIMD machine configured as a triangular array. An achievable data throughput is in the order of 1OkHz for a STAP with MN = 16 and 120 PEs using the MEIKO Computing Surface. A data throughput of the order of 100 kHz should be feasible either with advanced transputers or with devices like the Texas TMS320C40. These conclusions, which date back ten years, should be reconsidered in the light of the more powerful COTS (commercial off the shelf) machine available today; see Section 9.7. A preliminary evaluation of the pros and cons of the hardware implementation of STAP based on COTS is summarised in Table 9.1.

9.6

Experiments with VLSI-based CORDIC board

To explore the possibility of achieving better computational performance and using compacter systems - for installation in an operational radar - a QRD algorithm has been mapped onto an application specific prototyping platform which contains four VLSI CORDIC ASICs (application specific integrated circuits) and some FPGAs (field programmable gate arrays) [H]; this work was done in cooperation with the Technical University of Delft (The Netherlands). For details on the CORDIC algorithm and its use in adaptive beamforming see Sections 9.13 and 9.14, Appendices C and D, respectively. The test-bed platform mainly consists of a large (modular) memory buffer that is connected to a Sun workstation via a VME (versa module eurocard) bus. The memory buffer stores data that flow through the application board, back into the buffer. The application board consists of four CORDIC processors which are mesh-connected. These four processors perform complex rotations on two-dimensional complex vectors. The CORDIC processor is a pipeline processor operating in block floating

point. The physical connections between the CORDIC have been implemented via Xilinx chips. In the benchmark described in Reference 11, the triangular systolic array was mapped onto the 2 x 2 CORDIC application board of the tested platform. This four CORDIC mesh corresponds functionally to one of the processing nodes constituting the triangular systolic array. However, as the CORDIC processors are pipelined processors, many of these rotations can be performed at a very high throughput rate (the clock rate of the pipe), provided a schedule can be found such that the pipe can be kept filled. Such a schedule can indeed be found for the QRD algorithm. The results of the benchmark may be briefly summarised as follows. With a 100 per cent pipeline utilisation of the CORDIC, the throughput can be computed simply as: throughput =

clockfreqCORDIC —\ number of rotations

(9.7)

where clockfreqCORDIC is the clock frequency of the CORDIC processor (only 5 MHz in the experiments, just to show that no extremal values are needed), and number of rotations is the number of rotations (vectorisations included) for the case where we simulate a system of MN degrees of freedom. For MN = 1 0 the throughput is approximately 8OkHz, i.e. 80000 input vectors could be processed per second, which is better than the results reported in Section 9.5 where larger computers and higher clock frequencies were used. In a non-experimental implementation of the CORDIC system described in this section, clock frequencies up to 40 MHz are easily achievable; this would improve the throughput even further within a factor of 8. Table 9.2 summarises the pros and cons of the hardware implementation of STAP based on custom VLSI. Selection between COTS and VLSI is still an open question; the specialised technical literature reports descriptions of experimental systems using both the two technologies: a consensus has not been found yet on which technology to use, even though the trend seems today in favour of COTS. Further considerations on this problem are reported in Section 9.7. Also Section 9.14, Appendix E, lists several implementation examples of STAP taken by the open technical literature; these testify the wide spectrum of technologies used.

Table 9.2 Pros and cons of VLSI Pros

Cons

extremely high throughput (bulk processing) limited size and power consumption

low degree of flexibility expensive for limited number of pieces to produce

9.7

Modern signal processing technology overview and its impact on real-time STAP

In the chapter we have mentioned the role of the VLSI custom chip and the relevance of chips that may implement the CORDIC algorithm. In this section we give attention to more commercial technology and evaluate its possible use for real-time STAR The impact of modern signal processing technology on real-time STAP is provided in this section to complement the algorithmic aspects of STAP described up to now in the chapter. We summarise the state of the art of relevant devices for signal processing and the way to design complex signal processing schemes which are of interest for the real-time implementation of STAR Perhaps one of the most significant advances in radar in the past 30 years has been the application of digital technology to allow the radar designer to make practical what in the past were only academic curiosities. An impressive drawing of the advancement of digital technology is in Figure 9.5. It illustrates Moore's law, named for Intel cofounder Gordon Moore, which predicts that transistor density on microprocessors will double every 18 months. This prediction so far has proven amazingly accurate. In recent years the processing technology adopted for radar systems has evolved along the following steps: • •

design and implementation of proprietary circuits which, however, have the following cons: high life cycle cost and obsolescence proprietary circuits exploiting the digital signal processing (DSP) devices available from the market pentium processor 1993 intel 486 microprocessor

number of transistors 10 million

286 microprocessor 1982 1 million 8086 microprocessor 1978 - i n t e l 386 microprocessor 1985 microprocessor 8080 microprocessor 1974

Figure 9.5

Moore s Law, named for Intel co-founder Gordon Moore, predicts that transistor density on microprocessors will double every 18 months. This prediction, so far, has proven amazingly accurate. If it continues, Intel processors should contain between 50 and 100 million transistors by the turn of the century (From IEEE Aerosp. Electron. Syst. Mag., October 2000, 15, (10), Jubilee Issue, p. 13 (©2000 IEEE))

•

•

a tremendous interest in COTS technology which, however, has the following cons: need of engineering resources to track technology evolution and developing tools the more recent system COTS (SCOTS) also embedding communication, operative system and developing tools.

Today modern radar systems, including those with adaptive features, require a wide spectrum of technologies; e.g. ASIC, FPGA, DSP, fibre optic communication channel to use each one matched to a suitable purpose. Examples of the application of heterogeneous technology in adaptive radar, and also STAP, are: • • • •

ASIC for analogue to digital converter (ADC), filtering and channel equalisation DSP for matrix algebra calculation reduced instruction set computer (RISC) for data processing fibre optic for communication channels to distribute/collect data and command.

A taste of figures for recent technologies are (this is a not exhaustive list and by no means a commercial indication, but just a sample taken from the specialised literature): •

• • •

Analog Device's very recent processing board is characterised by the following features: eight ADSP-TSlOl Tiger Shark give 9000MFlops, the processor is running at 250 MHz, has 64 bits at 66 MHz on compact PCI (peripheral computer interconnect), with three banks of memory with 64 Mbytes; it is programmable in C, with library and software tools in Sharklab linked to Matlab status of the art for FPGA (year 2002): 10 Mgates, they are reprogrammable via software status of the art for ADC technology: 14 bits at 100 MHz sampling rate, 10 bits at 1.5GHz, 8 bits at 3 GHz status of the art for FFT: DoubleBW 1 K complex points FFT with windowing in 10 iis [21].

These technologies are heterogeneous but need to be approached, in the design phase of the whole radar system, in an homogeneous fashion; this has prompted the so-called concurrent design technology, or system codesign. It is a methodological approach based on: tools for cost estimate and analysis of requirements (e.g. Rational Rose), algorithmic analysis (with Matlab and Simulink), functional design (Ptolemy II, System C, Handel C), core library etc. In more detail, the rationale of codesign technology is the following. Systems are becoming more and more complex in terms of both functionality and hardware architecture. The need to include interaction with other design domains, such as data processing, control processing, input/output etc. is also increasing. Therefore there is a need for a true system level design capability which not only allows the design/simulation of the constituent parts of the system but also their interaction. To bring together the different design domains, system design languages are being developed which allow a model of the behaviour of the entire system to be generated, thus speeding up the design of the entire system by finding problems early in the design cycle rather than at the system integration stage.

Codesign techniques permit the functional specification to be explicitly mapped onto a model of a candidate architecture, in terms of both functional processing, memory access and communication interfaces between hardware and software elements. The resulting partitioned design can then be analysed for performance and the suitability of the candidate architectures investigated. Modifications of the architectural structure and mapping of the functional specification onto the modified architecture can then be made until the design meets the requirements. The level of abstraction of the architecture model can then be increased until the designer is satisfied that an implementation of the design will be 'right first time'. In addition to this simulation capability, codesign methodologies and supporting tools need to be able to export the design information to hardware-software coverification environments and implementation tools.

9.8

Processing of recorded live data

The data recorded by the Naval Research Laboratory (NRL-USA) airborne multichannel radar system have been processed by a systolic trapezoidal array which implements the STAP [9]. The performance of the algorithm has been evaluated against ground clutter, littoral clutter and jammer. Vehicular traffic has also been detected. The systolic array processing has been emulated with a MATLAB software tool. The airborne radar system used by NRL for its STAP flight test program is a modified AN/APS-125 surveillance radar; the operating frequency is 420-450 MHz. The side-looking linear array consists often hooked dipole antennas spaced approximately a half wave length apart, mounted in a 90° corner reflector to provide elevation pattern shaping. The two outer dipoles are terminated yielding eight channels with roughly equivalent element patterns and — 3 dB beam widths of 80° for both azimuth and elevation. The array was energised with a high power corporate feed which applied a taper on transmit such that the maximum azimuth sidelobe level is 25 dB down with respect to the main beam. The receiving system consists of eight identical channels with each channel having a UHF preamplifier, mixer, VHF amplifier bandpass filter and a synchronous demodulator. The synchronous demodulator consists of two demodulators, one referenced to the coherent oscillator (COHO) and the other referenced to the COHO shifted by 90°. This yields two bipolar video channels, one in phase (I), the other quadrature phase (Q). Each I and Q signal is converted to digital by a 10 bit, 5 MHz ADC. The radar pulse repetition frequency (PRF) is 300/750 pps. The output of the receiving system is 16 digital channels for a total digital word width of 160 bits with a clock of 200 ns. This yields a data bandwidth of 800 Mbps which is buffered in real time and stored on magnetic tape.

9.8.1 Systolic algorithm for live data processing As indicated in Figure 9.2, the radar has an array of N = 8 antennas and receiving channels. Each of these receives M echoes from a transmitted train of M (up to 18 in the actual radar) coherent pulses with a PRI (pulse repetition interval) of T = Kz s

where r is the Nyquist sampling period (i.e. typically, the range cell duration) and K is the range cell number in the PRI. The STAP provides a two-dimensional filter in the direction of arrival (DoA) Doppler frequency (/b) plane with a main beam focused towards the target and a wide null in the regions of the ' D O A - / D ' plane containing the interference. QRD constitutes the fundamental component of the voltage-domain algorithm. It operates recursively by using each snapshot of data to update the online estimation of the disturbing environment without forming the interference covariance matrix and only requires 0(N2M2) arithmetic operations to be performed every sample time. The scheme of Figure 9.2 has been applied to the data recorded by the NRL radar.

9.8.2 Data files used in the data reduction experiments This section describes the data files, recorded by NRL radar, used for space-time processing experiments. The files refer to ground clutter, land-sea clutter interface and jamming. The following information has been extracted by the data files, namely: (i) echo power in a radar receiving channel versus range, (ii) the probability density function (PDF) of the amplitude and phase of the radar echoes, (iii) the eigenvalues spectrum, and (iv) the two-dimensional power spectral density of the clutter versus / D and DoA. In this chapter, just a subset of this information is enclosed. 9.8.2.1 Ground clutter Two data files were examined, namely DL050 and DL087. For these files we have calculated the amplitude and phase histograms of the radar echoes. The histograms have been estimated using 896 echoes along range. The amplitude histograms show visually a good fit with the Rayleigh PDF. One more test to verify whether the histogram adequately matches the Rayleigh PDF is to calculate the mean to median ratio. The estimated value is 1.115, and the exact value is 1.442. The histogram of phase is approximately uniform. For file DL050 the spectrum of eigenvalues of the interference covariance matrix is reported in Figure 9.6. The number of antennas is 8, and the number of PRIs is the parameter of the curves ranging from 1 to 18. The covariance matrix has been estimated by averaging 896 independent samples along range, and the maximum eigenvalue has been normalised to O dB. The minimum eigenvalue, corresponding to the curve labelled '18', gives a good estimate of the noise floor in each receiving channel; before normalisation this value is about 10 dB. The clutter-plus-noise power value amounts to 45 dB in each receiving channel; this value has been determined by averaging along range the received signal on the first antenna. Thus the input average clutter-to-noise power ratio has been assumed to be equal to 35 dB for each receiving channels, i.e. for each antenna and for each range sample. 9.8.2.2 Land-sea clutter Figure 9.7 portrays the power versus range of the echoes collected by the first antenna for the data DR075. At the 480th range cell the transition from sea to land is clearly visible. The sea clutter power, estimated along the first 200 range cells,

amplitude of eigenvalues, dB

number of eigenvalues

Eigenvalue spectrum for data file DL050 (ground clutter) [9]. The parameter of the curves represents the number of PRIs

power (1st ant.)

Figure 9.6

range

Figure 9.7

Power versus range of the radar echoes collected by the first antenna of the array [9], At the 480th range cell the transition from sea to land is clearly visible

amplitude of eigenvalues, dB

number of eigenvalues

Figure 9.8

Spectrum of eigenvalues of jamming interference. Curve a: N = 8 antennas and M = I PRI; curve b: N = 8, M = 2 [9]

amounts to 12.8 dB. The land clutter power estimated from 600th to 800th range cells measures 30.2 dB. 9.8.2.3 Jamming The data file DWO15 refers to jamming overland. The jammer appears at the end fire, i.e. DoA = 90°. Figure 9.8 reports the eigenvalues (normalised to OdB) of the estimated covariance matrix (over 300 range cells) for N = 8 antennas and M = 1 PRI (curve a) and N = S and M = I (curve b). The presence of one principal eigenvalue in curve a indicates the presence of one jamming source. We also estimate (over 300 range cells) from the data file that the jammer plus noise power is equal to 36.5 dB. The thermal noise, evaluated by the minimum eigenvalue of the interference covariance matrix is 30 dB. Thus the jammer-to-noise power ratio is 6.5 dB.

9.8.3 Performance evaluation The detection performance of the systolic array of Figure 9.2 depends upon the array parameters, the interference environment and the target signal features. The parameters defining the trapezoidal array are: (i) the dimension NM of the data snapshot vector which equals the number of input lines to the triangular systolic canceller, (ii) the forgetting factor (which controls the adaptation speed of the canceller) of the QRD canceller, and (iii) the number L of linear columns for constraints. Synthetic targets as well as signals injected into the receiver are used to determine the integration of target echoes. Performance during steady state is measured in

terms of: (a) improvement factor (IF) defined as the ratio of the signal-to-total disturbance power ratios at the output and input of STAP, (b) visibility curve, i.e. IF versus target / D sweeping across the PRF, and (c) the two-dimensional response of the adaptive system versus DoA and /D9.8.3.1 Performance against ground clutter Consider the file DL087. Assume a trapezoidal array with one antenna (N = 1), eighteen pulses (M = 18) and L = 3 linear columns (processing cells DE of Figure 9.2). The constraints in the three columns are set to detect a target having the following Doppler frequencies: 0.5 PRF, 0.25 PRF and 0 PRF. A synthetic target having a Doppler frequency value of 0.5 PRF was added at the 264th range cell. Figures 9.9a, b and c show the power in dB of the residue signals at the output of the three columns. Note that the target echo appears only in Figure 9.9a as expected (being the constraint set at / b = 0.5 PRF); the estimated IF is 35 dB. 9.8.3.2 Performance against sea-land clutter The file DR075 contains a test target, injected in the receiver at the 3547th range cell. The Doppler frequency of the target is 0.5 PRF and the DoA is 0°. Figure 9.10 portrays the power in dB of the residue signal obtained by adaptively processing the echoes received by N = S and M = 18 PRIs. The trapezoidal systolic array has one vertical column (L = 1) with the constraints / D = 0.5 PRF and DoA = 0° which are fully matched to the target signal. The spike appears at the 3691st cell which differs from the original target range due to the space-time filter delay which is equal to the total number of degrees of freedom, i.e. 144. The visibility curve for a fictitious target having DoA = 0° and Doppler frequency sweeping across the radar PRF is reported in Figure 9.11; the visibility curve is approximately flat except around / D = 0 which is the mean Doppler frequency of clutter after compensation of the platform speed. The maximum value of the clutter cancellation equals the clutter-to-noise power ratio which has been estimated to be 23.9 dB while the maximum gain in the target direction of arrival and Doppler frequency is equal to 21.5 dB having used all the 144 degrees of freedom; this results in an IF of 45.5 dB. From the visibility curve the maximum IF value amounts to 44 dB, while the optimum IF would be 45.5 dB which is just few dBs higher than the values shown in visibility curve. 9.8.3.3 Performance against jammer The improvement factor of an array of N = 8 antennas, one PRI (M = 1) and one column constraint (the constraint is set along the expected target direction of arrival) is shown in Figure 9.12 as a function of the DoA of a simulated target scanning the angular interval [-90°, +90°]. The jammer is that described in Section 9.8.2.3. It is noted that the maximum IF is about 13 dB, while the optimum IF value would be 17 dB. The 4 dB loss is due to the adaptation of the systolic arrays [9, p. 600]. We note that adaptation loss is higher for jamming than for clutter; possible explanations are the following: (i) the number of spatial degrees of freedom is 8, which is lower than

residue power, dB

target

residue power, dB

range cells

residue power, dB

range cells

c

Figure 9.9

range cells

Processing of ground clutter live data [9]

target

power, dB

initialisation of space-time filter

range

Power of residue signal for data file DRO 75 [9]

IF, dB

Figure 9.10

F

Figure 9.11

Doppler/PRF

Visibility curve for data file DR075 [9]

the number of temporal degrees of freedom (=18), (ii) the jammer-to-thermal noise power has been estimated as being equal to 6.5 dB [9, p. 598], considerably lower than the clutter-to-thermal noise power. This will cause higher loss due to the need for precise estimation of jamming direction of arrival.

degree

Figure 9.12 IF versus DoA of a simulated target against jamming [9] 9.8.4

Detection of vehicular traffic

The detection of vehicular traffic has been attempted along US route 50 (see, for details, Reference 9). Four points on the route have been selected (bearing angle relative to the array normal, with positive values coming from the right-hand side of the array): 1st point: range = 39268 m, azimuth = —5.8° 2nd point: range = 39268 m, azimuth = —3.4° 3rd point: range = 39429 m, azimuth = -0.6° 4th point: range = 39429 m, azimuth =1.0°. The systolic array processes the snapshots along the range cells received by 8 antennas and 18 PRIs (i.e. it works with the maximum number of adaptive degrees of freedom). The adapted residue along the range cells has been further processed by a constant false alarm rate (CFAR) thresholding device based on the cell average (CA) technique. The CFAR-CA has two guard range cells on each side of the range cell under test and twenty range cells on each side to estimate the detection threshold. The CFAR-CA has been set to guarantee a PFA of 10~4. Figure 9.13 depicts the adapted residue versus range when the receiving antenna pattern is focused at —5.8°, which is the azimuth value corresponding to the first point on the US route 50. The analysed Doppler frequency is 0.225 PRF which corresponds to a radial speed of 23.2 m/s (i.e. 83.52 km/h) compatible with vehicular traffic. A detection appears at the 932th range cell that (it can be shown) comfortably compares with the expected location of the target in the first point. Similar results have been obtained for the other three points on the US route 50 [9].

range cells

Figure 9.13 Adapted residue power and detection threshold curves versus range cell [9]

9.9

Concluding remarks

The research work described in this chapter and the enclosed references is also relevant for other radar applications, sometimes simpler than the STAP, namely (i) ground-based or ship-borne radars for clutter cancellation and (ii) ground-based or ship-borne radars equipped with a multichannel phased array antenna for jamming cancellation. The STAP reverts to the first application by setting Af = 1, while it becomes the second application for M = 1. Thus, the adaptive processing architectures described in this chapter are applicable also to the systems in (i) and (ii). In general, the number of degrees of freedom involved is one order of magnitude less than for the STAP case; this makes less critical the implementation of a VLSI-based systolic array. A practical application of systolic processing for classical ground-based or ship-borne radar is described in Reference 19 where it is shown how to combine in one systolic scheme the two functions of adaptive interference cancellation and sidelobe blanking. The application of STAP to synthetic aperture radar for detecting and imaging of slowly moving targets is discussed in References 7, 15 and Chapter 3 of this book. In this respect the procedure to form the SAR image by one-bit processing plays a role; this procedure is also applied in along-track interferometry (ATI)-SAR to detect moving targets [20]. It can be shown that this approach offers a considerable computational advantage; FPGA technology has been successfully applied to implementing one-bit SAR processing. The enormous progress made in signal processing technology is under our eyes; this progress is also exploited and, at the same time, motivated by STAR Today the

key words are: heterogeneous processing (i.e. based on VLSI, ASIC, FPGA, RISC, MEMS, photonic technology etc.), virtual and rapid prototyping, modularity and flexibility of processing architectures, reuse and porting of the same, COTS approach to software and hardware, software language (e.g. System C; Handel C for FPGA), design tools like Ptolemy. All these techniques and technologies are conceived to counteract the obsolescence which is one of the most important problems to face today in signal processing.

9.10

Appendix A: Givens rotations and systolic implementation of sidelobe canceller

The QRD, which mainly performs orthogonal rotations, may be efficiently implemented by a recursive application of Givens rotations. A complex Givens rotation is an elementary transformation of the form: (9.8) where /3 is a scaling factor. The rotation coefficients, c and s, satisfy: (9.9) These relationships uniquely specify the rotation coefficients, c and s: (9.10) (9.11) The QRD by Givens rotations may efficiently be mapped onto a systolic array computer. A systolic computer is an array of processing cells. Each cell has a local memory and is connected with its neighbouring cells in the form of a regular grid. The more common configurations of the systolic array are linear and triangular. The operations performed by the systolic array are synchronised by a clock. On each clock cycle, every cell receives data from its neighbouring cells and performs operations. The resulting data are stored within the cell and passed to the neighbouring cells on the next clock cycle. The triangular systolic array is shown in Figure 9.14 for the simple case of an SLC (sidelobe canceller) system equipped with one auxiliary antenna. The triangular systolic array comprises three types of computational cell: the boundary cell (circular cell in Figure 9.14), the internal cell (rectangular cell in Figure 9.14) and the final cell which is a simple two-input multiplier. The function of each computational cell is specified in the Figure. Each cell performs the specified functions on its input data and delivers the appropriate output values to the neighbouring cells. The least-squares residue constitutes the noise-reduced output signal from the adaptive beamformer.

boundary cell

otherwise

internal cell

radio frequency (RF), intermediate frequency (IF) and baseband (BB) receiving channels

residual

Figure 9.14

Implementation of an SLC with one auxiliary antenna by means of a triangular systolic array (Adapted from WARD et al., IEEE Trans Antennas Propag., AP-34, (3), March 1986, pp. 338-346, (©1986 IEEE))

The processing scheme can be applied to the STAP case as shown in Figure 9.15. One limitation of this scheme derives from the need to reinitialise the systolic array every time that the look direction for searching the target is changed; in fact, the processor of Figure 9.15 focuses one quiescent beam to gather the echoes from a target possibly present in a specific region of the space-time plane. Because the direction of arrival and the Doppler frequency values of the target are not known a priori, it needs to monitor a number of lines of residue power for target detection purpose. The above mentioned limitation is overcome with the scheme of Figure 9.2.

triangular systolic array

processing elements

Figure 9.15

9.11

residue

Calculation of the adapted STAP residue via a sequence of Givens rotations implemented with a triangular systolic array. Comparison of residue to a detection threshold X to check for the two alternative hypotheses: H\ (target presence) versus HQ (no target)

Appendix B: lattice working principle

The lattice systolic array requires three working phases to correctly process the data samples. Indicate with i — PRT (pulse repetition time: PRT = PRI) the data matrix having dimensions TV (rows) and k (columns) containing the data pertinent to the /th pulse; N denotes the number of antennas and k the number of data snapshots to process in the adaptation phase. Indicate also with (/ — j) PRT the data matrix (of dimension N by k), pertinent to the data of the ith PRT after the application (by means of the squared array) of the rotation coefficients computed in the triangular array starting from the data captured during the jth PRT. For the study case described here the number (M) of PRI is three. The first working phase of the lattice processor is shown in Figure 9.16. The triangular and squared systolic processors, also shown in Figure 9.3, have dimension N by N; the number of operations of this phase is k by O(N2). Following the above mentioned notations, the second lattice working phase is reported in Figure 9.17; note that this phase costs 3k O(N2) operations. Finally, in Figure 9.18 is presented the third lattice work phase. Note also that this phase costs 3k O(N2) operations. The total number of operations is Ik O(N2) which is approximately 2 by M (i.e the number of pulses) by k O(N2); thus, the number of operations k 0(M2N2) required by the full triangular array of Figure 9.2 of the text has been reduced.

1 st phase data matrix of 2 PRT

data matrix of 1 PRT

squared array of processing elements data matrix of (1-2) PRT total number of operations = k O(N2)

Figure 9.16

1st working phase of lattice

2nd phase

(2-3) PRT total number of operations = k O(N2)

(3-2) PRT total number of operations = k Q(N2)

(l-2)-(3-2)PRT total number of operations = k O(N2)

Figure 9.17

9Al

2nd working phase of lattice

Appendix C: the CORDIC algorithm

Since QR-based algorithms mainly perform orthogonal rotations (see Section 9.10, Appendix A), the CORDIC algorithm may be selected for implementing the processing cells of the above described systolic arrays. A further motivation comes from the fact that some CORDIC-based VLSI processor arrays have already been developed for radar and more general signal processing applications.

3rd phase 3 PRT fictitious PRT = O total number of operations = k 0(N2)

(2-3) PRT total number of operations = k O(N2)

(l-2)-(3-2)PRT total number of operations = k O(N2)

Figure 9.18

3rd working phase of lattice

The basic idea underlying CORDIC [22] is to decompose a desired rotation angle O into a weighted sum of a given number n (e.g. n > 6) of predefined elementary rotation angles Qf(O, such that the overall rotation can be carried out via a sequence of n shift-and-add operations, called /JL-rotations. More specifically, given the vector Xin of components [x in ,y in ], the CORDIC algorithm transforms it, by means of a sequence of /x-rotations, into a new vector xout = [xout, youtlThe rotations are attained through the following operations: Xout = *in COSQf(Z) -

)>jit SnIQf(O

yout = xin sin Qf(Z) - yin cos a(i) ' IgVd) = Pd)I-1 pd) = ±1 = sign(xin)sign(yin)

^AZ)

The CORDIC algorithm can operate either in rotating or in vectoring modes. In rotating mode, the rotation angle 6 encoded by the sequence a(i) is applied to the vector [xinyin\T to give a new rotated vector [xoutyoutY'• Conversely, in vectoring mode, the CORDIC algorithm computes the coding sequence of the rotations which when applied to [xinyin\T yields \xout 0 ] r . The input/output description of the CORDIC cell considered for implementation of systolic algorithms is given in Figure 9.19 where m is a control bit selecting either the vectoring or rotating modes, and a represents the /[x-rotations sequence. The CORDIC algorithm operates on real valued vectors while, in adaptive beamforming, complex valued vectors must be handled. In particular, for the vectoring

Figure 9.19

Schematic of CORDIC processing function

mode

mode 0-CORDIC

-CORDIC

CORDIC

Re(r)

ImO) Re

Figure 9.20

twl

Im[X0UtI

CORDIC supercell for circular rotation on complex valued numbers. Adapted from Figure 4 of: CM. Rader, Wafer-Scale Integration of a Large Scale Systolic Array for Adaptive Nulling', The Lincoln Laboratory Journal, 1991, 4, (1), pp. 3-29

mode, a unitary transformation Q must be computed, which annihilates the second component of a given vector [rx]T, with r e R (i.e. r is a real valued number) and x e C (i.e. x is a complex valued number). This step occurs in QR and inverse QR algorithms [14, equation 37]. It is possible to see that such a transformation can be represented as [14]: Q

Tcos0 -[-sin0

sin0iri 0 I cos0][o e-J°\

(9 13)

'

with 0 — arc ^g (Im Qt)/Re (x)) and 0 = arcfg(|;t|/r). Subsequently, in the rotating mode the transformation Q can be applied to a generic two-dimensional complex vector. An example of a processor realising rotations on complex valued vectors, and using the same structure for vectoring and rotating mode, is shown in Figure 9.20. The processor is obtained by interconnecting three CORDIC cells, of the type of

Figure 9.19, named O and 0 CORDICs and two registers to store the real and imaginary parts of r (r e C when the processor is working in rotating mode). For the vectoring mode, this architecture allows us to annihilate the second component of a given vector [rx]T. In more detail, with reference to Figure 9.20 (r e R, thus Im(r) = 0), the imaginary part of x is annihilated in the 0 CORX)IC cell and, subsequently, \x\ is annihilated in the left 0 CORDIC cell. The right 0 CORDIC cell is not operating. The Q transformation of equation 9.13 is therefore coded by the sequence (fie, / ^ ) and they will be applied in the rotating mode. In the rotating mode the rotation angle 6 is applied to the incoming vector [Re(jc) Im(x)] r in the O CORDIC and, subsequently, the rotation angle 0 is applied by the left and right 0 CORDIC cells, respectively, to the real and imaginary parts of r (now r 6 C, as requested by QR and IQR algorithms) and the rotated vector x.

9.13

Appendix D: the SLC implementation via CORDIC algorithm

The sidelobe canceller (SLC) may be implemented by means of the CORDIC cells described in Section 9.12. Figure 9.21 refers to the case of a main antenna and one auxiliary antenna (the same application example as in Section 9.10, Appendix A, Figure 9.14). On the left-hand side of the Figure, the SLC algorithm is realised by means of a systolic triangular array computing the Givens rotations. On the right-hand side of Figure 9.21, the same algorithm is implemented by means of the CORDIC arithmetic. The architecture is basically composed of four computational cells having as input the data from the main and the auxiliary antennas, plus a computational cell auxiliary channel

main channel

auxiliary channel

main channel

<j> CORDIC vectoring

(f> CORDIC rotating

9 CORDIC vectoring

6 CORDIC rotating

residue

residue

Figure 9.21

The SLC implemented with CORDIC algorithm

6 CORDIC rotating

required for normalisation of the residue. The cells may work either in vectoring mode or in rotating mode: the following operations are performed in vectoring mode. Given the vector [x(0), y(0)] the rotation sequence is computed such that: (9.14) where ns is the required number of rotations. In rotating mode, given the sequence /x(7), the following operations are applied: y(ns)

= V(O) - QfX(O)

(9.15)

The cells (numbers 1 and 3 in the Figure) working in vectoring mode operate directly on the auxiliary data, computing the /x-rotations required to annihilate the second coordinate of the complex data xi = Qtir,Jti/), which changes in x'i = (x'lr,0). The rotating cells (numbers 2 and 4 in the Figure) operate on the main channel data applying the /x-rotations computed by the adjacent vectoring cells; the remaining computational cell (number 5 in the Figure) works as the previous ones and is required to normalise the cancellation residue.

9.14

Appendix E: an example of existing processors for STAP

This appendix summarises in a tabular form some of the most relevant processors for STAP as they are perceived by the authors in the open technical literature. The table is organised in three columns that report, respectively, the name of the processor and of the organisation, the features and some relevant references. The table entries are in accordance to the publication date of the references.

Name

Features

References

Rome Air Development Center RADC (USA)

Systolic array implemented with digital (chips from ESL Company) and optical technologies. QU factorisation based on Givens method; systolic weight computer and a digital weight applier; ESL systolic chip is a custom VLSI chip with 32-bits floating points. Acousto-optic adaptive processor: use of Bragg cells, a liquid spatial light modulator and an

LIS, S. etal.: 'Digital and optical systolic architectures for airborne adaptive radars'. Agard conference proceedings 381, Multifunction radar for airborne applications, pp. 18-1, 18-13, 1986

Name

Features

References

optical detector; GaAlAs semiconductor diode laser provides the illumination for the time integration correlator. Hazeltine, funded by RADC (USA)

Systolic array brass-board of 1.25 billion floating-point operations/s; solution of multiple simultaneous equations with twelve unknowns; weight update every 50 |xs. In 1988 brass-board was integrated into the flexible adaptive spatial signal processor test bed of RADC.

LACKEY, R. J., BAURLE, H. R, and BARILE, J.: 'Application specific supercomputer', SPIE, 977, Real Time Signal Processing XI, 1988, pp. 187-195

MUSE, MIT-Lincoln Laboratory (USA)

Matrix update systolic experiment (MUSE) for 64 degrees of freedom. 96 CORDIC processors update the 64 weights - to apply, say, to 64 receiving channels - on the basis of 300 new observations in only 6.7 ms; equivalent to 2.8 Ginstructions/s. MUSE has been realised on a single large wafer of 5 in by 5 in by using restructurable VLSI. Each CORDIC cell has 54 000 CMOS transistors. 50 dB of signal-to-interference-plus-noise power ratio is achievable. Mapping strategies and estimation of achieved computational throughput of QR decomposition by using: Meiko surface computer with 128 processing elements (PEs), nCube2 with 64 PEs, connection machine CM-200 with 8192 PEs, and MasPar MP-I with 1024 PEs. Application to an adaptive array of antennas and STAR

RADER, C. M.: 'Wafer scale integration of a large scale systolic array for adaptive nulling', Line. Lab. J., 1991, 4,(1), pp. 3-29 RADER, C. M.: 'VLSI systolic arrays for adaptive nulling', IEEE Signal Process. Mag., July 1996, pp. 29-49

Benchmarks on general purpose parallel computers (It)

D ' A C I E R N O , A.,

CECCARELLI, M., FARINA, A., PETROSINO, A., and TIMMONERI, L.: 'Mapping QR decomposition on parallel computers: a study case for radar applications', IEICE Trans. Commun., October 1994, E77-B, (10), pp. 1264-1271

References

Name

Features

Test bed (MIT-Lincoln Laboratory)

One of the first world-class systems MARTINEZ, D. R. and McPHEE, J. V.: ever developed to demonstrate an end-to-end real-time STAP 'Real-time test bed for processing capability designed STAP'. IEEE 1994 around commercial off-the-shelf Adaptive antenna integrated hardware components. systems symposium, The peak throughput amounts to Long Island, 7-8 22 Gops/s. The system is divided November 1994, into front end digital system with pp. 135-141 capability of 19 Gop/s and a back MARTINEZ, D. R., end programmable processor with MOELLER, T. J., and capability of 2.5 Gflops/s. This back TEITELBAUM, K.: end is based on DSP TI TMS320C30 'Application of microprocessor. The processor reconfigurable architecture is sufficiently flexible in computing to a high programming to implement different performance front-end classes of STAP algorithms. The radar signal processor', mapping of algorithm is on identical J. VLSI Signal Process., PEs operating under the same May/June 2001, 28, set of program instructions (1-2) but on different data input streams. Application of reconfigurable computing to high throughput front-end radar.

CORDIC test-board (It, Ne)

A board with four VLSI CORDIC chips used to implement the QR decomposition for adaptive array processing; the estimation of achieved computational throughput is also obtained.

KAPTEIJN, P., TIMMONERI, L., DEPRETTERE, E., and FARINA, A.: 'Implementation of the recursive QR algorithm on a 2*2 CORDIC test-board: a study case for radar applications'. 25th European Microwave conference, 4-7 September 1995, Bologna, Italy

Name

Features

References

Maui High Performance Computer Center (MHPCC), MIT-Lincoln Laboratory (USA)

A network configuration with the 400-way IBM supercomputer SP2 hardware and software, visualisation hardware, mass storage system, file servers, parallel tools, compilers, preprocessors, debuggers, parallel operating environment etc. Crest environments I and II for STAP related to data of Mountaintop program.

1996 Adaptive Sensor Array Processing (ASAP) workshop, Maui High Performance Computer Center (MHPCC) Training Session, 12 March 1996

Mountaintop is UHF radar with 18 channels (16 of which are active) operating with the concept of inverse displaced phase centre antenna (IDPCA). An auxiliary transmitting aperture is added to a stationary radar. The auxiliary array is linear with the number of elements equal to the number of pulses in a coherent processing interval; the element spacing is chosen to create the desired aircraft motion. Mercury Computer Systems, Inc. (USA)

Description of strategies to distribute three-dimensional data set for STAP over available computing elements in a parallel computer system.

SKALABRIN, M. F. and EINSTEIN, T. H.: 'STAP processing on a multi-computer: distribution of 3-D data sets and processor allocation for optimum interprocessor communication'. Proceedings of Adaptive sensor array processing (ASAP) workshop, 13-15 March 1996, pp. 429-447

Name

Features

References

STAP on GP parallel computer, Honeywell Inc. (USA)

Coarse grained data flow mapping for STAP; up to 234 nodes on Rome Lab. 321 node machine; sequential C code for four benchmarks for Doppler filtering, adaptive processing etc.

SAMSON, R., GRIMM, D., MORRILL, K., and ANDRESEN, T.: 'STAP performance on a Paragon ™Touchstone system'. IEEE National Radar Conference, Natrad 96, Ann Arbor, MI, 13-16 May 1996, pp. 315-320

Massive parallel processor (USA)

Experience in porting the MTI-Lincoln Laboratory STAP benchmark programs onto the IBM-SP2, Cray T3D and Intel Paragon. Benchmark performance results along with scalability analysis on machine and problem size.

HWANG, K. and XU, Z.: 'Scalable parallel computers for real-time signal processing', IEEE Signal Process. Mag., July 1996, pp. 50-66

MeshSP, MIT-Lincoln Laboratory (USA)

McMAHON, J. O.: Investigates the application of commercially available massively 'Space-time adaptive parallel processors for STAR These processing on the mesh processors are sufficiently flexible to synchronous processor', accommodate different STAP MIT Line. Lab. J., 1996, architectures and algorithms and are 9, (2), pp. 131-152 scalable over a wide parameter space to support the requirements of different radar systems. The mesh synchronous processor is an SIMD architecture with an array of processors connected via a two-dimensional or three-dimensional nearest-neighbour mesh. It incorporates the single monolithic processor element (PE) of the Analog Devices ADSP-21060 SHARC. Each PE permits 120 Mflops/s peak performance and 512 kB of internal memory,

Name

Features

References

six processor communication ports, each capable of 40 MB/s peak throughput and two I/O ports, each capable of 5 MB/s peak throughput. A MeshSP processing board (7 inc by 13 inc) dissipates 100 W, contains 64 SHARCs and is capable of 7.7 Gflops/s peak performance. The higher order post Doppler (HOPD), an embodiment of STAP algorithm, has been mapped onto the MeshSP. In the HOPD the method for computing the QR decomposition of the data matrix has been the Householder reflection algorithm. It was found that the real-time processing for a study case of 48 channels, 128 Doppler bins and 1250 range gates required 16 boards for a total of 123 GFlops. ONEST: on line experimental space time, FGAN-FFM (Ge)

Implements algorithms of moving target extraction in SAR by means of STAR Use of heterogeneous DSP network, VME bus boards; Sharp processors for range and azimuth compression FFT; bunch of 24 -i- 32 TMS320C40 for filtering of slow moving targets; 16 TMS320C40 for moving target detection, position finding and concurrent SAR image generation.

JANSEN, W. and KIRCHNER, C : 'ONEST: concept of a real time SAR/MTI processor'. EUSAR96, Konigswinter, Germany, 1996, pp. 349-352

High Performance Computer (HPC), Rome Lab. (USA)

Honeywell ruggedised Touchstone used in four flight experiments, 2 5 + 4 processing nodes; each node has three i860 processors; 300 Mflops per node, 7.5 Gflops overall; weights update with QRD, sustained overall throughput 3.15 Gflops, efficiency 48 per cent. Data are passed from IF digital down conversion to the 29 nodes via a

LINDERMAN, M. H. and LINDERMAN, R. W.: 'Real time STAP demonstration on an embedded high performance computer'. IEEE National Radar Conference, Natrad 97, 13-15 May 1997,

Name

Features

References

high performance parallel interconnect (HiPPI) channel having 100 Mbytes/s. Hardware housed in two racks (19 in).

Syracuse, NY, pp. 54-59

Real-time multi-channel airborne radar measurements (RT-MCARM) with onboard Intel Paragon computer with 25 compute nodes running Sunmos operating systems. Each node has three i860 processors accessing common memory of 64 Mbytes as shared resource; two HiPPI; two service nodes. Linear speed up was obtained for up to 236 compute nodes. The adaptive beamforming is done applying the QRD. Real-time multichannel airborne radar measurements (RT-MCARM), Rome Lab. (USA)

In May-June 1996 Rome Laboratory conducted experiments of real-time STAP on board the BAC-III. Two processing chains have been tested contemporaneously: a) conventional analogue beamforming without STAP on a Mercury computer, b) 16 simultaneous beams provide digital data to the ruggedised 28 nodes of Paragon using SUNMOS as operating system and a Pentium PC to control radar, processing chain and display. Four flights included urban and rural clutter, land-sea interface, target was a Sabreliner, a moving target simulator and various targets of opportunity plus a CW jammer operating during random periods. Paragon functions: digital beamforming (six receiving beams within a wide transmitter beam),

CHOUDARY, A., LIAO, W-., WEINER, D. et al.: 'Design implementation and evaluation of parallel pipelined STAP on parallel computers', IEEE Trans. Aerosp. Electron. SySt., April 2000, 36, (2), pp. 528-548

LITTLE, M. V. and BERRY, W. P.: 'Real time multichannel airborne radar measurements'. IEEE national Radar conference, Natrad 97, 13-15 May 1997, Syracuse, NY, pp. 138-142

Name

Lockheed Martin (USA)

Features

References

pulse compression, two alternative STAP algorithms, CFAR detection, data recording. The flights demonstrated the feasibility of using high performance computer to conduct STAP of radar data in real time: a unique capability within DoD USA. High performance scalable computer MANSUR, H. H.: 4 (HPSC) employs 716 Analog STAP architecture Devices Share processing elements implementations using (PEs); two identical chassis and only high performance two board types are needed. scalable computer Sustained processing throughput of (HPCS)MEEE national the order of 32 Gflops. The Share Radar conference, PEs are grouped in four forming a Natrad97, 13-15 May processing node. Myrinet switching 1997, Syracuse, NY, technology (129Mbytes/s) provides pp. 325-330 the connections between the nodes. The recursive modified Gram Schmidt QR algorithm is implemented. The HPCS is currently (1997) under development.

References 1 FARINA, A.: 'Antenna based signal processing techniques for radar systems' (Artech House, 1992) 2 WARD, J.: 'Space-time adaptive processing for airborne radar'. MIT-Lincoln Laboratory, TR 1015, 13 December 1994 3 KLEMM, R.: 'Principles of space-time adaptive processing' (IEE, UK, 2002) 4 FARINA, A. and TIMMONERI, L.: 'Space-time processing for AEW radar'. Proceedings of international Radar conference, Radar 92, Brighton, UK, 12-13 October 1992, pp. 312-315 5 TIMMONERI, L., PROUDLER, I. K., FARINA, A., and McWHIRTER, J. C : 'QRD-based MVDR algorithm for multipulse antenna array signal processing', IEEProc. Radar, Sonar Navig., April 1994,141, (2), pp. 93-102 6 FARINA, A., BARBAROSSA, S., CECCARELLI, M., PETROSINO, A., TIMMONERI, L., and VINELLI, F.: 'Application of the extreme eigenvalue

7

8

9

10

11

12

13

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analysis to signal and image processing for radar'. Invited paper, Colloque International sur Ie Radar, Paris, 3-6 May 1994, pp. 207-213 FARINA, A. and BARBAROSSA, S.: 'Space-time-frequency processing of synthetic aperture radar signals', IEEE Trans. Aerosp. Electron. Syst, 1994, 30, (2), pp. 341-358 D'ACIERNO, A., CECCARELLI, M., FARINA, A., PETROSINO, A., and TIMMONERI, L.: 'Mapping QR decomposition on parallel computers: a study case for radar applications', IEICE Trans. Commun., October 1994, E77-B, (10), pp.1264-1271 FARINA, A., GRAZIANO, R., LEE, F., and TIMMONERI, L.: 'Adaptive spacetime processing with systolic algorithm: experimental results using recorded live data'. Proceedings of the international conference on Radar, Radar 95, Washington DC, 8-11 May 1995, pp. 595-602 FARINA, A. and TIMMONERI, L.: 'Antenna based signal processing techniques and space-time processing'. Tutorial, international conference, Radar 95, Washington DC, USA, 8-11 May 1995 KAPTEIJIN, P., DEPRETTERE, E., TIMMONERI, L., and FARINA, A.: 'Implementation of the recursive QR algorithm on a 2 x 2 CORDIC test-board: a case study for radar application'. Proceeding of the 25th European Microwave conference, Bologna, Italy, 1995, pp. 490-^95 FARINA, A., SAVERIONE, A., and TIMMONERI, L.: The MVDR vectorial lattice applied to space-time processing for AEW radar with large instantaneous bandwidth', IEEProc, Radar Sonar Navig., February 1996,143, (1), pp. 4 1 ^ 6 FARINA, A. and TIMMONERI, L.: 'Parallel algorithms and processing architectures for space-time adaptive processing', CIE international conference on Radar, ICR96, Beijing, P. R. of China, invited paper for the workshop on STAP, 1996, pp. 771-774 BOLLINI, P., CHISCI, L., FARINA, A., GIANNELLI, M., TIMMONERI, L., and ZAPPA, G.: 'QR versus IQR algorithms for adaptive signal processing: performance evaluation for radar applications', IEE Proc, Radar Sonar Navig., October 1996,143, (5), pp. 328-340 LOMBARDO, P. and FARINA, A.: 'Dual antenna baseline optimization for SAR detection of moving targets'. Proceedings of ICSP96, Beijing, RR. of China, 1996, pp. 431-433 FARINA, A. and LOMBARDO, P.: 'Space-time adaptive signal processing'. Tutorial, IEE international conference on Radar, Radar 97, Edinburgh, UK, 13 October 1997 FARINA, A. and TIMMONERI, L.: 'Real time STAP techniques'. Proceedings of IEE symposium on Space time adaptive processing, London, 6th April 1998, pp. 3/1-3/7 FARINA, A. and TIMMONERI, L.: 'Real time STAP techniques', Electron. Commun. Eng. J., Special Issue on STAP, February 1999,11, (1), pp. 13-22 FARINA, A. and TIMMONERI, L.: 'Systolic schemes for joint SLB, SLC and adaptive phased-array'. Proceedings of the IEEE international conference Radar 2000, Washington DC, 7-12 May 2000, pp. 602-607

20 PASCAZIO, V., SCHIRINZI, G., and FARINA, A.: 'Moving target detection by along track interferometry'. IGARSS 2001, Sidney, Australia, July 2001 21 BIERENS, L.: DoubleBW Systems B.V., May 2002, Private communication www.doublebw.com/brochures.htm 22 VOLDER, J. E.: 'The CORDIC trigonometric computing technique', IRE Trans. Electron. Computers, September 1959, pp. 330-334

Part IV

Clutter inhomogeneities

Chapter 10

STAP in heterogeneous clutter environments William L. Melvin

10.1

Introduction

Aerospace radar systems must detect a variety of target types in the presence of severe, dynamic clutter and jamming signals. Signal diversity - the exploitation of azimuthal, elevation, Doppler, range and polarisation measurement spaces - is a necessary component of advanced detection architectures. Space-time adaptive processing1 (STAP) improves the detection of slow moving and/or low radar cross section (RCS) targets competing with mainlobe and sidelobe ground clutter returns [I]. Additionally, in light of the equivalence between the maximum signal-to-interference-plus-noise ratio (SINR) filter and the minimum variance beamformer, we recognise STAP as a member of the class of superresolution algorithms [2]. For this reason, STAP is a key element of radar systems whose electrically small apertures, and hence relatively large beamwidths, would otherwise seriously affect clutter-limited detection performance. Adaptive filters adjust their response in accord with estimates of interference characteristics. A critical distinction exists between optimal and adaptive filters. Specifically, the optimum filter design requires clairvoyant knowledge of interference statistics (e.g. known covariance matrix), while the adaptive implementation relies on necessarily imperfect estimates of unknown interference parameters. A training stage generates estimates of these unknown parameters. Hence, STAP is a datadomain implementation of the optimum filter. The optimum filter defines the upper bound on STAP's detection performance potential. In the multivariate Gaussian case, maximising SINR equivalently maximises the probability of detection (PD) for a fixed probability of false alarm (PFA) [I]1 In the case of ground clutter suppression, we consider spatial and slow time (Doppler) degrees of freedom, thereby taking advantage of the clutter's angle-Doppler coupling. On the other hand, cancellation of jammer multipath requires spatial and fast time (range) degrees of freedom

Consider an N-channel array receiving M pulses. Given the space-time snapshot for the &th range, Xk e cMNxl, the optimal weight vector in the maximum SINR sense takes the well known form, Wk = /xQ^ 1 S 8 -^ where \i is an arbitrary scalar; Qk = £{Xk///0x£yH } e cNMxNM; Xk/H0 is the zero-mean, interference-only (nullhypothesis, Ho) space-time snapshot; and, ss_t € CNMxl is the target space-time signal vector [3]. In practice, both Qk and ss_t are unknown, and so the adaptive processor substitutes the estimate Qk for Qk and the surrogate steering vector vs_t for ss_t; the adaptive weight vector is then Wk = AQk vs-t> where it is common to set l//x = y v ^ Q ^ V s - t in an attempt to normalise the output noise to unit power. Using secondary (auxiliary, training) data taken from other range cells within the CPI, the processor computes Qk. Ideally, secondary data exhibit statistical behaviour identical to the null-hypothesis condition characterising the primary (test) range cell k. The bandwidth and PRF limit the maximum number of unambiguous range cells in the coherent dwell to Qtot = Ru/^R total vectors, where R11 is the unambiguous range extent and AR is range resolution.2 Just as the optimal processor bounds the performance of the STAP, finite sample support of o — TCB < a* < coo + xB, where co is the frequency in radians - yields the corresponding spatial correlation coefficient of the form: ps(m,n) = smc(7tB(rm - Xn))

(10.22)

where xp is the time delay between the pth channel and a suitable reference point due to direction of arrival (DoA). Bandwidth, the DoA embodied in the time delay, and the size of the array (influencing the maximum time difference between samples) affect ps (m, n). The channel-to-channel correlation matrix is then:

(10.23)

which is Toeplitz if the spatial sampling is uniform. (Non-dispersive errors yield non-Toeplitz structure; the model of equation (10.18) can incorporate such errors independent of equation (10.23).) As subsequently shown in Section 10.8.1, the model given by equation (10.18) is a good approximation to actual measured data. To summarise, the key components of the clutter space-time model include: the amplitude scaling term equation (10.26) can be written: (10.27) where cos 2 (p,u) = Ip^up/HpH^llull^ and sin 2 (p,u) = 1 — cos 2 (p,u). From equation (10.27) we make the following expected observations: 0 < Ls < l;whenaj = 0, we find Ls = 1; when Sd = vs_t (u = p) and a^ J=. 0, then Ls = 1; as aj —• oo, Ls -> 0; while in general, as a j ^9L5 | as long as Sd ^= v s _ t . We numerically verified the equivalence between equations (10.27) and (10.25). Discretes in the CUT will adversely affect the false alarm rate. Suppose the design threshold, vj, is set for the expected output noise power: (10.28) whereas the actual output noise power in the CUT is: (10.29)

5 In this case, Q c + n /k = Qc+n V k since we assume the distributed clutter environment is homogeneous ^ The SINR loss due to target mismatch is typically small in comparison with the loss associated with clutter heterogeneity. Since clutter heterogeneity is our focus, we'll assume perfect match between hypothesised and actual space-time steering vectors

The expected and actual false alarm rates, PfA,e and PFA,CI, are then: (10.30) from which we find (10.31) PFA,e serves as the design false alarm rate in this instance. Equation (10.31) indicates the following: (a) if Pa = Pe, then PFA,a = PFAy, (b) if Pe > Pa, then PFA,a < PFA*',

and, more importantly for the case of a discrete in the CUT, (c) if Pe < Pa, then PFA,a > PFA,e- Also, as a result of the exponential term, a small mismatch between the design and actual power leads to large changes in false alarm rate. For the case with the discrete in the training interval, we let w^ -* ^k — £[Wk] = ^(Qc+n/k+a^SdS^)" 1 v s _ t , where a j incorporates the 'averaging' process, to evaluate asymptotic performance degradation. The corresponding SINR loss is:

(10.32) Equation (10.32) can be rewritten:

(10.33)

Qc+n/ksd- Using the prior definitions for p and u, equation (10.33) becomes: (10.34) We observe the following from equation (10.33): 0 < Ls < 1; Ls = 1 when o2d = 0; Ls = 1 when Sd = vs_t (u = p) and c]c] 6= = B

,m-iON (10.39)

K J T(S)F \ P ) var[yc ]' H E[yc] where a and ft are shape parameters. The selection of the gamma distribution represents a likely choice for overland surveillance [7,8], Notice that as var[}/c] approaches zero while the mean is held constant, the environment tends to the homogeneous case. Figure 10.4 shows finite sample support SINR loss based on 150 Monte Carlo trials for varying levels of clutter amplitude heterogeneity for our nominal airborne radar simulation example. Figure 10.5 depicts the CNR sample mean, standard deviation (STD) and maximum values specified on a single channel, single pulse basis. The basic analysis procedure, described in Reference 10, involves the following:

(a)

compute 2MN + 1 space-time realisations for the nominal airborne radar scenario, where the clutter reflectivity for each clutter patch is randomly chosen to abide by the distribution of equation (10.39) with fixed mean and specified variance (b) compute and save the clairvoyant covariance matrix for the first space-time realisation (c) compute the covariance matrix estimate using the MLE and the remaining 256 realisations (RMB loss in an HD environment is —2.96 dB in this instance) (d) compute the adaptive weight vector for the transmit angle over all Doppler (e) calculate SINR loss (f) repeat in Monte Carlo fashion, averaging the various trials. Results given in Figure 10.4 are consistent with those described by Nitzberg in Reference 7, and seem to suggest the robustness of STAP to range-angle varying clutter reflectivity. Generally, the adaptive filter's null depth inadequately suppresses

SINR loss, dB

(l)mean/std=1000 (2)mean/std=100 (3)mean/std=10 (4)mean/std = 2/3 (5)mean/std=l/2 (6)mean/std=l/3 (7)mean/std=l/10 (8)mean/std=l/12 RMB Rule (-2.96 dB)

Doppler filter

Figure 10.4

SINR loss due to range-angle varying clutter reflectivity following a gamma distribution ([10J, © 2000 IEEE)

large clutter fluctuations and so residual clutter leads to performance degradation. Figure 10.4 indicates that the predominant loss occurs about the centre of the clutter spectrum, with only slight impact on MDV in this instance. However, the reader should keep in mind that the Figure does not capably capture instantaneous performance (i.e. the Monte Carlo procedure smoothes the results) or the impact on false alarm rate.

10.3.3

Clutter edges

Shadowing and edges lead to abrupt changes in the clutter power profile over range. Terrain obscuration leads to shadowing, while littoral or rural-urban interfaces are examples of edges. Both amplitude and spectral characteristics can vary across clutter edges or transition regions. For the moment we consider amplitude effects. The power variation describing a linear transition between distinct clutter regions A and B takes the form:

(10.40)

CNR sample mean CNR sample std.

case number

CNR sample maximum

case number

Figure 10.5

Mean, standard deviation, and maximum single channel, single pulse CNR for example in Figure 10.4 ([1O], © 2000 IEEE)

with AAB — (PC/B — Pc/A)/(?B — VA) representing the change in power over the transition region. The asymptotic clutter covariance matrix is: (10.41) rm is the rath discrete range sample and Q cx is a normalised clutter covariance matrix, where tr(Qcx) = 1. If an abrupt edge characterises the clutter environment, equation (10.41) takes the form:

(10.42)

Both formulations (10.41) and (10.42) assume uniform scaling of all clutter subspaces. In the latter instance, QrcA and QrcB characterise the clutter covariance matrices of clutter snapshots taken from either region A (r^) or region B (r#), respectively.

Consider the following cases: (i)

Scenario A: primary region tr(QrcA) = 65 dB,

a 2 = 0.0001 m 2 /s 2

secondary region tr(QrcB) = 53.5 dB,

a 2 = 0.01 m 2 /s 2 .

(ii) Scenario B: primary region tr(QrcA) = 76.5 dB,

o2v = 0m 2 /s 2

secondary region tr(QrcB) = 43.5 dB,

a2v = 0.25 m 2 /s 2 .

Scenario C: Same as Scenario A, but with primary and secondary region characteristics reversed, (iv) Scenario D: Same as Scenario B, but with primary and secondary region characteristics reversed.

SINR loss, dB

SINR loss, dB

(iii)

Scenario A Scenario C Scenario D

Scenario B

Figure 10.6 Asymptotic SINR loss for clutter edge scenarios ([W]t O 2000 IEEE)

Figure 10.6 shows the asymptotic loss due to the four edge scenarios listed above for the worst case Doppler, with the computation assuming that the test cell resides in the primary region. (Li = QA, L = Q). The abscissa indicates the per cent of training data taken from the primary region. Based on the characteristics listed above, we anticipate small losses for Scenarios A and C: the degree of mismatch between the two scenarios is relatively small. Undernulled clutter is the culprit leading to the larger losses seen for Scenario B. In summary, the modest degree of mismatch among the four scenarios, and the otherwise idealised nature of the clutter environment and platform configuration, tends to limit the severity of the observed losses.

10.4

Spectral heterogeneity

SINR loss, dB

Spectral heterogeneity results from the varying range-angle responses of different clutter classes to environmental conditions [7,8,10]. For instance, the intrinsic clutter spread of a windblown field differs from that of an urban region. Adaptive radar design for systems operating in littoral zones, over sea clutter, in the presence of weather effects, or under otherwise diverse conditions, should be particularly mindful of range-varying spectral properties. Since the adaptive processor tends to a response characterising the average behaviour of clutter in the training region, spectral

mean/std=1000 mean/std = 10 mean/std = 2 mean/std=l/2 mean/std= 1/5 RMB rule (-2.96 dB)

Doppler filter

Figure 10.7

SINR loss for varying degrees of spectral heterogeneity ([10], O 2000 IEEE)

heterogeneity leads to mismatch between adaptive and optimal filter notch widths. The inappropriately set adaptive notch width either increases clutter residue or partially cancels the target signal. In this section we examine the impact of spectral heterogeneity on STAP performance using both finite sample support Monte Carlo analysis and asymptotic evaluation. Taking an approach similar to that of Section 10.3.2, suppose the RJVIS clutter spread exhibits range-angle dependence given by the gamma distribution of equation (10.39) with av replacing y. We set E[av] = 0.1 m/s and alter the variance to cover cases of increasing spectral heterogeneity. The single channel, single pulse CNR is held constant at 25 dB (46 dB integrated CNR). Figure 10.7 shows the SINR loss based on 150 Monte Carlo trials. As in the case of range-angle varying clutter reflectivity considered in Section 10.3.2, we generated 257 space-time realisations per trial, using the latter 256 vectors to estimate the covariance matrix. As seen from the Figure, losses are small for the more homogeneous cases where the gamma distribution shape parameters abide by mean/STD >2. In accord with our expectations, the loss is negligible in the bin encompassing main beam clutter (Doppler filter 1), and the greatest losses occur in adjacent bins (Doppler filters 2 and 16). The roughly 3 dB loss in the Doppler filters adjacent to main beam clutter for the most heterogeneous case clearly indicates the deleterious nature of spectral heterogeneity on the radar MDV. In general, we expect the impact of spectral heterogeneity to further depend on CNR (by typical accounts, 46 dB CNR is modest). We examine this issue in a slightly different context in the next section.

eigenvalue number

Figure 10.8

Eigenspectrafor varying levels ofspectral spread ([1OJ, © 2 000 IEEE)

SINR loss, dB

Next Page

CNR1 = 58 dB

Doppler filter number

Figure 10.9 Asymptotic SINR loss for ([10], ©2000 IEEE)

varying levels of spectral spread

Next, suppose we train the adaptive filter in a region whose dominant spectral features differ from the test cell region (e.g. littoral zone or rural-urban interface). Figure 10.8 depicts the clutter-plus-noise eigenspectra for six distinct training regions. We assume the primary data exhibit an RMS clutter velocity spread of 0.8 m/s. Next, we suppose the training region encompasses one of the six regions identified in Figure 10.8. Figure 10.9 depicts the corresponding asymptotic loss over sixteen Doppler filters for the varying levels of spectral heterogeneity. The integrated CNR is set to 58 dB, a 12 dB increase over the preceding example. No loss occurs when training in the region with 0.8 m/s RMS spread, since this represents the matched condition. For values of RMS velocity spread of less than 0.8 m/s, the clutter notch width is inadequate, thereby leading to increased clutter residue and losses up to 3 dB in addition to those losses already associated with finite training. In contrast, the penalty for training in a region with greater spectral spread than the primary data is an apparently lesser degree of degradation. However, the result is dependent on the temporal resolution; we anticipate an increasingly severe, observable loss upon resolving the clutter spectrum via a longer dwell time. Additionally, degradation is CNR-dependent.

10.5

CNR-induced spectral mismatch

CNR-induced spectral mismatch refers to the range variation of clutter spectral width due to fluctuating CNR. ICM, clutter scintillation, dispersion, timing jitter,

SINR loss, dB

Previous Page

CNR1 = 58 dB

Doppler filter number

Figure 10.9 Asymptotic SINR loss for ([10], ©2000 IEEE)

varying levels of spectral spread

Next, suppose we train the adaptive filter in a region whose dominant spectral features differ from the test cell region (e.g. littoral zone or rural-urban interface). Figure 10.8 depicts the clutter-plus-noise eigenspectra for six distinct training regions. We assume the primary data exhibit an RMS clutter velocity spread of 0.8 m/s. Next, we suppose the training region encompasses one of the six regions identified in Figure 10.8. Figure 10.9 depicts the corresponding asymptotic loss over sixteen Doppler filters for the varying levels of spectral heterogeneity. The integrated CNR is set to 58 dB, a 12 dB increase over the preceding example. No loss occurs when training in the region with 0.8 m/s RMS spread, since this represents the matched condition. For values of RMS velocity spread of less than 0.8 m/s, the clutter notch width is inadequate, thereby leading to increased clutter residue and losses up to 3 dB in addition to those losses already associated with finite training. In contrast, the penalty for training in a region with greater spectral spread than the primary data is an apparently lesser degree of degradation. However, the result is dependent on the temporal resolution; we anticipate an increasingly severe, observable loss upon resolving the clutter spectrum via a longer dwell time. Additionally, degradation is CNR-dependent.

10.5

CNR-induced spectral mismatch

CNR-induced spectral mismatch refers to the range variation of clutter spectral width due to fluctuating CNR. ICM, clutter scintillation, dispersion, timing jitter,

clutter-only, yc = -20 dB clutter-plus-noise, yc = -20dB clutter-only, yc = -l0 dB clutter-plus-noise, yc = -10 dB

noise floor

ranked eigenvalue number

Figure 10.10

Illustration of eigenspectra variation for clutter spectral spread of 1.5 m/s and variable CNR

antenna motion and system instabilities, for instance, lead to subspace leakage [23]. Expressions (10.21) and (10.23) effectively model the temporal and spatial spectral spreading mechanisms; their effective application takes the form of a covariance matrix taper (CMT) [23,24]. As CNR increases, modulated components rise above the noise floor, thereby altering the width of the clutter spectrum. The adaptive processor must alter its response to mitigate these new coloured noise subspaces. Let us reconsider our 'typical' airborne radar example with the clutter spectral spread nominally set to 1.5 m/s and variable CNR controlled by the clutter reflectivity, yc. Figure 10.10 shows the corresponding clutter-only and clutter-plus-noise eigenspectra. The CNR-dependent nature of the dimension of the clutter subspace is evident in the Figure, viz. the apparent clutter rank increases with CNR. An increase in the rank suggests the presence of additional signal components - the modulated components resulting from signal decorrelation - and a consequent increase in clutter Doppler spectral spread. Guerci and Bergin describe this effect in detail in Reference 23. System effects, scintillation, multipath and other practical, non-ideal effects influence the nature of the spectral spread. Thus, all other effects held constant, if the CNR varies over range simply due to varying clutter RCS, a heterogeneous clutter condition arises distinct from simple amplitude mismatch. The corresponding spectral mismatch leads to either increased clutter residue or cancellation of potentially

SINR loss, dB

Doppler filter 1 Doppler filter 2 Doppler filter 3 Doppler filter 4 Doppler filter 5

asymptotic power, dB

Figure 10.11 Asymptotic SINR loss for CNR-induced spectral mismatch detectable target signals. As an example, Figure 10.11 depicts the asymptotic SINR loss for different Doppler filters as a function of CNR. The primary data has CNR set to 52 dB. Both training and primary data incorporate 0.45 m/s RMS spectral spread into the normalised covariance structure. The Figure suggests that training in a region with lower CNR markedly degrades MDV as a result of the joint amplitude and spectral mismatch; losses are substantial for only modest deviation in CNR. In contrast, training in a region with CNR greater than the primary data leads to a lesser degree of loss in this specific example. However, as the losses in Doppler filter 2 - the bin adjacent to main beam clutter - suggest, MDV is still significantly affected. Implementations employing overnulling strategies for adaptive training will suffer for this reason. An increase in the nominal RMS spectral spread (0.45 m/s is modest) will lead to an increase in the observable SINR degradation. To summarise, inappropriate filter notch width is the physical mechanism leading to performance degradation in the presence of CNR-induced spectral spread. Additionally, we note this scenario differs from that described in Section 10.3.2 as follows: in Section 10.3.2, the clutter RCS varied over angle and range in accordance with the gamma distribution in a manner representative of spiky clutter conditions; in contrast, the CNR-induced class of clutter heterogeneity indicates a persistent change in CNR over range that also leads to a consequent mismatch in spectral width, as described herein. Section 10.8 presents a measured data example corroborating CNR-dependent spectral spread and providing further clarification of this issue (see Figure R5 in the colour signature).

10.6

Targets in the secondary data

In this section we consider the impact of targets in the secondary data (TSD). From a practical perspective, the likelihood of target-like signals corrupting the secondary data set in a GMTI scenario is high. TSD affects STAP performance in several ways: from a filtering perspective, TSD leads to whitening of the desired signal component; TSD distorts the adapted pattern; TSD leads to inefficient use of the adaptive processor's DoFs; depending on the weight training strategy, TSD can also modulate the output power of the STAP, thereby biasing the constant false alarm rate (CFAR) threshold applied in subsequent processing; and, TSD impacts the variance of the target's angle of arrival (AoA) estimate. We now examine these points in further detail. To begin, we consider the following simple modification of equation (10.1):

(10.43)

where STSD is the space-time signal vector for a corruptive, target-like signal with power a\SD and Qk is the covariance matrix estimate of an assumed homogeneous clutter-plus-noise component. The corresponding weight vector is then:

(10.44)

Two main cases of interest arise: (a) perfect match to the target response, SJSD = v s _t; (b) mismatch between target and TSD responses, SJSD = vs_t + 5, where 8 represents the steering vector mismatch. In case (a) it is readily seen that W^/TSD is proportional to Qj^ vs_t, and so no penalty in SINR results from the TSD. Next, considering case (b), we express the weight vector in equation (10.44) as:

(10.45)

with p = Q^" ' s s _ t and z = Q^ ' S representing whitened target response and mismatched steering vectors, respectively, and where we otherwise assume v s _ t = s s _ t (i.e. no array manifold errors or mismatch to target angle-Doppler response). Several observations are in order: as expected, r\ - • 0 as a\SD -^ 0; the magnitude of T] depends on both TSD power, Oj finding both expressions to be numerically equivalent. The embedded power of the TSD measures the corruptive power included in the covariance estimate and is essentially the TSD-to-noise ratio (noise floor at 0 dB) after the averaging process leading to equation (10.43). Moving scatterers spread over the range extent, such as vehicles on a highway, contribute to TSD. Additionally, tractor-trailers and multiple vehicles in a resolution cell lead to a strong echo. As expected, we observe zero loss when the target and TSD have the same direction of arrival and Doppler. However, slight misalignment between target and TSD directions leads to substantial losses within the main beam due to signal whitening. The null near seven degrees corresponds with a null in the quiescent pattern. Figure 10.12 depicts the spatial filter responses in Doppler bin 2 for cases of moderate and strong main beam TSD; for comparison, we also show the optimal

normalised gain, dB

target and TSD separation: 1°

optimal strong TSD (22 dB) moderate TSD (15 dB)

direction of arrival, deg

Figure 10.12

Filter response distortion due to target-like signal corrupting covariance matrix estimate ([13], © 2001 IEEE)

filter response. The Figure clarities the issue of signal cancellation due to TSD: observe the decreased gain in the target direction of 0° due to the migrating adaptive null when comparing with the optimal case. As will be shown in Section 10.8.1, we observe this same effect in actual measured airborne radar data taken in regions with ample roadways in the radar field of view. Upon detecting a target, a bearing estimate is then necessary to initiate target tracking. A method seamlessly integrating with STAP processing is desirable. Relevant approaches based on maximum likelihood estimation are discussed in References 25 and 26. In developing the bearing estimator, first consider the alternative hypothesis space-time snapshot: (10.48) where y is a complex constant, g = [fs / b ] , and ntot is the interference-plusnoise (total noise) vector. The basic problem is to estimate g with g. If ntot ~ CN(O, Q k ), then: (10.49)

Given this likelihood function, we first require an estimate for the complex constant. Equation (10.49) is maximal when: n(K,g) = (*k - KSs-ICg))^Qk1CXk - yss-t(g))

(10.50)

is minimal. Differentiating equation (10.50) with respect to y and setting the result to zero yields: (10.51) Next, substituting equation (10.51) into (10.50) leads to: (10.52) Differentiating equation (10.52) with respect to g and setting the result to zero yields the MLE for g, given as g. Consequently, the estimator is: (10.53) In practice, we replace Qk in equation (10.53) with QkFigure 10.13 shows the DoA cost surface of equation (10.53) for a 2OdB SNR target with a true AoA of—2 degrees. The target signal competes with 60 dB integrated CNR and receiver noise for the typical eight-channel, side-looking airborne array. For comparison, we also include the MLE in the presence of TSD by incorporating a target-like component with crjSD = 20 dB and a true AoA of 3 degrees. By searching for the peak of each of the two cost surfaces, we find unbiased estimates of the target AoA. However, flattening of the MLE cost surface in the presence of TSD translates into a substantial increase in the estimate's variance. Constant false alarm rate (CFAR) performance is highly desirable in radar detectors; the false alarm rate is a critical design factor influenced by computational and algorithmic processing capabilities. In some cases, the normalisation applied to the STAP weight vector influences CFAR performance. For example, Robey et al. describe the adaptive matched filter (AMF) as a CFAR detection statistic [27]. The AMF takes the form: (10.54) where §i is the threshold and vs_t = ss_t (no steering vector mismatch). The AMF follows from the STAP weight vector when \x = \/Jv^_tQ^ v s _t, and normalises the output noise power to unity; this characteristic is highly desirable, since in theory it enables a single threshold setting for all angle, Doppler and range to achieve specified false alarm behaviour. The output noise for range cell k under the AMF setting,

no TSD TSD

true target AoA: -2° TSD AoA: 3°

direction of arrival, deg

Figure 10.13

Target angle of arrival estimate in the presence of TSD

WAMF/k, is:

(10.55)

Equation (10.55) suggests an output noise level roughly set to unity, and for this reason the AMF is sometimes referred to as the unit-power constraint. Suppose we now incorporate the TSD model of equation (10.43) into equation (10.54). Using the matrix inversion lemma, assuming vs_t = ss_t, and coaligned TSD and target signal (8 = 0), we find: (10.56) Thus, while TSD does not degrade SINR in this instance, as previously shown, it does effectively bias the threshold upwards by 1+ ^j5Z>ss^tQk Ss ~t' thereby leading to target masking. This same effect is seen in traditional scalar CFAR algorithms. Since mismatch and clutter residue are always concerns, it is common to follow the AMF with a traditional scalar CFAR with adaptive threshold; depending on the STAP training strategy (e.g. sliding window), the AMF normalisation in the presence

of TSD suppresses the target response prior to the scalar CFAR, thereby effectively biasing the target response below the adaptive threshold. Interestingly, some non-CFAR-type normalisations do not suffer from the preceding effect. The unit norm constraint on the weight vector, w^Wk = 1 ? leads to v s-tQk vs-t> a n d the well known minimum variance distortionless response (MVDR) constraint, w^s s _ t = 1, leads to: AMVDR = l / ( v ^ t Q k l y s-t)- In the case where TSD and desired target steering vectors are coaligned, one can confirm the impervious nature of the decision statistic to corruptive TSD by employing equation (10.43) with STSD = v s _t. These latter normalisations are less desirable in theory than the AMF since the detection processor requires a different threshold setting for each angle-Doppler resolution cell, at least in a range homogeneous environment. More to the point, in a heterogeneous environment, these latter normalisations tend to modulate the output noise in the range dimension. Now we consider the impact of TSD on STAP performance when using finite sample support. To wit, we employ a Poisson distribution to seed targets in various range-angle sectors of the radar field of regard. Otherwise, we assume a homogeneous clutter environment so that we may specifically isolate the effects of TSD. Melvin and Guerci presented related analysis in Reference 13. A more complete treatment using site-specific clutter and road layout is given by Bergin et al. in Reference 28. Suppose dense traffic regions occur in specific range-azimuth sectors, with certain densities Acars and Atrucks defining the expected number of vehicles per square kilometer. A Poisson distribution is a natural selection for seeding targets within the space-time data cube. Figure 10.14 shows a single trial seeding for the parameters of Table 10.2. We generate a space-time signal for each vehicle location shown in the Figure; additionally, we assume each vehicle response follows a Swerling I target model, with a mean radar cross section of 10 dBsm for cars/light trucks and 22 dBsm for tractor trailer trucks. Next, we generate 279 radar clutter-plus-noise data realisations from a starting range of 32 km towards the end of the unambiguous range interval at 75 km. We use the same typical airborne radar parameters as in the preceding asymptotic analysis, with a waveform bandwidth set to 1 MHz (150m resolution). Using all 279 data vectors in equation (10.1) yields E[LS^] ~ —3dB in an otherwise homogeneous clutter environment. Beginning with the homogeneous clutter-plus-noise data cube of dimension TV = 8 by M = 16 by Q = 279, we then independently seed the Poisson-distributed TSD for varying trials using the parameters in Table 10.2. The TSD is uniformly distributed over the specified range-angle sector. We set the TSD Doppler response to correspond with ground moving targets - cars and truck on roadways in the radar field of view - nominally spread over velocities in the range of ±30 m/s. The Doppler is fixed by region (see Table 10.2), as one might expect for a roadway with a specific orientation, but uniformly spread over the corresponding Doppler filter width. Figure 10.15 compares SINR loss for the HD and homogeneous clutter-plus-TSD cases shown over a ±30 m/s target velocity interval. In this Figure we show the complete loss, LSt\ • L8^, characterising finite sample support, TSD, radar system

slant range, km

cars trucks

azimuth, deg

Figure 10.14

Target seeding scenario, one trial ([13], © 2001 IEEE) Table 10.2 Poisson target seeding scenario Region

1

2

3

4

A-carsCkm"2) ^trucks (km"2) Start range (km) Stop range (km) Azimuth (degrees)

0.5 0.1 32 39 - 5 to - 3

1 0.09 48 56 6 to 7

0.2 0.1 64 66 6 to 10

0.01 0.02 43 60 12 to 15

and homogeneous clutter effects. The upper bound on performance is also shown in Figure 10.15 and labelled as 'known covariance'. We obtained the TSD curve by averaging 200 different Poisson trials. As expected from our earlier discussion, TSD in a finite sample support scenario leads to significant performance loss when using the proposed Poisson model. Figure P.2 (see colour signature) shows SINR loss over ±50 m/s for each individual Poisson trial. The impact of TSD on the adaptive radar's MDV is evident in this plot, which we may further contrast against SES[R loss in the homogeneous (no TSD) case in Figure P.3 (see colour signature). TSD degrades the MDV in this instance by roughly a factor of three.

SINR loss, dB

known covariance estimated: with TSD (200 trials) estimated: HD secondary data

velocity, m/s

Figure 10.15

SINR loss comparison using finite training data and 200 Poisson trials to seed TSD ([13], © 2001 IEEE)

In Section 10.8.1 we show measured multichannel airborne radar measurements (MCARM) data illustrating that TSD is a practical concern when implementing STAP and corroborating the effects discussed in this section of the chapter using synthetic data. Section 10.9.4 suggests some strategies to mitigate TSD effects.

10.7

Joint angle-Doppler mismatch and clutter heterogeneity

STAP maximises SINR by filtering ground clutter in the angle-Doppler domain. Radar geometry determines the filter null location in this higher-dimensional space. When the null location varies over range, the adaptive filter produces an incorrect frequency response. Indeed, the filter tends to an average response with the potential for very poor instantaneous performance. We briefly highlight angle-Doppler properties for the monostatic radar case; relevant discussion applicable to bistatic geometry is given in References 3, 5 and 6. Consider a right-handed coordinate system with the x-axis pointing north, the y-axis pointing west and the z-axis pointing upwards. A unit vector pointing from the platform to a stationary point on the ground is: k(0,0) = cos 0 sin 0x + cos 0 cos 0y + sin Oi

(10.57)

where 0 is azimuth measured positive in the clockwise direction from the y-axis and 0 is elevation measured negative in the downward direction from the horizon. The direction vector to the mth subarray is: (10.58) while the platform velocity vector is: (10.59) The spatial phase at the mth channel is: (10.60) A denotes wavelength. Also, the normalised Doppler frequency of a stationary point is: (10.61) where T is the pulse repetition interval. If the channel spacing is d and we consider a side-looking array configuration (i.e. (Is9Hi = (m — l)d\) we can define the spatial frequency as: (10.62) where 0cone represents cone angle [3]. Normalised Doppler in the side-looking case can be written: (10.63) In other words, the angle-Doppler properties of a continuum of stationary points (ground clutter) fall on a line with the slope determined by platform velocity, pulse repetition interval and sensor spacing, and there is no dependence of the angle-Doppler contours with range (elevation angle). Hence, platform geometry does not induce non-stationary behaviour. The forward-looking geometry is a contrasting case. With the platform in level flight in the x-direction: (10.64) The angle-Doppler contours are ellipses that vary over range. As a rule-of-thumb, when the slant range divided by the platform height is less than five, range dependence is significant [3]; otherwise, the beam traces tend to align with the isodops at farther range, and so the angle-Doppler contour locations tend to stabilise. This example shows that geometry induces non-stationary angle-Doppler behaviour.

Range-varying angle-Doppler loci further exacerbates culturally induced heterogeneous clutter effects. For example, residue from clutter discretes further increases in the presence of adaptive filter null migration associated with the non-stationary clutter mechanism described in this section.

10.8

Site-specific examples of clutter heterogeneity

10.8.1 Measured multichannel airborne radar data This section briefly examines measured data taken from the multichannel airborne radar measurements (MCARM) programme [29]. Figure 10.16 shows the MCARM platform with a port-mounted, multichannel radar system housed within the radome. Table 10.3 provides some characteristics of the MCARM system. We consider data taken from Flight 5, Acquisition 575. Our objectives in considering this data are two fold: (a) we wish to corroborate the model of equation (10.18); (b) we identify a few instances of heterogeneous clutter behaviour described in the preceding sections.

Figure 10.16 Table 10.3

• • • • • • • • • •

MCARM radar system Some MCARM

characteristics

L-band transmit frequency 15 kW peak transmit power variable PRF (0.5 kHz, 2 kHz, 7 kHz) LFM or gated-RF 0.8 microsecond range resolution 0.8 MHz receiver bandwidth 7.5 degree Tx beam or blob (3 x) pattern for broad coverage 1.25 MHz IF centre frequency 5 MHz IF sampling rate (4 x oversample for digital I/Q) test manifold for channel balancing

• • •

• • • •

range-measured steering vectors 32 transmit subarrays (16 over 16 planar configuration) 24 receivers (sum, delta, and 11 over 11 additional channels oriented in a planar configuration) 128 radiating elements total (32 subarrays x 4 elements per subarray) 1 acquisition = 1 CPI nominally 128 pulses per CPI at the 2 kHz PRF collection region: DelMarVa Peninsula, USA

estimated SINR loss, dB

simulated

Doppler, Hz

Figure 10.17

Estimated SINR lossfor MCARM 575 data, different training intervals

As a means of corroborating the model of equation (10.18), Figure P.4 (see colour signature) compares the minimum variance distortionless response (MVDR) spectra for the actual data against simulation. The plots generally exhibit close correspondence. Clutter ridge slope and shape show good match; the additional azimuthal power spread in the actual data is a likely result of near-field scattering, an effect not included in the simulation model. Figure P.4 (see colour signature) confirms the suitability of equation (10.18) as a basic space-time model for ground clutter. Using test manifold data, we estimate the MCARM receiver noise floor. Next, we select training data in block regions from near range to far and estimate the clutter-plusnoise covariance matrix. Figure 10.17 shows estimated SINR loss for training data taken over different regions, identified in the legend, as well as the simulated curve using the model of equation (10.18). Good correspondence exists between actual and simulated clutter null locations. However, the impact of amplitude heterogeneity and TSD affects the shape of the measured data SINR loss curves. For example, scalloping in the loss curves is most likely due to TSD. To verify this conjecture, Figure 10.18 shows estimated SINR loss when training over a contiguous block, and after removing roadways intersecting the main beam (MB) and first sidelobe (SL) regions; we also apply some diagonal loading (denoted as DL) to stabilise the noise floor after removing training samples. We use map data (see Figure 10.20) and ownship navigation data to identify roadways in the radar field of view. As can be seen, the scalloping disappears after excising certain training data potentially containing target-like signals,

estimated SINR loss, dB

excise Hwy 15 MB excise Hwy 15 SL excise Hwy 15 SL, 0 dB DL simulated

Doppler, Hz

Figure 10.18

Estimated SINR loss after removing training data overlaying roadways

thereby yielding much closer correspondence between actual and simulated curves. Figure 10.19 shows the adaptive filter patterns within a single Doppler bin for the same training intervals (labelled by range bin number) as shown in Figure 10.17. The quiescent beam points to 1 degree off boresight. Migration of the null due to TSD is apparent in the upper two plots where the corresponding training data comes from regions with dense roadway networks. Varying clutter reflectivity affects the depth of the clutter null shown in Figure 10.17. Figure P.5 (see colour signature) shows range-Doppler and power versus range information for the subject acquisition. The power versus range curve clearly shows three distinct regions corresponding, from near to far range, to the predominantly farmland terrain of the DelMarVa Peninsula, USA, Delaware River and terrain in New Jersey, USA, opposite the Delaware River. A map of the collection region, along with the locations of several adjacent acquisitions, is shown in Figure 10.20; the aircraft flew a southerly route, with the array normal pointing almost due east. The three distinct terrain regions, along with many roadways in the radar field of view, are evident from viewing the map. Additionally, the CNR-dependent nature of the main beam clutter spread is seen in the range-Doppler map. From this single measured data acquisition we find examples of TSD, rangevarying clutter edges (three distinct regions) and CNR-dependent spectral spread, thereby corroborating several heterogeneous clutter models described in prior sections. Additionally, from Figure P.4 (see colour signature), we find that equation (10.18) adequately characterises the basic features of ground clutter.

Figure 10.19

10.8.2

azimuth angle, deg

azimuth angle, deg

azimuth angle, deg

azimuth angle, deg

Comparison of adaptive patterns for MCARM 575 data, different training regions ([13], © 2001 IEEE)

Site-specific

simulation

Realistic clutter environments, as the measured data from the prior section suggests, are site-specific. A variety of databases describing terrain cultural features are available to researchers investigating STAP performance in site-specific, heterogeneous clutter environments [28,30-34]. In addition, the signal processor can use these databases to enhance STAP implementation (e.g. by improving training data selection, predicting clutter edges, or prefiltering the data) [28,30,32]. For example, the United States Geological Survey (USGS) database includes land use and land cover (LULC) data and National Land Characterisation Data (NLCD) classifying predominant clutter types by geographic coordinate; digital line graph (DLG) data characterising discrete features, such as railway tracks, power transmission lines, etc.; digital elevation model (DEM) data providing terrain height information [30,32,33]. The US Census Bureau provides a variety of mapping products, including the Topologically Integrated Geographic Encoding and Referencing (TIGER/Line) road overlay data [28,30,34]. Combining cultural databases, such as those described in the preceding paragraph, with the clutter model of equation (10.18) enables site-specific clutter simulation. Different reflectivities are assigned to different clutter classes based on a query of the database [28,30]. Incorporating ground moving vehicles involves placing road

Figure 10.20

Mapping data of acquisition region showing roadways and Delaware River [34]

power, dB

MCARM acquisition 575 site-specific model

slant range, km

Figure 10.21 Measured and site-specific synthetic power versus range curves for MCARM 575 scenario ([30], © 2003 IEEE)

segments - given, for instance, by the TIGER/Line database - onto the earth's surface [28,30] and seeding targets using a particular probability distribution, such as the Poisson distribution employed in Section 10.6 or Reference 13. Database information can potentially provide very accurate prediction of ground clutter characteristics. Figure P.6 (see colour signature) shows a site-specific clutter RCS map of the data collection region for the MCARM Flight 5 data analysed in the prior section. The shape of the reflectivity map corresponds with our expectations based on the US Census Bureau map in Figure 10.20. Using the RCS map of Figure P.6 in the model of equation (10.18) leads to a remarkable match between the actual and site-specific, synthetic MCARM power versus range curves, as shown in Figure 10.21. Finally, Figures P.7 and P.8 (see colour signature) contrast the site-specific and homogeneous (bald earth) synthetic range-Doppler maps for the MCARM scenario. (Note: the ordinate has units of velocity, obtained simply by scaling Doppler frequency by half the wavelength.) Figure P.7 compares favourably against the measured MCARM range-Doppler map shown in Section 10.8.1.

10.9

STAP techniques in heterogeneous environments

In this section we highlight some STAP techniques applicable in heterogeneous clutter environments. This listing of methods is by no means exhaustive. A thorough examination and comparison of the various methods is beyond the scope of this chapter. We provide corresponding references for readers interested in delving further.

10.9.1 Data-dependent training techniques Data-dependent training techniques are valuable in heterogeneous clutter environments. The non-homogeneity detector (NHD) [35,36], power-selected training (PST) [37-39] and map-based training selection [28,30] are three examples of data-dependent training schemes. The non-homogeneity detector (NHD) assumes that gross changes in the underlying data structure lead to degraded performance [35,36]; the processor enhances adaptive capability by detecting and excising secondary data realisations significantly deviating from the surrounding realisations. The processor's goal is to select the most homogeneous set of secondary data based on a measure of covariance structure. The generalised inner product (GIP) is one viable metric and is given by: (10.65) Next, observe that the GIP can be written: (10.66) where Xk represents the whitened data vector, Ek is the matrix of eigenvectors resulting in the unitary similarity transform and Lk is a diagonal matrix containing the eigenvalues ofQk. Further notice that E[XkX1^] = Q^ QkQk , thereby implying

that when Qk = Qk(10.67) where am are the Karhunen-Loeve coefficients and e m are the eigenvectors of Qk. In this sense, the GIP measures the similarity in covariance structure between Qk and QkNotice that an ideal measure of difference in covariance structure is dk =

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