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1、ANovelVariableStepSizeLMSAdaptiveFilteringAlgorithmYiSun,RuiXiao,Liang-RuiTang,andBingQiSchoolofElectricandElectronicEngineeringNorthChinaElectricPowerUniversityBeijing,China,102206QIBing2011@yeah.netAbstract.ThispaperproposesanovelvariablestepsizeLMSadaptivefilteringalgor
2、ithm.Thealgorithmisestablishedbasedonnonlinearrelationshipbetweenstepanderrorsignalinhyperbolictangentfunction.Thestepisadjustedbytheautocorrelationvalueoftheerrorsignalwhichisonlyinfluencedbytheinputsignals.Sothisalgorithmcanaccuratelyreflecttheadaptivestateandmaketheweig
3、htvectorapproachthebestvalue.Thealgorithmnotonlyperformsfasterinconvergencespeedandtrackingspeed,butalsohasbettersteady-stateperformanceeveninlowsignaltonoiseratio(SNR)environment.Theoreticalanalysisandcomputersimulationshowthatthisalgorithmoutperformedtheotheralgorithmsde
4、scribedinthisarticle.Keywords:variablestepsize,leastmeansquares(LMS)algorithm,hyperbolictangentfunction,autocorrelationvalue.1IntroductionAdaptivefilteringtechniquesarewidelyusedinradarcommunications,signalprocessing,adaptiveequalization,adaptivenoisecancellation,smartante
5、nnasandotherfields[1].Theminimummeansquareerror(leastmeansquares,LMS)algorithmiswidelyusedbecauseofitssimplestructure,goodrobustnessandeasyimplementation.However,itcannotovercomethecontradictionbetweenconvergencespeedandsteady-stateerror.Althoughtheconvergenceratewillimpro
6、vewhenthestepsizegetsbiggerundertheconvergencecondition,thesteady-stateerrorwillalsoincrease.Onthecontrary,thestabilitystateerrorwillreducewhileslowingtheconvergencerate[2].Recentresearchfocusesonhowtogetsmallsteady-stateoffsetwhilemaintainingtheconvergencespeedandtracking
7、speed.Someimprovementmethodshavebeenpresentedinresponsetotheseproblems.Ref.[3]proposedavariablestepsizeLMSalgorithm,thestepdecreasedwiththeincreasednumberofiterations.Thealgorithmachievedsmallersteady-statemisadjustmentnoise,butdidnothavetheabilitytotracktime-varying.Ref.[
8、4]gaveavariablestepsizeLMSalgorithm(SVSLMS)basedontheSigmoidfunction.Itcangetfasterconver
