Convex optimization in signal processing and communications

514 Pages·2010·3.233 MB·English

by  Eldar, Yonina C., Palomar, Daniel P (ed.)

This page intentionally left blank
ConvexOptimizationinSignalProcessingandCommunications
Overthepasttwodecadestherehavebeensignificantadvancesinthefieldofoptimiza-
tion. In particular, convex optimization has emerged as a powerful signal-processing
tool, and the range of applications continues to grow rapidly. This book, written by a
teamofleadingexperts,setsoutthetheoreticalunderpinningsofthesubjectandprovides
tutorialsonawiderangeofconvex-optimizationapplications.Emphasisthroughoutis
placedoncutting-edgeresearchandonformulatingproblemsinconvexform,making
thisanidealtextbookforadvancedgraduatecoursesandausefulself-studyguide.
Topicscovered:
• automaticcodegeneration
• graphicalmodels
• gradient-basedalgorithmsforsignalrecovery
• semidefiniteprogramming(SDP)relaxation
• radarwaveformdesignviaSDP
• blindsourceseparationforimageprocessing
• modernsamplingtheory
• robustbroadbandbeamforming
• distributedmultiagentoptimizationfornetworkedsystems
• cognitiveradiosystemsviagametheory
• thevariational-inequalityapproachforNash-equilibriumsolutions
DanielP.PalomarisanAssistantProfessorintheDepartmentofElectronicandComputer
Engineering at the Hong Kong University of Science and Technology (HKUST). He
receivedhisPh.D.fromtheTechnicalUniversityofCatalonia(UPC),Spain,in2003;was
aFulbrightScholaratPrincetonUniversityduring2004–2006;andhassincereceived
numerousawardsincludingthe2004YoungAuthorBestPaperAwardbytheIEEESignal
ProcessingSociety.
YoninaC.EldarisaProfessorintheDepartmentofElectricalEngineeringattheTechnion,
IsraelInstituteofTechnology,andisalsoaResearchAffiliatewiththeResearchLabo-
ratoryofElectronicsatMIT.ShereceivedherPh.D.fromtheMassachusettsInstituteof
Technology(MIT)in2001.Shehasreceivedmanyawardsforherresearchandteach-
ing,including,theWolfFoundationKrillPrizeforExcellenceinScientificResearch,the
HershelRichInnovationAwardandtheMuriel&DavidJacknowAwardforExcellence
inTeaching.

Convex Optimization in
Signal Processing and
Communications
Editedby
DANIEL P. PALOMAR
HongKongUniversityofScienceandTechnology
and
YONINAC.ELDAR
Technion–IsraelInstituteofTechnology
CAMBRIDGEUNIVERSITYPRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore,
São Paulo, Delhi, Dubai, Tokyo
Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521762229
© Cambridge University Press 2010
This publication is in copyright. Subject to statutory exception and to the
provision of relevant collective licensing agreements, no reproduction of any part
may take place without the written permission of Cambridge University Press.
First published in print format 2009
ISBN-13 978-0-511-69123-2 eBook (NetLibrary)
ISBN-13 978-0-521-76222-9 Hardback
Cambridge University Press has no responsibility for the persistence or accuracy
of urls for external or third-party internet websites referred to in this publication,
and does not guarantee that any content on such websites is, or will remain,
accurate or appropriate.
Contents
Listofcontributors page ix
Preface xi
1 Automaticcodegenerationforreal-timeconvexoptimization 1
JacobMattingleyandStephenBoyd
1.1 Introduction 1
1.2 Solversandspecificationlanguages 6
1.3 Examples 12
1.4 Algorithmconsiderations 22
1.5 Codegeneration 26
1.6 CVXMOD:apreliminaryimplementation 28
1.7 Numericalexamples 29
1.8 Summary,conclusions,andimplications 33
Acknowledgments 35
References 35
2 Gradient-basedalgorithmswithapplicationstosignal-recovery
problems 42
AmirBeckandMarcTeboulle
2.1 Introduction 42
2.2 Thegeneraloptimizationmodel 43
2.3 Buildinggradient-basedschemes 46
2.4 Convergenceresultsfortheproximal-gradientmethod 53
2.5 Afastproximal-gradientmethod 62
2.6 Algorithmsforl -basedregularizationproblems 67
1
2.7 TV-basedrestorationproblems 71
2.8 Thesource-localizationproblem 77
2.9 Bibliographicnotes 83
References 85
vi Contents
3 Graphicalmodelsofautoregressiveprocesses 89
JitkomutSongsiri,JoachimDahl,andLievenVandenberghe
3.1 Introduction 89
3.2 Autoregressiveprocesses 92
3.3 Autoregressivegraphicalmodels 98
3.4 Numericalexamples 104
3.5 Conclusion 113
Acknowledgments 114
References 114
4 SDPrelaxationofhomogeneousquadraticoptimization:approximation
boundsandapplications 117
Zhi-QuanLuoandTsung-HuiChang
4.1 Introduction 117
4.2 NonconvexQCQPsandSDPrelaxation 118
4.3 SDPrelaxationforseparablehomogeneousQCQPs 123
4.4 SDPrelaxationformaximizationhomogeneousQCQPs 137
4.5 SDPrelaxationforfractionalQCQPs 143
4.6 MoreapplicationsofSDPrelaxation 156
4.7 Summaryanddiscussion 161
Acknowledgments 162
References 162
5 Probabilisticanalysisofsemidefiniterelaxationdetectorsformultiple-input,
multiple-outputsystems 166
AnthonyMan-ChoSoandYinyuYe
5.1 Introduction 166
5.2 Problemformulation 169
5.3 AnalysisoftheSDRdetectorfortheMPSKconstellations 172
5.4 ExtensiontotheQAMconstellations 179
5.5 Concludingremarks 182
Acknowledgments 182
References 189
6 Semidefiniteprogramming,matrixdecomposition,andradarcodedesign 192
YongweiHuang,AntonioDeMaio,andShuzhongZhang
6.1 Introductionandnotation 192
6.2 Matrixrank-1decomposition 194
6.3 Semidefiniteprogramming 200
6.4 Quadraticallyconstrainedquadraticprogrammingand
itsSDPrelaxation 201
Contents vii
6.5 PolynomiallysolvableQCQPproblems 203
6.6 Theradarcode-designproblem 208
6.7 Performancemeasuresforcodedesign 211
6.8 Optimalcodedesign 214
6.9 Performanceanalysis 218
6.10 Conclusions 223
References 226
7 Convexanalysisfornon-negativeblindsourceseparationwith
applicationinimaging 229
Wing-KinMa,Tsung-HanChan,Chong-YungChi,andYueWang
7.1 Introduction 229
7.2 Problemstatement 231
7.3 Reviewofsomeconceptsinconvexanalysis 236
7.4 Non-negative,blindsource-separationcriterionviaCAMNS 238
7.5 Systematiclinear-programmingmethodforCAMNS 245
7.6 Alternatingvolume-maximizationheuristicsforCAMNS 248
7.7 Numericalresults 252
7.8 Summaryanddiscussion 257
Acknowledgments 263
References 263
8 Optimizationtechniquesinmodernsamplingtheory 266
TomerMichaeliandYoninaC.Eldar
8.1 Introduction 266
8.2 Notationandmathematicalpreliminaries 268
8.3 Samplingandreconstructionsetup 270
8.4 Optimizationmethods 278
8.5 Subspacepriors 280
8.6 Smoothnesspriors 290
8.7 Comparisonofthevariousscenarios 300
8.8 Samplingwithnoise 302
8.9 Conclusions 310
Acknowledgments 311
References 311
9 Robustbroadbandadaptivebeamformingusingconvexoptimization 315
MichaelRübsamen,AmrEl-Keyi,AlexB.Gershman,andThiaKirubarajan
9.1 Introduction 315
9.2 Background 317
9.3 Robustbroadbandbeamformers 321
9.4 Simulations 330
viii Contents
9.5 Conclusions 337
Acknowledgments 337
References 337
10 Cooperativedistributedmulti-agentoptimization 340
AngeliaNedic´andAsumanOzdaglar
10.1 Introductionandmotivation 340
10.2 Distributed-optimizationmethodsusingdualdecomposition 343
10.3 Distributed-optimizationmethodsusingconsensusalgorithms 358
10.4 Extensions 372
10.5 Futurework 378
10.6 Conclusions 380
10.7 Problems 381
References 384
11 CompetitiveoptimizationofcognitiveradioMIMOsystemsviagametheory 387
GesualsoScutari,DanielP.Palomar,andSergioBarbarossa
11.1 Introductionandmotivation 387
11.2 Strategicnon-cooperativegames:basicsolutionconceptsandalgorithms 393
11.3 Opportunisticcommunicationsoverunlicensedbands 400
11.4 Opportunisticcommunicationsunderindividual-interference
constraints 415
11.5 Opportunisticcommunicationsunderglobal-interferenceconstraints 431
11.6 Conclusions 438
Acknowledgments 439
References 439
12 Nashequilibria:thevariationalapproach 443
FranciscoFacchineiandJong-ShiPang
12.1 Introduction 443
12.2 TheNash-equilibriumproblem 444
12.3 Existencetheory 455
12.4 Uniquenesstheory 466
12.5 Sensitivityanalysis 472
12.6 Iterativealgorithms 478
12.7 Acommunicationgame 483
Acknowledgments 490
References 491
Afterword 494
Index 495