Using random matrix theory in array processing applications_ the small sample size regime

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1、Usingrandommatrixtheoryinarrayprocessingapplications:thesmallsamplesizeregimeXavierMestrexavier.mestre@cttc.catCentreTecnològicdeTelecomunicacionsdeCatalunya(CTTC)ParcMediterranidelaTecnologia,Castelldefels,Barcelona,SpainThethirdEPFL-UMLVWorkshoponRandomMatrices,InformationTheoryandApplicati

2、ons,3-4December2009CentreTecnològicdeTelecomunicacionsdeCatalunya-CTTCOutline•Introductiontoarraysignalprocessing.•Directionofarrivalestimationandsignalpowerdetermination.TheMLapproach.•TheMUSICapproach:asymptoticbehavioroftheeigenvectorsofthesamplecovariancematrix.•Estimatingwithrandommatrix

3、theory.-consistencyversus-consistency.Estimationoftheeigenvectorsofthesamplecovariancematrix.•Estimatingthepowerofthesourcesandtheeigenvaluesofthesamplecovariancematrix.XavierMestre:Usingrandommatrixtheoryinarrayprocessingapplications:thesmallsamplesizeregime.2/40CentreTecnològicdeTelecom

4、unicacionsdeCatalunya-CTTCArraysignalprocessing:introductionAssumethatwereceivenarrowbandsignalsfromareceiverequippedwithanantennaarrayofelements:X£¤y()=()a()+n()=⇒y()=A(Θ)s()+n()A(Θ)=a(1)a(2)···a()=1CommontermSpatialsignatureXavierMestre:Usingrandommatrixtheoryinarrayproces

5、singapplications:thesmallsamplesizeregime.3/40CentreTecnològicdeTelecomunicacionsdeCatalunya-CTTCSignalmodelsinarrayprocessingTraditionally,twodifferentassumptionsareusedinarraysignalprocessing,givingrisetotwodifferentsignalmodels.y()=A(Θ)s()+n()•Theconditionalordeterministicsignalmodel:thec

6、ollectionofsignalvectorss()istreatedasanunknowndeterministicparameter.Thismodelissometimesreferredtoastheinformation-plus-noisemodel.•Theunconditionalorrandomsignalmodel:thecollectionofsignalvectorss()istreatedasarandomparameter,usuallyhavingzeromean,circularsymmetryandcovariance£¤£¤Φ=Es

7、()s()Es()s()=0Thispresentationwillonlyfocusontherandom(orunconditional)signalmodel.XavierMestre:Usingrandommatrixtheoryinarrayprocessingapplications:thesmallsamplesizeregime.4/40CentreTecnològicdeTelecomunicacionsdeCatalunya-CTTCProblem