an improved weighted music algorithm for small sample size scenarios

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1、ANIMPROVEDWEIGHTEDMUSICALGORITHMFORSMALLSAMPLESIZESCENARIOSXavierMestreCentreTecnològicdeTelecomunicacionsdeCatalunya(CTTC)ParcMediterranidelaTecnologia,Av/delCanalOlímpics/n,Castelldefels,08860Barcelona,Spainxavier.mestre@cttc.catABSTRACTbehavior,i.e.weassumethatbothquantitiesarelargebuthave

2、thesameorderofmagnitude(M→∞,N→∞,M/N→c,Anewmethodfordirectionofarrival(DoA)detectioninarray0

3、ubspacesig-architectures.nalprocessingalgorithmsinthelowsamplesizeregime.First,anLetusconsideracollectionofNcomplexvaluedarrayobser-asymptoticanalysisofthetraditionalMUSICalgorithmiscarriedM×1vations,y(n)∈C,n=1...Nobtainedfromanarrayofoutassumingthatthenumberofantennasandthenumberofsam-M>1sen

4、sors.LetRrepresentthetrueM×Mcovariancema-plesincreasewithoutboundbuthavethesameorderofmagnitude.trixoftheobservation.AssumingthatthereareK

5、betweenthesignalanddescribedasnoiseeigenvalueclustersintheasymptoticsampleeigenvaluedis-tribution.WeprovethatMUSICisinconsistentinthisasymptoticH+σ2IR=S(Θ)ΦSS(Θ)Mregime,andthatpartoftheenergyinthenoisesampleeigenvec-torsspillsintothesignalsubspacewheneverthequotientbetweenwhereS(Θ)isanM×Kmatr

6、ixthatcontainsthesteeringvectorsthenumberofsamplesandthenumberofantennasisfinite.There-correspondingtotheKdifferentsources,namelyafter,weprovideaweightedMUSICalgorithmthatisspecifically£¤designedtoprovideconsistentestimatesevenwhentheobserva-S(Θ)=s(θ1)s(θ2)···s(θK)tiondimensionincreaseswithoutb

7、oundatthesamerateasthe2andwhereσandΦSrespectivelydenotetheomnidirectionalnumberofobservations.Thisguaranteesagoodbehaviorinfi-backgroundnoisepowerandtheK×Ksourcecorrelationmatrix.nitesamplesizesituations,wherethenumberofsensorsandtheWewilldeno