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1、EfficientSingleFrequencyEstimatorsCurrentaddress:VaughanClarksonSchoolofInformationTechnology&ElectricalEngineeringElectronicsResearchLaboratoryTheUniversityofQueenslandDefenceScienceandTechnologyOrganisationQueensland4072POBox1500AustraliaSalisbury,SouthAustralia,5108v.clarkson@itee.
2、uq.edu.auAnumberofsinglefrequencyestimatorsareexamined.ThefailureofKay’swindowestimatorisdiscussed.Arefinementisproposedwhichisasymptoticallyunbiassed.Theresultsofnumericalsimulationsshowthattheimprovedestimatorhassuperiorperformancetotwosimilarestimators:thePSCFDandKay’scircularesti
3、mator(weightedlinearpredictor).1INTRODUCTIONTheestimationofthefrequencyofasinglesinusoidembeddedinadditivewhiteGaussiannoiseisoneoftheclassicalproblemsofsignalprocessing.Ithasimportanceinmanyapplicationsincommunications,wherefrequencyestimationisusedfordecoding,andinradarprocessinga
4、ndsonarprocessing.Theproblemoffrequencyestimationhasbeenwidelyexplored,butthereisstillroomforabetterestimator:anestimatorwhichapproachesstatisticalefficiencyoveralargerregionofparameterspace,andwhichislesscomputationallyintensive.Animprovedestimatorispresentedwhichbettermeetsthesecrit
5、eria.Consideracomplexsinusoidalsignalwhichhasbeencorruptedbynoiseinthereceiver.Thereceivedsamples,xn,canbeexpressedasfollows:x=Aej(ωn+φ0)+z,(1)nnwheren=0,...,N−1,andNisthenumberofsamplesreceived,Aistheamplitudeofthesinusoid,ωisitsfrequency,φ0istheinitialphaseandtheznarethenoise.Thep
6、arametersA,ωandφ0areunknown,andωistobeestimated.ItisassumedthatthesignalhasbeensampledinaccordancewiththeNyquistcriterionforaunittimestep.Hence,thefrequencyωlieswithintherange[−π,π).Theznareindependent,identicallydistributed,zero-mean,complexnormalrandomvariables,withuncorrelatedrea
7、landimaginaryparts,eachwithvarianceσ2.Thesignal-to-noiseratio(SNR),2r,canthenbedefinedasr=A.2σ2TheCram´er-Raolowerboundtothevarianceofanunbiassedfrequencyestimatorhasbeenderived[1]forthesignalmodeldescribedin(1).Thelowerboundis26σωˆ>2,(2)rN(N−1)whereσ2isthemeansquareerroroftheestimat
8、or.Themeansquareerr
