Diss / (Springer Series in Information Sciences 25) S. Haykin, J. Litva, T. J. Shepherd (auth.), Professor Simon Haykin, Dr. John Litva, Dr. Terence J. Shepherd (eds.)-Radar Array Processing-Springer-Verlag
.pdfSpringer Series in Information Sciences |
25 |
Editor: Thomas S. Huang |
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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
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7Number Theory in Science
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15Fundamentals
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16Radon and Projection 'fransformBased Computer Vision
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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
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© Springer-Verlag Berlin Heidelberg 1993 .
Softcover reprint ofthe hardcover 1st edition 1993
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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 |
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Part I Detection and Estimation |
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2. Radar Detection Using Array Processing |
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By Z. Zhu and S. Haykin (With 2 Figures). . . . . . . . . . . . . . . . . . . . |
3 |
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2.1 |
Observation Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
4 |
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2.2 |
Coherent Radar Detection. . . . . . . . . . . . . . . . . . . . . . . . . . . . |
6 |
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2.2.1 |
Signal and Noise Model. . . . . . . . . . . . . . . . . . . . . . . . . |
6 |
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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 |
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2.3.1 |
Signal and Noise Model. . . . . . . . . . . . . . . . . . . . . . . . . |
16 |
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2.3.2 |
Detection of Targets with Known Directions . . . . . . . . . |
17 |
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2.3.3 |
Detection of Targets with Unknown Directions: |
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|
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Deterministic Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
22 |
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2.3.4 |
Detection of Targets with Unknown Directions: |
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Gaussian Signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
28 |
2.4 |
Passive Radar Detection .. . . . . . . . . . . . . . . . . . . . . . . . . . . . |
33 |
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2.4.1 |
Signal and Noise Model. . . . . . . . . . . . . . . . . . . . . . . . . |
33 |
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2.4.2 |
Detection of Emitters with Known Directions . . . . . . . . |
33 |
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2.4.3 |
Detection of Emitters with Unknown Directions: |
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Deterministic Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
35 |
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2.4.4 |
Detection of Emitters with Unknown Directions: |
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Gaussian Signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
40 |
2.5 |
Discussion........................................ |
43 |
|
References. |
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
44 |
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Additional References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
45 |
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3. Radar Target Parameter Estimation with Array Antennas |
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By U. Nickel (With 18 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
47 |
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3.1 |
Radar Parameter Estimation Problem. . . . . . . . . . . . . . . . . . . |
47 |
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3.1.1 |
Range and Angle Estimation. . . . . . . . . . . . . . . . . . . . . . |
48 |
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3.1.2 |
Frequency and Power Estimation. . . . . . . . . . . . . . . . . . |
51 |
3.2 |
Angle Estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
51 |
VIII |
Contents |
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3.2.1 |
Monopulse Estimation (Single Target Estimation) . . . . . |
52 |
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3.2.2 Covariance Matrix Estimation . . . . . . . . . . . . . . . . . . . . |
56 |
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3.2.3 |
Linear Prediction Methods. . . . . . . . . . . . . . . . . . . . . . . |
58 |
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3.2.4 Capon-Pisarenko-Type Methods . . . . . . . . . . . . . . . . . . |
62 |
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3.2.5 |
Signal Subspace Methods. . . . . . . . . . . . . . . . . . . . . . . . |
64 |
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3.2.6 Parametric Target Model Fitting . . . . . . . . . . . . . . . . . . |
73 |
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3.2.7 Aspects ofImplementation . . . . . . . . . . . . . . . . . . . . . . . |
83 |
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3.3 |
Frequency Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
86 |
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3.3.1 |
Doppler Filter Bank. . . . . . . . . . . . . . . . . . . . . . . . . . . . |
86 |
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3.3.2 |
Superresolution Methods. . . . . . . . . . . . . . . . . . . . . . . . . |
87 |
3.4 |
Range, Amplitude and Power Estimation . . . . . . . . . . . . . . . . |
90 |
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3.4.1 |
Conventional Range Estimation. . . . . . . . . . . . . . . . . . . |
90 |
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3.4.2 Superresolution in Range. . . . . . . . . . . . . . . . . . . . . . . . |
91 |
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3.4.3 Amplitude and Power Estimation. . . . . . . . . . . . . . . . . . |
93 |
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3.5 |
Summary......................................... |
94 |
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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 |
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4.2 |
Chapter Outline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
101 |
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4.3 |
Sensor Array Processing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
102 |
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4.3.1 |
Narrowband Data Model. . . . . . . . . . . . . . . . . . . . . . . . |
103 |
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4.3.2 |
Parametric Data Model. . . . . . . . . . . . . . . . . . . . . . . . . . |
104 |
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4.3.3 Assumptions and Problem Formulation. . . . . . . . . . . . . |
106 |
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4.3.4 |
Parameter Identifiability. . . . . . . . . . . . . . . . . . . . . . . . . |
107 |
4.4 |
Exact Maximum Likelihood Estimation. . . . . . . . . . . . . . . . . |
108 |
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4.4.1 |
Stochastic Maximum Likelihood Method. . . . . . . . . . . . |
109 |
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4.4.2 Deterministic Maximum Likelihood Method . . . . . . . . . |
111 |
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4.4.3 |
Bounds of Estimation Accuracy . . . . . . . . . . . . . . . . . . . |
112 |
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4.4.4 Asymptotic Properties of Maximum Likelihood Estimates |
115 |
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4.4.5 |
Order Relations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
117 |
4.5 Large Sample Maximum Likelihood Approximations. . . . . . . |
118 |
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4.5.1 |
Subspace Based Approach. . . . . . . . . . . . . . . . . . . . . . . . |
118 |
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4.5.2 |
Relation Between Subspace Formulations. . . . . . . . . . . . |
121 |
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4.5.3 |
Relation to Maximum Likelihood Estimation. . . . . . . . . |
123 |
4.6 |
Calculating the Estimates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
125 |
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4.6.1 |
Newton-Type Search Algorithms. . . . . . . . . . . . . . . . . . . |
126 |
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4.6.2 |
Gradients and Approximate Hessians. . . . . . . . . . . . . . . |
127 |
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4.6.3 |
Uniform Linear Arrays. . . . . . . . . . . . . . . . . . . . . . . . . . |
129 |
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4.6.4 |
Practical Aspects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
130 |
4.7 |
Detection of Coherent/Noncoherent Signals. . . . . . . . . . . . . . |
133 |
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4.7.1 |
Generalized Likelihood Ratio Test Based Detection. . . . |
133 |
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4.7.2 |
Subspace Based Detection. . . . . . . . . . . . . . . . . . . . . . . . |
135 |
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Contents |
IX |
4.8 |
Numerical Examples and Simulations .. : . . . . . . . . . . . . . . . . |
137 |
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4.9 |
Conclusions....................................... |
143 |
||
Appendix |
4.A |
Differentiation of the Projection Matrix. . . . . . . . . . |
144 |
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Appendix 4.B |
Asymptotic Distribution of the Weighted |
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|
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Subspace Fitting Criterion. . . . . . . . . . . . . . . . . . . . |
144 |
References. |
. . . |
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
147 |
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Part II |
Systolic Arrays |
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5. Systolic Adaptive Beamforming |
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By T.J. Shepherd and J.G. McWhirter (With 27 Figures).. . . . .. .. |
153 |
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5.1 |
Adaptive Antenna Arrays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
153 |
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5.2 Systolic and Wavefront Arrays. . . . . . . . . . . . . . . . . . . . . . . . . |
155 |
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5.3 |
Canonical Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
157 |
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5.3.1 |
Canonical Configuration. . . . . . . . . . . . . . . . . . . . . . . . . |
158 |
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5.3.2 Least-Squares Formulation. . . . . . . . . . . . . . . . . . . . . . . |
160 |
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5.4 QR Decomposition by Givens Rotations. . . . . . . . . . . . . . . . . |
163 |
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5.4.1 |
QR Decomposition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
163 |
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5.4.2 |
Givens Rotations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
164 |
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5.4.3 |
Systolic Array Implementation. . . . . . . . . . . . . . . . . . . . |
166 |
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5.4.4 Square-Root-Free Algorithm. . . . . . . . . . . . . . . . . . . . . . |
169 |
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5.4.5 |
Sensitivity to Arithmetic Precision . . . . . . . . . . . . . . . . . |
173 |
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5.5 |
Direct Residual Extraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . |
175 |
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5.5.1 |
Definition of Residuals. . . . . . . . . . . . . . . . . . . . . . . . . . |
175 |
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5.5.2 |
Properties of Rotation Matrix Q(n). . . . . . . . . . . . . . . . . |
175 |
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5.5.3 |
A Posteriori Residual Extraction. . . . . . . . . . . . . . . . . . . |
178 |
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5.5.4 |
A Priori Residual Extraction. . . . . . . . . . . . . . . . . . . . . . |
179 |
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5.6 |
Weight Freezing and Flushing. . . . . . . . . . . . . . . . . . . . . . . . . |
180 |
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5.6.1 |
Basic Concept. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
180 |
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5.6.2 |
Frozen Networks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
181 |
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5.6.3 |
Serial Weight Flushing. . . . . . . . . . . . . . . . . . . . . . . . . . |
185 |
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5.6.4 |
Further Insights. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
187 |
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5.7 |
Linear Constraint Pre-Processor. . . . . . . . . . . . . . . . . . . . . . . |
189 |
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5.7.1 |
Single Constraint Pre-Processor. . . . . . . . . . . . . . . . . . . |
190 |
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5.7.2 |
Multiple Constraint Pre-Processor. . . . . . . . . . . . . . . . . |
193 |
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5.7.3 |
Generalized Sidelobe Canceller. . . . . . . . . . . . . . . . . . . . |
196 |
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5.8 Minimum Variance Distortionless Response Beamforming . . . |
200 |
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5.8.1 |
Schreiber's Algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . |
201 |
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5.8.2 |
Systolic Array Implementation . . . . . . . . . . . . . . . . . . . . |
204 |
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5.8.3 |
Square-Root-Free Minimum Variance Distortionless |
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Response Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
207 |
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5.9 |
Adaptive Antenna Processor Test-Bed. . . . . . . . . . . . . . . . . . . |
210 |
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5.9.1 |
Wavefront Array Processor. . . . . . . . . . . . . . . . . . . . . . . |
211 |
X |
Contents |
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5.10 Further Developments. . . . . . . . . . . . . . . . . . . . . . . . |
. . . . . . . |
215 |
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5.10.1 Parallel Weight Extraction. . . . . . . . . . . . . . . |
. . . . . . . |
215 |
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5.10.2 QR-with-Feedback. . . . . . . . . . . . . . . . . . . . . . |
. . . . . . . |
218 |
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5.10.3 Structures for Broad-Band Adaptive Beamforming. . . . |
220 |
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5.10.4 QR Decomposition and Neural Networks. . . |
. . . . . . . |
222 |
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5.11 |
Comments and Conclusions. . . . . . . . . . . . . . . . . . . . |
. . . . . . . |
225 |
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5.11.1 Additional Topics. . . . . . . . . . . . . . . . . . . . . . |
. . . . . . . |
226 |
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Appendix 5.A Modified Gram-Schmidt Algorithm. . . . . . |
. . . . . . . |
229 |
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Appendix 5.B Constraints with Leading Zeros . . . . . . . . . |
. . . . . . . |
232 |
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Appendix 5.C Weighted Least-Squares and Hyperbolic Rotations. |
235 |
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Appendix 5.D Principal Symbols Used in this Chapter. . . |
. . . . . . . |
241 |
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References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
. . . . . . . |
243 |
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6. Two-Dimensional Adaptive Beamforming: Algorithms and Their |
|
||||
Implementation By T. V. Ho and J. Litva (With 19 Figures). |
. . . . . . |
249 |
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6.1 |
Arrangement of the Chapter .................... |
: . . . . . . |
251 |
||
6.2 Adaptive Beamforming Techniques. . . . . . . . . . . . . . . |
. . . . . . . |
252 |
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6.2.1 |
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
. . . . . . . |
252 |
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6.2.2 |
Classical Adaptive Beamforming. . . . . . . . . . . . . |
. . . . . . . |
255 |
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6.2.3 |
Modern Adaptive Beamforming . . . . . . . . . . . . . |
. . . . . . . |
261 |
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6.3 |
2D Adaptive Beamforming Algorithm and Implementation. . . . |
264 |
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6.3.1 |
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
. . . . . . . |
264 |
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6.3.2 |
Classical Approaches. . . . . . . . . . . . . . . . . . . . . . . |
. . . . . . |
266 |
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6.3.3 |
2D QRD-LS Algorithm and Systolic Array |
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Implementation. . . . . . . . . . . . . . . . . . . . . . . . . . . |
. . . . . . |
276 |
6.4 |
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Simulation Results. . . . . . . . . . . . . . . . . . . . . . . . . . . |
. . . . . . . |
283 |
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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