robust M-estimation for array processing_ a random matrix approach

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1、1RobustM-EstimationforArrayProcessing:ARandomMatrixApproachRomainCouillet1,Fred´ericPascal´2,andJackW.Silverstein31Telecommunicationdepartment,Supelec,GifsurYvette,France.´2SONDRALaboratory,Supelec,GifsurYvette,France.´3DepartmentofMathematics,NorthCarolinaStateUniversity

2、,NC,USA.Abstract—Thisarticlestudiesthelimitingbehaviorofarobustrecognizedinadaptiveradarandsonarprocessing,whereM-estimatorofpopulationcovariancematricesasboththethesignalsunderstudyarecharacterizedbyimpulsivenoisenumberofavailablesamplesandthepopulationsizearelarge.andou

3、tlyingdata.RobustestimationtheoryaimsattacklingUsingtoolsfromrandommatrixtheory,weprovethatthethisproblem[5].Amongothersolutions,theso-calledrobustdifferencebetweenthesamplecovariancematrixand(ascaledversionof)therobustM-estimatortendstozeroinspectralnorm,M-estimatorsofth

4、epopulationcovariancematrix,originallyalmostsurely.ThisresultisappliedtoprovethatrecentsubspaceintroducedbyHuber[4]andinvestigatedintheseminalworkmethodsarisingfromrandommatrixtheorycanbemaderobustofMaronna[6],haveimposedthemselvesasanappealingwithoutalteringtheirfirstorde

5、rbehavior.alternativetotheSCM.Thisestimator,whichwedenoteC^N,isdefinedimplicitlyasasolutionof1I.INTRODUCTIONXnC^=1u1xC^1xxxManymulti-variatesignalprocessingdetectionandestima-NnNiNiiitiontechniquesarebasedontheempiricalcovariancematrixofi=1asequenceofsamplesx1;:::;xnf

6、romarandompopulationforuanonnegativefunctionwithspecificproperties.Thesees-vectorx2CN.AssumingE[x]=0andE[xx]=C,theNtimatorsareparticularlyappropriateastheyarethemaximumstronglawoflargenumbersensuresthat,forindependentandlikelihoodestimatesof(ascaledversionof)CNforspecifici

7、denticallydistributed(i.i.d.)samples,distributionsofx,suchasthefamilyofellipticaldistributions1Xn[7].TheyarealsousedtocopewithdistributionsofxwithS^=xx!Cheavier-than-Gaussiantails,suchastheK-distributionoftenNiiNni=1metinthecontextofadaptiveradarprocessingwithimpulsiveal

8、mostsurely(a.s.),asthenumbernofsamplesincreases.clutter[8].Manysubspacemethods,suchastheMUSICalg