Introduction to Direction-of-Arrival Estimation
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Introduction to Direction-of-Arrival Estimation
Zhizhang Chen
Gopal Gokeda
Yiqiang Yu
a r t e c h h o u s e . c o m
Library of Congress Cataloging-in-Publication Data
A catalog record for this book is available from the U.S. Library of Congress.
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library.
Cover design by Vicki Kane
ISBN 13: 978-1-59693-089-6
© 2010 ARTECH HOUSE
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Norwood, MA 02062
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10 9 8 7 6 5 4 3 2 1
Contents
|
Preface |
9 |
1 |
Introduction |
11 |
1.1 |
Smart Antenna Architecture |
12 |
1.2 |
Overview of This Book |
17 |
1.3 |
Notations |
18 |
|
References |
19 |
2 |
Antennas and Array Receiving System |
21 |
2.1 |
Single Transmit Antenna |
23 |
2.1.1 |
Directivity and Gain |
23 |
2.1.2 |
Radiation Pattern |
24 |
2.1.3 |
Equivalent Resonant Circuits and Bandwidth |
25 |
2.2 |
Single Receive Antenna |
26 |
2.3 |
Antenna Array |
27 |
5
6 Introduction to Direction-of-Arrival Estimation
2.4 |
|
Conclusion |
29 |
|
|
Reference |
30 |
3 |
|
Overview of Basic DOA Estimation Algorithms |
31 |
3.1 |
|
Introduction |
31 |
3.2 |
|
Data Model |
32 |
3.2.1 |
Uniform Linear Array (ULA) |
33 |
|
3.3 |
|
Centro-Symmetric Sensor Arrays |
38 |
3.3.1 |
|
Uniform Linear Array |
40 |
3.3.2 |
|
Uniform Rectangular Array (URA) |
41 |
3.3.3 |
|
Covariance Matrices |
45 |
3.4 |
|
Beamforming Techniques |
46 |
3.4.1 |
|
Conventional Beamformer |
47 |
3.4.2 |
Capon’s Beamformer |
49 |
|
3.4.3 |
|
Linear Prediction |
51 |
3.5 |
|
Maximum Likelihood Techniques |
52 |
3.6 |
|
Subspace-Based Techniques |
54 |
3.6.1 |
|
Concept of Subspaces |
54 |
3.6.2 |
|
MUSIC |
57 |
3.6.3 |
|
Minimum Norm |
61 |
3.6.4 |
|
ESPRIT |
62 |
3.7 |
|
Conclusion |
63 |
|
|
References |
63 |
4 |
|
Preprocessing Schemes and Model Order Estimation |
65 |
4.1 |
|
Introduction |
65 |
4.2 |
|
Preprocessing Schemes |
66 |
4.2.1 |
|
Forward-Backward Averaging |
67 |
4.2.2 |
|
Spatial Smoothing |
69 |
4.3 |
|
Model Order Estimators |
74 |
4.3.1 |
|
Classical Technique |
75 |
4.3.2 |
|
Minimum Descriptive Length Criterion |
75 |
|
Contents |
7 |
|
|
|
4.3.3 |
Akaike Information Theoretic Criterion |
77 |
4.4 |
Conclusion |
78 |
|
References |
79 |
5 |
DOA Estimations with ESPRIT Algorithms |
81 |
5.1 |
Introduction |
81 |
5.2 |
Basic Principle |
82 |
5.2.1 |
Signal and Data Model |
83 |
5.2.2 |
Signal Subspace Estimation |
84 |
5.2.3 |
Estimation of the Subspace Rotating Operator |
85 |
5.3 |
Standard ESPRIT |
86 |
5.3.1 |
Signal Subspace Estimation |
88 |
5.3.2 |
Solution of Invariance Equation |
91 |
5.3.3 |
Spatial Frequency and DOA Estimation |
91 |
5.4 |
Real-Valued Transformation |
92 |
5.5 |
Unitary ESPRIT in Element Space |
94 |
5.5.1 |
One-Dimensional Unitary ESPRIT in Element Space |
94 |
5.5.2 |
Two-Dimensional Unitary ESPRIT in Element Space |
98 |
5.6 |
Beamspace Transformation |
105 |
5.6.1 |
DFT Beamspace Invariance Structure |
107 |
5.6.2 |
DFT Beamspace in a Reduced Dimension |
112 |
5.7 |
Unitary ESPRIT in DFT Beamspace |
113 |
5.7.1One-Dimensional Unitary ESPRIT in DFT
Beamspace |
113 |
5.7.2Two-Dimensional Unitary ESPRIT in DFT
|
Beamspace |
116 |
5.8 |
Conclusion |
120 |
|
References |
122 |
6 |
Analysis of ESPRIT-Based DOA Estimation |
|
|
Algorithms |
123 |
6.1 |
Introduction |
123 |
6.2 |
Performance Analysis |
126 |
8 |
Introduction to Direction-of-Arrival Estimation |
|
|
|
6.2.1 |
Standard ESPRIT |
126 |
|
6.2.2 |
The One-Dimensional Unitary ESPRIT |
138 |
|
6.2.3 |
The Two-Dimensional Unitary ESPRIT |
148 |
|
6.3 |
Comparative Analysis |
158 |
|
6.4 |
Discussions |
167 |
|
6.5 |
Conclusion |
173 |
|
|
References |
174 |
|
7 |
Discussions and Conclusion |
175 |
|
7.1 |
Summary |
175 |
|
7.2 |
Advanced Topics on DOA Estimations |
176 |
|
|
References |
177 |
|
|
Appendix |
179 |
|
A.1 |
Kronecker Product |
179 |
|
A.2 |
Special Vectors and Matrix Notations |
180 |
|
A.3 |
FLOPS |
180 |
|
|
List of Abbreviations |
183 |
|
|
About the Authors |
185 |
|
|
Index |
187 |