Introduction to Direction-of-Arrival Estimation (Artech House Signal Processing Library)

196 Pages·2010·2.37 MB·English

by  Zhizhang Chen

Introduction to
Direction-of-Arrival Estimation
For a listing of related titles in the
ArtechHouse Signal Processing Library
turn to the back of this book.
Introduction to
Direction-of-Arrival Estimation
Zhizhang Chen
Gopal Gokeda
Yiqiang Yu
artechhouse.com
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Cover design by Vicki Kane
ISBN 13: 978-1-59693-089-6
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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 DirectivityandGain 23
2.1.2 RadiationPattern 24
2.1.3 EquivalentResonantCircuitsandBandwidth 25
2.2 Single Receive Antenna 26
2.3 Antenna Array 27
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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 UniformLinearArray(ULA) 33
3.3 Centro-SymmetricSensor Arrays 38
3.3.1 UniformLinearArray 40
3.3.2 UniformRectangularArray(URA) 41
3.3.3 CovarianceMatrices 45
3.4 BeamformingTechniques 46
3.4.1 ConventionalBeamformer 47
3.4.2 Capon’sBeamformer 49
3.4.3 LinearPrediction 51
3.5 Maximum Likelihood Techniques 52
3.6 Subspace-Based Techniques 54
3.6.1 ConceptofSubspaces 54
3.6.2 MUSIC 57
3.6.3 MinimumNorm 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-BackwardAveraging 67
4.2.2 SpatialSmoothing 69
4.3 Model Order Estimators 74
4.3.1 ClassicalTechnique 75
4.3.2 MinimumDescriptiveLengthCriterion 75
Contents 7
4.3.3 AkaikeInformationTheoreticCriterion 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 SignalandDataModel 83
5.2.2 SignalSubspaceEstimation 84
5.2.3 EstimationoftheSubspaceRotatingOperator 85
5.3 Standard ESPRIT 86
5.3.1 SignalSubspaceEstimation 88
5.3.2 SolutionofInvarianceEquation 91
5.3.3 SpatialFrequencyandDOAEstimation 91
5.4 Real-Valued Transformation 92
5.5 Unitary ESPRIT in Element Space 94
5.5.1 One-DimensionalUnitaryESPRITinElementSpace 94
5.5.2 Two-DimensionalUnitaryESPRITinElementSpace 98
5.6 BeamspaceTransformation 105
5.6.1 DFTBeamspaceInvarianceStructure 107
5.6.2 DFTBeamspaceinaReducedDimension 112
5.7 Unitary ESPRIT inDFTBeamspace 113
5.7.1 One-DimensionalUnitaryESPRITinDFT
Beamspace 113
5.7.2 Two-DimensionalUnitaryESPRITinDFT
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 StandardESPRIT 126
6.2.2 TheOne-DimensionalUnitaryESPRIT 138
6.2.3 TheTwo-DimensionalUnitaryESPRIT 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 KroneckerProduct 179
A.2 Special Vectors and Matrix Notations 180
A.3 FLOPS 180
List of Abbreviations 183
About the Authors 185
Index 187
Preface
Direction-of-arrival (DOA) estimation (or direction finding) essentially
concerns the estimation of direction-of-arrival of signals, either in the
form of electromagnetic (i.e., radio) or acoustic waves, impinging on a
sensor or antenna array. The requirement for DOA estimation arises
fromtheneedsoflocatingandtrackingsignalsourcesinbothcivilianand
military applications, such as search and rescue, law enforcement, sonar,
seismology,andwireless911emergencycalllocating.
Various theories and techniques have been developed for array sig-
nal processing related to DOA estimations. A large body of literature has
also existed on the subject. However, during our course of research and
development for real-world implementations, we have found that rele-
vantpublicationshavebeenquitescattered,makingithardforthebegin-
ners or students who want to enter the area in a relatively short time. In
other words, few review books are available that systematically describe
theprinciplesandbasictechniquesofDOAestimationunderoneroof.
This book is intended to cover the issue by providing an overview
and performance analysis of the basic DOA algorithms and comparisons
among themselves. In particular, systematic descriptions, performance
analysis,and comparisonsofvariousDOA algorithmsare presented with
afinalfocusonthefamilyofESPRIT(estimationofsignalparametersvia
rotationalinvariancetechniques).
This book is aimed at beginners such as graduate students or engi-
neers or government regulators who need to gain insight into the funda-
mentals of DOA estimations in a relatively quick manner. It is also
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