CombinedAdaptiveFilterwithLMS-BasedAlgorithms´Abstract:Acombinedadaptivefilterisproposed.ItconsistsofparallelLMS-basedadaptiveFIRfiltersandanalgorithmforchoosingthebetteramongthem.Asacriterionforcomparisonoftheconsideredalgorithmsintheproposedfilter,wetaketheratiobetweenbiasandvarianceoftheweightingcoefficients.Simulationsresultsconfirmtheadvantagesoftheproposedadaptivefilter.Keywords:Adaptivefilter,LMSalgorithm,Combinedalgorithm,Biasandvariancetrade-off1．IntroductionAdaptivefiltershavebeenappliedinsignalprocessingandcontrol,aswellasinmanypracticalproblems,[1,2].Performanceofanadaptivefilterdependsmainlyonthealgorithmusedforupdatingthefilterweightingcoefficients.ThemostcommonlyusedadaptivesystemsarethosebasedontheLeastMeanSquare(LMS)adaptivealgorithmanditsmodifications(LMS-basedalgorithms).TheLMSissimpleforimplementationandrobustinanumberofapplications[1–3].However,sinceitdoesnotalwaysconvergeinanacceptablemanner,therehavebeenmanyattemptstoimproveitsperformancebytheappropriatemodifications:signalgorithm(SA)[8],geometricmeanLMS(GLMS)[5],variablestep-sizeLMS(VSLMS)[6,7].EachoftheLMS-basedalgorithmshasatleastoneparameterthatshouldbedefinedpriortotheadaptationprocedure(stepforLMSandSA;stepandsmoothingcoefficientsforGLMS;variousparametersaffectingthestepforVSLMS).Theseparameterscruciallyinfluencethefilteroutputduringtwoadaptationphases:transientandsteadystate.Choiceoftheseparametersismostlybasedonsomekindoftrade-offbetweenthequalityofalgorithmperformanceinthementionedadaptationphases.WeproposeapossibleapproachfortheLMS-basedadaptivefilterperformanceimprovement.Namely,wemakeacombinationofseveralLMS-basedFIRfilterswithdifferentparameters,andprovidethecriterionforchoosingthemostsuitablealgorithmfordifferentadaptationphases.ThismethodmaybeappliedtoalltheLMS-basedalgorithms,althoughwehereconsideronlyseveralofthem.Thepaperisorganizedasfollows.AnoverviewoftheconsideredLMS-basedalgorithmsisgiveninSection2.Section3proposesthecriterionforevaluationandcombinationofadaptivealgorithms.Simula