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Springer Series in Information Sciences

25

Editor: Thomas S. Huang

 

Springer Series in Information Sciences

Editors: Thomas S. Huang Teuvo Kohonen Manfred R. Schroeder Managing Editor: H. K. V. Lotsch

1Content-Addressable Memories By T. Kohonen 2nd Edition

2Fast Fonrier 'fransform and Convolution Algorithms

By H. J. Nussbaumer 2nd Edition

3Pitch Determination of Speech Signals Algorithms and Devices By W. Hess

4Pattern Analysis and Understanding By H. Niemann 2nd Edition

5Image Sequence Analysis Editor: T. S. Huang

6Picture Engineering

Editors: King-sun Fu and T. L. Kunii

7Number Theory in Science

and Communication With Applications in Cryptography, Physics, Digital Information, Computing, and SelfSimilarity By M. R. Schroeder

2nd Edition

8Self-Organization

and Associative Memory By T. Kohonen 3rd Edition

9Digital Picture Processing

An Introduction By L. P. Yaroslavsky

10Probability, Statistical Optics, and Data Testing

A Problem Solving Approach By B. R. Frieden 2nd Edition

11 Physical and Biological Processing

of Images Editors: O. J. Braddick

and A. C. Sleigh

12Multiresolution Image Processing and Analysis Editor: A. Rosenfeld

13VLSI for Pattern Recognition and Image Processing Editor: King-sun Fu

14Mathematics of Kalman-Bucy Filtering By P. A. Ruymgaart and T. T. Soong 2nd Edition

15Fundamentals

of Electronic Imaging Systems

Some Aspects of Image Processing

By W. F. Schreiber 3rd Edition

16Radon and Projection 'fransformBased Computer Vision

Algorithms, A Pipeline Architecture, and

Industrial Applications By J. L. C. Sanz, E. B. Hinkle, and A. K. Jain

17 Kalman Filtering

with Real-TIme Applications

By C. K. Chui and G. Chen 2nd Edition

18Linear Systems and Optimal Control By C. K. Chui and G. Chen

19Harmony: A Psychoacoustical Approach By R. Parncutt

20Group-Theoretical Methods in Image Understanding By Ken-ichi Kanatani

21Linear Prediction Theory A Mathematical Basis for Adaptive Systems By P. Strobach

22Psychoacoustics Facts and Models By E. Zwicker and H. Fast!

23Digital Image Restoration Editor: A. K. Katsaggelos

24Parallel Algorithms

in Computational Science

By D. W. Heermann and A. N. Burkitt

25Radar Array Processing Editors: S. Haykin, J. Litva, and T. J. Shepherd

26Signal Processing and Systems Theory Selected Topics

By C. K. Chui and G. Chen

273D Dynamic Scene Analysis A Stereo Based Approach By Z. Zhang and O. Faugeras

28Theory of Reconstruction from Image Motion

By S. Maybank

29Motion and Structure from Image Sequences By J. Weng, T.S. Huang, andN. Ahuja

S. Haykin J. Litva T. J. Shepherd (Eds.)

Radar Array Processing

With Contributions by

 

s. Haykin

T. V. Ho J. Litva

J. G. McWhirter

A. Nehorai

U. Nickel B.Ottersten

T. J. Shepherd B. D. Steinberg

P. Stoica

M. Viberg

Z. Zhu

 

With 84 Figures

Springer-Verlag

Berlin Heidelberg New York

London Paris Tokyo

Hong Kong Barcelona

Budapest

Professor Simon Haykin

Dr. John Litva

Communications Research Laboratory, McMaster University, U80 Main Street West,

Hamilton, Ontario, Canada, LSS 4Kl

Dr. Terence J. Shepherd

Royal Signals and Radar Establishment, St. Andrew's Road,

Malvern, Worcs. WR14 3PS, UK

Series Editors:

Professor Thomas S. Huang

Department of Electrical Engineering and Coordinated Science Laboratory, University of Illinois, Urbana, IL 61801, USA

Professor Teuvo Kohonen

Laboratory of Computer and Information Sciences, Helsinki University of Technology, SF-02150 Espoo 15, Finland

Professor Dr. Manfred R. Schroeder

Drittes Physikalisches Institut, Universitat Gottingen, Biirgerstrasse 42-44, W-3400 Gottingen, Fed. Rep. of Germany

Managing Editor: Dr.-Ing. Helmut K. V. Lotsch

Springer-Verlag, TIergartenstrasse 17,

W-6900 Heidelberg, Fed. Rep. of Germany

ISBN-13:978-3-642-77349-5 e-ISBN-978-3-642-77347-1

DOl: 10.1007/978-3-642-77347-1

Library of Congress Cataloging-in-Publication Data. Radar array processing 1S. Haykin, J. Litva, T.J. Shepherd (eds.); with contributions by S. Haykin ... let al.]. p. cm. - (Springer series in information sciences; 25) Includes bibliographical references and index. ISBN 3-540-55224-3 (alk. paper). - ISBN 0-387-55224-3 (alk. paper: U.S.) 1. Radar-Antennas. 2. Signal processing-Digital techniques. I. Haykin, Simon S., 1931-. II. Litva, J. (John), 1937-. III. Shepherd, T.J. (Terence J.), 1952-. IV. Series. TK6590.A6R33 1993 621.3848'3-<lc20 92-10763

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law.

© Springer-Verlag Berlin Heidelberg 1993 .

Softcover reprint ofthe hardcover 1st edition 1993

The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

54/3140-5 4 3 2 1 0 - Printed on acid-free paper

Preface

The objective of this book is to present various modem techniques and methods for processing radar signals received by an array of antenna elements. Recent years have seen a rapid growth in the technology of hardware for manipulating data in numerical or digital form, and the application of such enabling techno.: logy to radar signals has provided some of the principal motivation for its development. Seen in the context of digital signal processing, the output of radar signals from an antenna array receiver may be regarded as a matrix of numbers, with each column ofthe matrix deriving from an individual antenna element; the processing of the signals may then be regarded as the extraction of information from the matrix. With the data in this form, it becomes possible to enlist the full power of modem sophisticated computational algorithms, many of which are contained in this volume.

The techniques described in the following chapters are almost universally relevant to all applications for which arrays of detectors are employed; thus, besides being ofinterest to researchers and students in the radar community, the book should also appeal to those in related fields such as sonar, seIsmology, acoustics, radio astronomy, and possibly even some areas of optical

astronomy.

 

Ontario, Canada

Simon Haykin

Great Malvern, UK

John Litva

November 1992

Terry Shepherd

Contents

1. Overview By S. Haykin, J. Litva, and T.J. Shepherd. . . . . . . . . . . . .

1

Part I Detection and Estimation

 

2. Radar Detection Using Array Processing

 

By Z. Zhu and S. Haykin (With 2 Figures). . . . . . . . . . . . . . . . . . . .

3

2.1

Observation Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

2.2

Coherent Radar Detection. . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

 

2.2.1

Signal and Noise Model. . . . . . . . . . . . . . . . . . . . . . . . .

6

 

2.2.2

Detection of Targets with Known Directions . . . . . . . . .

7

 

2.2.3

Detection of Targets with Unknown Directions. . . . . . .

13

2.3

Noncoherent Radar Detection. . . . . . . . . . . . . . . . . . . . . . . . .

16

 

2.3.1

Signal and Noise Model. . . . . . . . . . . . . . . . . . . . . . . . .

16

 

2.3.2

Detection of Targets with Known Directions . . . . . . . . .

17

 

2.3.3

Detection of Targets with Unknown Directions:

 

 

 

Deterministic Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

 

2.3.4

Detection of Targets with Unknown Directions:

 

 

 

Gaussian Signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

2.4

Passive Radar Detection .. . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

 

2.4.1

Signal and Noise Model. . . . . . . . . . . . . . . . . . . . . . . . .

33

 

2.4.2

Detection of Emitters with Known Directions . . . . . . . .

33

 

2.4.3

Detection of Emitters with Unknown Directions:

 

 

 

Deterministic Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

 

2.4.4

Detection of Emitters with Unknown Directions:

 

 

 

Gaussian Signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40

2.5

Discussion........................................

43

References.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

Additional References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

3. Radar Target Parameter Estimation with Array Antennas

 

By U. Nickel (With 18 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

3.1

Radar Parameter Estimation Problem. . . . . . . . . . . . . . . . . . .

47

 

3.1.1

Range and Angle Estimation. . . . . . . . . . . . . . . . . . . . . .

48

 

3.1.2

Frequency and Power Estimation. . . . . . . . . . . . . . . . . .

51

3.2

Angle Estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

VIII

Contents

 

 

3.2.1

Monopulse Estimation (Single Target Estimation) . . . . .

52

 

3.2.2 Covariance Matrix Estimation . . . . . . . . . . . . . . . . . . . .

56

 

3.2.3

Linear Prediction Methods. . . . . . . . . . . . . . . . . . . . . . .

58

 

3.2.4 Capon-Pisarenko-Type Methods . . . . . . . . . . . . . . . . . .

62

 

3.2.5

Signal Subspace Methods. . . . . . . . . . . . . . . . . . . . . . . .

64

 

3.2.6 Parametric Target Model Fitting . . . . . . . . . . . . . . . . . .

73

 

3.2.7 Aspects ofImplementation . . . . . . . . . . . . . . . . . . . . . . .

83

3.3

Frequency Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

 

3.3.1

Doppler Filter Bank. . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

 

3.3.2

Superresolution Methods. . . . . . . . . . . . . . . . . . . . . . . . .

87

3.4

Range, Amplitude and Power Estimation . . . . . . . . . . . . . . . .

90

 

3.4.1

Conventional Range Estimation. . . . . . . . . . . . . . . . . . .

90

 

3.4.2 Superresolution in Range. . . . . . . . . . . . . . . . . . . . . . . .

91

 

3.4.3 Amplitude and Power Estimation. . . . . . . . . . . . . . . . . .

93

3.5

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

94

References.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95

4.Exact and Large Sample Maximum Likelihood Techniques for Parameter Estimation and Detection in Array Processing

By B. Ottersten, M. Viberg, P. Stoica, and A. Nehorai (With 7 Figures)

99

4.1

Background.......................................

100

4.2

Chapter Outline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

101

4.3

Sensor Array Processing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

102

 

4.3.1

Narrowband Data Model. . . . . . . . . . . . . . . . . . . . . . . .

103

 

4.3.2

Parametric Data Model. . . . . . . . . . . . . . . . . . . . . . . . . .

104

 

4.3.3 Assumptions and Problem Formulation. . . . . . . . . . . . .

106

 

4.3.4

Parameter Identifiability. . . . . . . . . . . . . . . . . . . . . . . . .

107

4.4

Exact Maximum Likelihood Estimation. . . . . . . . . . . . . . . . .

108

 

4.4.1

Stochastic Maximum Likelihood Method. . . . . . . . . . . .

109

 

4.4.2 Deterministic Maximum Likelihood Method . . . . . . . . .

111

 

4.4.3

Bounds of Estimation Accuracy . . . . . . . . . . . . . . . . . . .

112

 

4.4.4 Asymptotic Properties of Maximum Likelihood Estimates

115

 

4.4.5

Order Relations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

117

4.5 Large Sample Maximum Likelihood Approximations. . . . . . .

118

 

4.5.1

Subspace Based Approach. . . . . . . . . . . . . . . . . . . . . . . .

118

 

4.5.2

Relation Between Subspace Formulations. . . . . . . . . . . .

121

 

4.5.3

Relation to Maximum Likelihood Estimation. . . . . . . . .

123

4.6

Calculating the Estimates. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

125

 

4.6.1

Newton-Type Search Algorithms. . . . . . . . . . . . . . . . . . .

126

 

4.6.2

Gradients and Approximate Hessians. . . . . . . . . . . . . . .

127

 

4.6.3

Uniform Linear Arrays. . . . . . . . . . . . . . . . . . . . . . . . . .

129

 

4.6.4

Practical Aspects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

130

4.7

Detection of Coherent/Noncoherent Signals. . . . . . . . . . . . . .

133

 

4.7.1

Generalized Likelihood Ratio Test Based Detection. . . .

133

 

4.7.2

Subspace Based Detection. . . . . . . . . . . . . . . . . . . . . . . .

135

 

 

 

Contents

IX

4.8

Numerical Examples and Simulations .. : . . . . . . . . . . . . . . . .

137

4.9

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

143

Appendix

4.A

Differentiation of the Projection Matrix. . . . . . . . . .

144

Appendix 4.B

Asymptotic Distribution of the Weighted

 

 

 

 

Subspace Fitting Criterion. . . . . . . . . . . . . . . . . . . .

144

References.

. . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

147

Part II

Systolic Arrays

 

5. Systolic Adaptive Beamforming

 

By T.J. Shepherd and J.G. McWhirter (With 27 Figures).. . . . .. ..

153

5.1

Adaptive Antenna Arrays. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

153

5.2 Systolic and Wavefront Arrays. . . . . . . . . . . . . . . . . . . . . . . . .

155

5.3

Canonical Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

157

 

5.3.1

Canonical Configuration. . . . . . . . . . . . . . . . . . . . . . . . .

158

 

5.3.2 Least-Squares Formulation. . . . . . . . . . . . . . . . . . . . . . .

160

5.4 QR Decomposition by Givens Rotations. . . . . . . . . . . . . . . . .

163

 

5.4.1

QR Decomposition. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

163

 

5.4.2

Givens Rotations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

164

 

5.4.3

Systolic Array Implementation. . . . . . . . . . . . . . . . . . . .

166

 

5.4.4 Square-Root-Free Algorithm. . . . . . . . . . . . . . . . . . . . . .

169

 

5.4.5

Sensitivity to Arithmetic Precision . . . . . . . . . . . . . . . . .

173

5.5

Direct Residual Extraction. . . . . . . . . . . . . . . . . . . . . . . . . . . .

175

 

5.5.1

Definition of Residuals. . . . . . . . . . . . . . . . . . . . . . . . . .

175

 

5.5.2

Properties of Rotation Matrix Q(n). . . . . . . . . . . . . . . . .

175

 

5.5.3

A Posteriori Residual Extraction. . . . . . . . . . . . . . . . . . .

178

 

5.5.4

A Priori Residual Extraction. . . . . . . . . . . . . . . . . . . . . .

179

5.6

Weight Freezing and Flushing. . . . . . . . . . . . . . . . . . . . . . . . .

180

 

5.6.1

Basic Concept. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

180

 

5.6.2

Frozen Networks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

181

 

5.6.3

Serial Weight Flushing. . . . . . . . . . . . . . . . . . . . . . . . . .

185

 

5.6.4

Further Insights. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

187

5.7

Linear Constraint Pre-Processor. . . . . . . . . . . . . . . . . . . . . . .

189

 

5.7.1

Single Constraint Pre-Processor. . . . . . . . . . . . . . . . . . .

190

 

5.7.2

Multiple Constraint Pre-Processor. . . . . . . . . . . . . . . . .

193

 

5.7.3

Generalized Sidelobe Canceller. . . . . . . . . . . . . . . . . . . .

196

5.8 Minimum Variance Distortionless Response Beamforming . . .

200

 

5.8.1

Schreiber's Algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . .

201

 

5.8.2

Systolic Array Implementation . . . . . . . . . . . . . . . . . . . .

204

 

5.8.3

Square-Root-Free Minimum Variance Distortionless

 

 

 

Response Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . .

207

5.9

Adaptive Antenna Processor Test-Bed. . . . . . . . . . . . . . . . . . .

210

 

5.9.1

Wavefront Array Processor. . . . . . . . . . . . . . . . . . . . . . .

211

X

Contents

 

 

5.10 Further Developments. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . .

215

 

 

5.10.1 Parallel Weight Extraction. . . . . . . . . . . . . . .

. . . . . . .

215

 

 

5.10.2 QR-with-Feedback. . . . . . . . . . . . . . . . . . . . . .

. . . . . . .

218

 

 

5.10.3 Structures for Broad-Band Adaptive Beamforming. . . .

220

 

 

5.10.4 QR Decomposition and Neural Networks. . .

. . . . . . .

222

5.11

Comments and Conclusions. . . . . . . . . . . . . . . . . . . .

. . . . . . .

225

 

 

5.11.1 Additional Topics. . . . . . . . . . . . . . . . . . . . . .

. . . . . . .

226

Appendix 5.A Modified Gram-Schmidt Algorithm. . . . . .

. . . . . . .

229

Appendix 5.B Constraints with Leading Zeros . . . . . . . . .

. . . . . . .

232

Appendix 5.C Weighted Least-Squares and Hyperbolic Rotations.

235

Appendix 5.D Principal Symbols Used in this Chapter. . .

. . . . . . .

241

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . .

243

6. Two-Dimensional Adaptive Beamforming: Algorithms and Their

 

Implementation By T. V. Ho and J. Litva (With 19 Figures).

. . . . . .

249

6.1

Arrangement of the Chapter ....................

: . . . . . .

251

6.2 Adaptive Beamforming Techniques. . . . . . . . . . . . . . .

. . . . . . .

252

 

6.2.1

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

. . . . . . .

252

 

6.2.2

Classical Adaptive Beamforming. . . . . . . . . . . . .

. . . . . . .

255

 

6.2.3

Modern Adaptive Beamforming . . . . . . . . . . . . .

. . . . . . .

261

6.3

2D Adaptive Beamforming Algorithm and Implementation. . . .

264

 

6.3.1

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

. . . . . . .

264

 

6.3.2

Classical Approaches. . . . . . . . . . . . . . . . . . . . . . .

. . . . . .

266

 

6.3.3

2D QRD-LS Algorithm and Systolic Array

 

 

 

 

 

Implementation. . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . .

276

6.4

 

Simulation Results. . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . .

283

6.5

 

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

. . . . . . .

289

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . .

292

Part III

Imaging

 

 

7. The Radio Camera By B.D. Steinberg (With 11 Figures) . .

. . . . . . .

295

7.1

Problems..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . .

295

7.2 Adaptive Beamforming: Dominant Scatterer Algorithm.

. . . . . .

296

7.3

Experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . .

299

7.4 Adaptive Beamforming: Spatial Correlation Algorithm.

. . . . . .

303

7.5

Experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . .

305

7.6 Number of Elements. . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . .

307

7.7

Number of Bits per Sample. . . . . . . . . . . . . . . . . . . . . .

. . . . . .

308

7.8 Data Truncation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . .

308

7.9

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

. . . . . .

309

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . .

309

Subject Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . .

311

Contributors

Haykin, Simon

Communications Research Laboratory, McMaster University 1280 Main Street West, Hamilton, Ontario, L8S 4K1, Canada

Ho, Terence V.

Com Dev Ltd., 155 Sheldon Dr., Cambridge Ontario, NIR 7H6, Canada

Litva, John

Communications Research Laboratory, McMaster University 1280 Main Street West, Hamilton, Ontario, L8S 4K1, Canada

McWhirter, John G.

Royal Signals and Radar Establishment, St. Andrew's Road Malvern, Worcs. WR14 3PS, UK

Nehorai, Arye

Department of Electrical Engineering, Yale University P.O. Box 2157, Yale Station, New Haven, CT 06520, USA

Nickel, Ulrich

Electronics Department, Forschungsinstitut fur Funk und Mathematik

(FGAN-FFM), Neuenahrer Str. 20, W-5307 Wachtberg 7, Fed. Rep. of

Germany

Ottersten, Bjorn

Signal Processing Division, Department of Telecommunication Theory, Royal Institute of Technology S-100 44 Stockholm, Sweden

Shepherd, Terence J.

Royal Signals and Radar Establishment, St. Andrew's Road Malvern, Worcs. WR14 3PS, UK

Steinberg, Bernard D.

The Moore School of Electrical Engineering, University of Pennsylvania Philadelphia, PA 19104, USA