Robust Adaptive Beamforming

435 Pages·2006·9.571 MB·English

by  Jian Li (editor), Petre Stoica (editor)

TEAM LinG
Robust Adaptive
Beamforming

Robust Adaptive
Beamforming
Edited by
Jian Li and Petre Stoica
A JOHN WILEY & SONS, INC., PUBLICATION
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LibraryofCongressCataloging-in-PublicationData:
Robustadaptivebeamforming/editedbyJianLiandPetreStoica.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN-13978-0-471-67850-2(cloth)
ISBN-100-471-67850-3(cloth)
1.Adaptiveantennas. 2.Antennaradiationpatterns. I.Li,Jian. II.Stoica,Petre.
TK7871.67.A33R632005
621.38204--dc22 2004065908
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
CONTENTS
Contributors ix
Preface xi
1 Robust MinimumVariance Beamforming 1
RobertG.LorenzandStephenP.Boyd
1.1 Introduction 1
1.2 APractical Example 8
1.3 Robust Weight Selection 12
1.4 ANumerical Example 23
1.5 Ellipsoidal Modeling 28
1.6 Uncertainty Ellipsoid Calculus 31
1.7 BeamformingExamplewith Multiplicative Uncertainties 41
1.8 Summary 44
Appendix:Notationand Glossary 44
References 45
2 Robust Adaptive BeamformingBased on Worst-Case
Performance Optimization 49
AlexB.Gershman,Zhi-QuanLuo,andShahramShahbazpanahi
2.1 Introduction 49
2.2 Background and TraditionalApproaches 51
2.3 Robust Minimum Variance Beamforming Based on
Worst-Case Performance Optimization 60
2.4 NumericalExamples 74
2.5 Conclusions 80
Appendix2.A: Proof of Lemma 1 81
Appendix2.B: Proof of Lemma 2 81
Appendix2.C:Proof of Lemma 3 82
Appendix2.D:Proof of Lemma 4 84
Appendix2.E: Proof of Lemma 5 85
References 85
v
vi CONTENTS
3 Robust CaponBeamforming 91
JianLi,PetreStoica,andZhisongWang
3.1 Introduction 91
3.2 Problem Formulation 93
3.3 StandardCaponBeamforming 95
3.4 Robust Capon Beamforming with SingleConstraint 96
3.5 Capon Beamforming with Norm Constraint 112
3.6 Robust Capon Beamforming with DoubleConstraints 116
3.7 Robust Capon Beamforming with Constant Beamwidth
andConstant Powerwidth 133
3.8 Rank-Deficient Robust Capon Filter-Bank
Spectral Estimator 148
3.9 AdaptiveImagingfor Forward-LookingGround
Penetrating Radar 166
3.10 Summary 185
Acknowledgments 185
Appendix3.A: RelationshipbetweenRCB andthe
Approach in [14] 185
Appendix3.B: Calculating theSteering Vector 188
Appendix3.C: RelationshipbetweenRCB and the
Approachin [15] 189
Appendix3.D: Analysisof Equation (3.72) 190
Appendix3.E: Rank-DeficientCapon Beamformer 191
Appendix3.F: Conjugate Symmetry ofthe Forward-Backward
FIR 193
Appendix3.G: Formulations ofNCCF andHDI 194
Appendix3.H: Notationsand Abbreviations 195
References 196
4 DiagonalLoading for Finite SampleSize Beamforming:
AnAsymptotic Approach 201
XavierMestreandMiguelA.Lagunas
4.1 Introduction andHistorical Review 202
4.2 Asymptotic OutputSINR with DiagonalLoading 213
4.3 Estimating theAsymptoticallyOptimum Loading Factor 225
4.4 Characterizationof theAsymptoticallyOptimum Loading
Factor 236
4.5 Summary andConclusions 243
Acknowledgments 243
Appendix4.A: Proofof Proposition 1 243
Appendix4.B: Proofof Lemma 1 246
Appendix4.C: Derivation ofthe Consistent Estimator 247
Appendix4.D: Proof of Proposition 2 249
References 254
CONTENTS vii
5 Mean-Squared Error Beamforming forSignalEstimation:
ACompetitive Approach 259
YoninaC.EldarandAryeNehorai
5.1 Introduction 259
5.2 Background and Problem Formulation 261
5.3 Minimax MSE Beamforming for Known Steering Vector 271
5.4 RandomSteering Vector 281
5.5 PracticalConsiderations 284
5.6 NumericalExamples 285
5.7 Summary 294
Acknowledgments 295
References 296
6 ConstantModulusBeamforming 299
Alle-JanvanderVeenandAmirLeshem
6.1 Introduction 299
6.2 The Constant ModulusAlgorithm 303
6.3 Prewhitening and RankReduction 307
6.4 MultiuserCMATechniques 312
6.5 The Analytical CMA 315
6.6 AdaptivePrewhitening 325
6.7 AdaptiveACMA 328
6.8 DOA Assisted Beamforming of ConstantModulus Signals 338
6.9 Concluding Remarks 347
Acknowledgment 347
References 347
7 Robust Wideband Beamforming 353
ElioD.DiClaudioandRaffaeleParisi
7.1 Introduction 353
7.2 Notation 357
7.3 Wideband Array SignalModel 358
7.4 Wideband Beamforming 363
7.5 Robustness 369
7.6 Steered AdaptiveBeamforming 381
7.7 Maximum Likelihood STBF 389
7.8 ML-STBF Optimization 393
7.9 SpecialTopics 399
7.10 Experiments 401
7.11 Summary 410
Acknowledgments 411
References 412
Index 417

CONTRIBUTORS
STEPHEN P. BOYD, Information Systems Laboratory, Stanford University,
Stanford,CA 94305
ELIO D. DI CLAUDIO, INFOCOM Department, University of Roma “La
Sapienza,” Via Eudossiana 18, I-00184 Roma, Italy
YONINA C. ELDAR, Department of Electrical Engineering, Technion—Israel
Institute ofTechnology,Haifa 32000, Israel
ALEX B. GERSHMAN, Darmstadt University of Technology, Institute of Tele-
communications,Merckstrasse25, 64283 Darmstadt,Germany
MIGUEL A. LAGUNAS, Centre Tecnolo`gic de Telecomunicacions de Catalunya,
NEXUS1 Building, Gran Capita 2–4,08034Barcelona, Spain
AMIR LESHEM, School of Engineering, Bar-Ilan University, 52900 Ramat-Gan,
Israel
JIAN LI, Department of Electrical and Computer Engineering, Engineering Bldg.,
CenterDrive, Universityof Florida, Gainesville, FL 32611
ROBERT G. LORENZ,Beceem Communications, Santa Clara,CA 95054
ZHI-QUANLUO,DepartmentofElectricalandComputerEngineering,University
of Minnesota,Minneapolis, MN 55455
XAVIER MESTRE, Centre Tecnolo`gic de Telecomunicacions de Catalunya,
NEXUS1 Building, Gran Capita 2–4,08034Barcelona, Spain
ARYE NEHORAI, Department of Electrical Engineering and Computer Science,
University ofIllinois at Chicago, Chicago, IL60607
RAFFAELEPARISI,INFOCOMDepartment,UniversityofRoma“LaSapienza,”
Via Eudossiana 18, I-00184 Roma, Italy
SHAHRAM SHAHBAZPANAHI, McMaster University, Hamilton, Ontario L8S
4L8,Canada
PETRE STOICA, Division of Systems and Control, Department of Information
Technology, UppsalaUniversity, SE-75105 Uppsala, Sweden
ALLE-JANVANDERVEEN,DepartmentofElectricalEngineering,DelftUniver-
sity ofTechnology, 2628 Delft, TheNetherlands
ZHISONGWANG,DepartmentofElectricalandComputerEngineering,Engineer-
ing Bldg.,CenterDrive, Universityof Florida, Gainesville, FL 32611
ix