Radar Array Processing

325 Pages·1993·14.1 MB·English

by  S. Haykin

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
1 Content-Addressable Memories 16 Radon and Projection 'fransform
By T. Kohonen 2nd Edition Based Computer Vision
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2 Fast Fonrier 'fransform and
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An Introduction By L. P. Yaroslavsky 24 Parallel Algorithms
10 Probability, Statistical Optics, in Computational Science
and Data Testing By D. W. Heermann and A. N. Burkitt
A Problem Solving Approach 25 Radar Array Processing
By B. R. Frieden 2nd Edition Editors: S. Haykin, J. Litva,
11 Physical and Biological Processing and T. J. Shepherd
of Images Editors: O. J. Braddick 26 Signal Processing and Systems Theory
and A. C. Sleigh Selected Topics
12 Multiresolution Image Processing By C. K. Chui and G. Chen
and Analysis Editor: A. Rosenfeld 27 3D Dynamic Scene Analysis
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Image Processing Editor: King-sun Fu By Z. Zhang and O. Faugeras
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Some Aspects of Image Processing By J. Weng, T.S. Huang,
By W. F. Schreiber 3rd Edition 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 -978-3-642-7734 7-1
DOl: 10.1007/978-3-642-77347-1
Library of Congress Cataloging-in-Publication Data. Radar array processing 1 S. 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
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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 of interest 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
Otters ten, 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