FundamentalsofSignalEnhancementand ArraySignalProcessing Fundamentals of Signal Enhancement and Array Signal Processing JacobBenesty INRS,UniversityofQuebec Montreal,Canada IsraelCohen Technion,IsraelInstituteofTechnology Haifa,Israel JingdongChen NorthwesternPolytechnicalUniversity Xi’an,China Thiseditionfirstpublished ©JohnWiley&SonsSingaporePte.Ltd Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,or transmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise, exceptaspermittedbylaw.Adviceonhowtoobtainpermissiontoreusematerialfromthistitleisavailable athttp://www.wiley.com/go/permissions. TherightofJacobBenesty,IsraelCohen,andJingdongChentobeidentifiedastheauthorsofthisworkhas beenassertedinaccordancewithlaw. 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LibraryofCongressCataloging-in-Publicationdataappliedfor HardbackISBN: CoverDesignbyWiley CoverImage:©naqiewei/Gettyimages Setin/ptWarnockbySPiGlobal,Pondicherry,India           v Contents Preface xi AbouttheCompanionWebsite xiii 1 Introduction  . SignalEnhancement  .. SpeechEnhancementandNoiseReduction  .. UnderwaterAcousticSignalEnhancement  .. SignalEnhancementinRadarSystems  .. SignalEnhancementinUltrasoundSystems  . ApproachestoSignalEnhancement  . ArraySignalProcessing  . OrganizationoftheBook  . HowtoUsetheBook  References  PartI SignalEnhancement  2 Single-channelSignalEnhancementintheTimeDomain  . SignalModelandProblemFormulation  . WienerMethod  .. LinearFiltering  .. PerformanceMeasures  .. OptimalFilters  . SpectralMethod  .. JointDiagonalizationandReformulationoftheProblem  .. NoiseReductionwithGains  .. PerformanceMeasures  .. DeterminationoftheGainsfromtheFullmodeOutputSNR  Problems  References  3 Single-ChannelSignalEnhancementintheFrequencyDomain  . SignalModelandProblemFormulation  . NoiseReductionwithGains  vi Contents . PerformanceMeasures  . OptimalGains  . ConstraintWienerGains  . ImplementationwiththeShort-timeFourierTransform  Problems  References  4 MultichannelSignalEnhancementintheTimeDomain  . SignalModelandProblemFormulation  . ConventionalMethod  .. JointDiagonalization  .. LinearFiltering  .. PerformanceMeasures  .. OptimalFilteringMatrices  . SpectralMethod  .. TemporalJointDiagonalizationandReformulationoftheProblem  .. SpatialJointDiagonalization  .. SpatialLinearFiltering  .. PerformanceMeasures  .. OptimalFilters  . CaseofaRankDeficientNoiseCorrelationMatrix  .. EigenvalueDecompositions  .. MaximizationoftheOutputSNR  .. MinimizationoftheOutputSNR  Problems  References  5 MultichannelSignalEnhancementintheFrequencyDomain  . SignalModelandProblemFormulation  . LinearFiltering  . PerformanceMeasures  .. InputSNR  .. OutputSNR  .. NoiseRejectionandDesiredSignalCancellation  .. DesiredSignalDistortionIndex  .. MSECriterion  . OptimalFilters  .. MaximumSNR  .. Wiener  .. MVDR  .. Tradeoff  .. LCMV  . GeneralizedSidelobeCancellerStructure  . ASignalSubspacePerspective  .. JointDiagonalization  .. EstimationoftheDesiredSignal  Contents vii . ImplementationwiththeSTFT  Problems  References  6 AnExhaustiveClassofLinearFilters  . SignalModelandProblemFormulation  . LinearFilteringforSignalEnhancement  . PerformanceMeasures  . OptimalFilters  .. Wiener  .. MVDR  .. Tradeoff  .. LCMV  .. MaximumSINR  .. MaximumSIR  . FillingtheGapBetweentheMaximumSINRandWienerFilters  Problems  References  PartII ArraySignalProcessing  7 FixedBeamforming  . SignalModelandProblemFormulation  . LinearArrayModel  . PerformanceMeasures  . SpatialAliasing  . FixedBeamformers  .. DelayandSum  .. MaximumDF  .. Superdirective  .. RobustSuperdirective  .. NullSteering  . ASignalSubspacePerspective  .. JointDiagonalization  .. CompromisingBetweenWNGandDF  Problems  References  8 AdaptiveBeamforming  . SignalModel,ProblemFormulation,andArrayModel  . PerformanceMeasures  . AdaptiveBeamformers  .. Wiener  .. MVDR  .. Tradeoff  .. MaximumArrayGain  .. LCMV  viii Contents . SNREstimation  . DOAEstimation  . ASpectralCoherencePerspective  .. Definitions  .. DerivationofOptimalBeamformers  Problems  References  9 DifferentialBeamforming  . SignalModel,ProblemFormulation,andArrayModel  . Beampatterns  . Front-to-backRatios  . ArrayGains  . ExamplesofTheoreticalDifferentialBeamformers  . First-orderDesign  .. Principle  .. DesignExamples  . Second-orderDesign  .. Principle  .. DesignExamples  . Third-orderDesign  .. Principle  .. DesignExamples  . Minimum-normBeamformers  .. Principle  .. DesignExamples  Problems  References  10 BeampatternDesign  . BeampatternsRevisited  . NonrobustApproach  . RobustApproach  . Frequency-invariantBeampatternDesign  . Least-squaresMethod  . JointOptimization  Problems  References  11 BeamformingintheTimeDomain  . SignalModelandProblemFormulation  . BroadbandBeamforming  . PerformanceMeasures  . FixedBeamformers  .. DelayandSum  .. MaximumDF  .. DistortionlessMaximumDF  Contents ix .. Superdirective  .. NullSteering  . AdaptiveBeamformers  .. Wiener  .. MVDR  .. Tradeoff  .. MaximumSNR  .. LCMV  . DifferentialBeamformers  .. FirstOrder  .. SecondOrder  .. GeneralOrder  .. Hypercardioid  .. Supercardioid  Problems  References  Index  xi Preface Signal enhancement and array signal processing concern the problems of signal estimation,restoration,parameterestimation,anddecision-making.Thesetopicslieat theheartofmanyfundamentalapplications,suchashands-freevoicecommunications, sonar,radar,ultrasound,seismology,autonomouscars,robotics,andsoon.Thisbook is designed as a textbook and its principal goal is to provide a unified introduction to the theory and methods of signal enhancement and array signal processing. The targetedreadersareadvancedundergraduateandgraduatestudentswhoaretaking–or instructorswhoareteaching–coursesinsignalenhancement,arraysignalprocessing, andtheirapplications.Ofcourse,practitionersandengineerscanalsousethisbookas areferenceindesigningsignal-enhancementand/orarraysystems. Since the primary users of this book may come from many different fields, with differentbackgroundknowledge,wechoosetofocusonthekeyprinciples,theoryand methods of signal enhancement and array signal processing from a signal processing perspective without discussing in detail the introductory material related to specific applications.Studentsareencouragedtoreadbackgroundmaterialfromthespecialized academicbooksandresearchpapersintheirownfieldwhilestudyingthisbook. In most, if not all, application systems, signals are acquired in the time domain. Therefore, comprehensive coverage of the formulation, methods, and algorithms of signalenhancementandarraybeamformingisprovidedforthisdomain.Likewise,thor- oughcoverageofthematerialinthefrequencydomainisalsopresentedastheformula- tion,derivation,analysis,andimplementationofsignal-enhancementandbeamforming algorithms are often carried out in this domain. Readers are assumed to be familiar withFouriertransformsandtheshort-timeFouriertransform(STFT)bywhichatime- domainsignalismappedtoanequivalentsequenceinthefrequencydomain.Readers arealsoassumedtohavesomepriorknowledgeondiscrete-timelinearsystems,linear algebra,statisticalsignalprocessing,andstochasticprocesses. A solid theoretical understanding always goes hand-in-hand with practical imple- mentations.Therefore,thistextbookincludesalargenumberofexamplestoillustrate importantconceptsandshowhowthemajoralgorithmswork.MATLABfunctionsfor alltheexamplescanbefoundontheauthors’websites.Besidesexamples,exercisesand problems are provided at the end of every chapter to challenge readers and facilitate theircomprehensionofthematerial. xii Preface Withthelongexperienceoftheauthors(especiallythefirstone)inboththeindustry andacademia,wehopethatthisbookhasbeenwritteninsuchawaythatitiseasyand pleasanttoreadwithoutcompromisingontherigorofthemathematicaldevelopments. JacobBenesty IsraelCohen JingdongChen