Spectral correlation function in low SNR environment

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1、SpectralCorrelationFunctioninLowSNREnvironmentMaWenJie*.YangShiMing.RenWu.XueZhengHui.LiWeiMingDcpartmentofElectricEngineering.BeijingInstituteofTeclmology.Beijing100081.P.RChina*Enmil:IZr.coiiiAhstractThespectralcorrelationfunction(SCF)isan2.SpectralCorrelationTheon7e

2、fficienttoolforanalyzingthecyclostationarysignals.InCyclostationaysignalissuchkindofsignalwhosealowsigilal-to-noise(SNR)conditionhowever.spectralstatisticalparametersareperiodicfunctionsoflincsassociatedwiththesigmacluprateinSCFmaybetiiiie[1][2][7].Similarly.aprocess.s

3、ayx(r)issaidtobecomipted.TheuiostgeneralmeasurementsofSCFarecyclostationaryinthewidesenseifitsmeanandbasedonaveragemethodlodiminishtheeffectofnoise.autocorrelationareperiodicfunctions.Inotherwords.Herethenoise'scontributionisdiscussed.andanevithefollowingequations[l][3

4、]iuethodtotheestimationofparametersofmodulatedT?I>(/+T)=17Ir(t)(1)sigiralsisbroughtfonyard.TT7R,JI+T+I-,I+T--I=R,(I+;,~-;)(2)22i.'.Keywords:SpectralCorrelation.Qclostationay.aresatisfiedforsomeperiod7#0.whereAutocorrelation.WhiteGaussianNoise7TR,(r+-,I--)=E{.x(I+I),*(,

5、-5);(3)22&21.IntroductionandhereE{.}denotestheexpectationoperation..Incouuiiunicationarea.telemety.radar.andsonar.Rx(t+r12,r-dZ).whichisafunctionofhvopcriodicityarisesfromsampling.scanning.modulating.independentvariables.tandr.isperiodicintwithperiodnmltiplexing.andcod

6、ingoperations.ThespectralTforeachvalueofT.ItisassunedthattheFouricr.seriescorrelationfunction(SCF)iscoilsideredanefficienttoolrepresentationforthisperiodicfunctionconverges.soloranalyzingthosesignalsespeciallyinthesignalthatR,canbeexpressedasdctcction.parameterestimati

7、on.andmodulationmodeidentificationandclassfication[I1UsingSCF.somecharactersofthecyclostationaywhere{R,"}denotestheFouriercoeficienls.sigiuilcanbeexhibitcdclearly.ButinlowSNRconditions.theperformanceofSCFwillbecomeworse.becausethespectrumlinesassociatedtosomeimportantp

8、iiraiueterssuchascarrierfrequencyarewhelmedbyR:(r)iscalledcyclicautocorrelation(CA)thoseassociatedtonoise.However.som