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1220023()JOURNALOFGUANGZHOUUNIVERSITY(NaturalScienceEdition)Vol.1No12Mar.2002:1671-4229(2002)02-0044-07,(,510405):,.:;LMS;RLS;;;;QR:TN911.72:A130,..,,,.,,,,.,..Volterra..,,..1.1Fig.1Adaptivefilterscheme.W(n)n,x(n)=[x(n),x(n-1),,x(n-L+1)]Tn,d(n),v(n),e(n),L.,[1]:(LMS)(RLS).,LMSE[e2(n)].,RLSW(n)J(n)=ni=1n-i|e(i)|2.,01.,.22.1WidrowHoff(LMS),.(LMS):e(n)=d(n)-XT(n)W(n),W(n+1)=W(n)+2e(n)X(n).:2001-10-08;:2001-12-07:(1957-),,;:.©1995-2006TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.:W(n)n,X(n)n,d(n),v(n),e(n),L,.LMS:01/max,max..[1,2](LMS).,.v(n),.,..,.,.R.D.Gitlin[3],(n)n.Yasukawa[4]e(n).Gitlin[5].[6],e(n)x(n).[7],L.E-LMS,.,[7].,,;,v(n),.,SigmoidLMS(SVSLMS),e(n)Sigmoid:(n)=(1/(1+exp(-|e(n)|))-0.5)..,Sigmoid,e(n),,SVSLMS,.[8],e(n):(n)=(1-exp(-|e(n)|2)),,0,0.Sigmoid,e(n),Sigmoid.[2,6,7].2.2RLSLMS,,.,RLSW(n)J(n)=ni=1n-i|e(i)|2.RLSRxx(n),,.,RLS,,;Rxx(n),[1].RLS,RLS,RLS.RLS(FastRLS)[9,10],(FastRecur2siveLeastSquaresLattice)[11].RLS,.RLSRLS,RLSRLS.FIR.,FIR,,.,,,.RLS,.RLSRLS,.RLSRLS.RLSRLS,LMS.[11]RLS,T(n),,,,.542:©1995-2006TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.2.3,LMS,LMS.,LMS.,,.,Dentino1979[12],,.Narayan[13].:1),.2).3).:x(n)=[x(n),x(n-1),,x(n-N+1)]T,T:X(n)=Tx(n),TNN,[14]HartlyWalsh-Hadamard.:W(n)=Tw(n);:y(n)=WT(n)X(n);:e(n)=d(n)-y(n);:W(n+1)=W(n)+2e(n)p-1(n)X(n),P(n)=diag[P(n,0)P(n,1)P(n,N-1)],P(n,l)=P(n-1,l)+(1-)XT(n,l)X(n,l)l=0,1,,N-1.2=P(n),:W(n+1)=W(n)+2e(n)-2X(n).[15].,,[1621],:[19,20],,;[1618,21],,,.2.4K.OzekiT.Umeda[21],(NLMS).LMSRLS,RLS.(NLMS)LMS,NLMSLMS,.NLMS,P,:Y(k)=XT(k)[W(k-1)+W(k-1)],:Y(k)=[y(k),y(k-1),,y(k-P+1)];X(k)=[x(k),x(k-1),,x(k-P+1)].W(k-1),,[22,23]:e(k)=Y(k)-XT(k)W(k-1);g(k)=[XT(k)X(k)+I]-1e(k);W(k)=W(k-1)+W(k-1)=W(k-1)+X(k)g(k).(P+1)N+O(P3),RLS,NLMS.Gay[24,25].,[26],.,,.,Douglas[27],,.2.5RLS,,.,[2];,,.RLSRLS,.[28]RLS,RLS,RLS.Alan[29],,,.2.664()1©1995-2006TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.:,R(n),,.[3033],,[34,35].:,,,.,,;.,.,Gilloire[30,31],Peraglia[33]..,,,.,:,;,,.,[36],.,Deleon[36],,,MultirateReoeatingMethod,,.[37].,,.2.7QR[2]QR.QRQ,R.QRGivens,,.QR:1)QR-RLS;2)ExtendedQR-RLS;3)InverseQR-RLS.QR,,.QR,.QR,.2.8,,:[3840]LMF(RLF)[41,42]Leaky-LMS[43,44].,LMS(NLMS),,[3840],,,.:PeriodicLMS[38],M-MaxNLMS[39]MaxNLMS[40].:PeriodicLMS:Wi(n+1)=Wi(n)+elxl-i+1(n+i)mod=Oandl=N[n|N]Wi(n)otherwiseM-MaxNLMS:Wi(n+1)=Wi(n)+e(n)x(n-i+1)XT(n)X(n)iMmax|x(n-i+1)|,i=1,,LWi(n)otherwiseMaxNLMS:Wi(n+1)=Wi(n)+e(n)x(n-i+1)|x(n-i+1)|=max|x(n-j+1)|,j=1,,LWi(n)otherwise,LMSE[e2(n)];RLSJ(n)=742:©1995-2006TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.ni=1n-i|e(i)|2.[41,42]E[e4(n)]LMFni=1n-i|e(i)|4RLF;LMFRLFLMSRLS.Zerguine[42]LMS-LMF,.Leaky-LMS[43]:W(n+1)=(1-)W(n)+e(n)X(n),e(n)=d(n)-WT(n)X(n).,.Leaky-LMS.Mayyas[44],Leaky-LMS.3..,,.RLS,RLS.,.LMSRLS.RLSRLS.,,,.QR.,,,.,.,Volterra,,[45,46].:[1],.[J].,1997,12(3):171-194.QINJing-fan,OUYANGJing-zhen.Anewvariablestepsizeadaptivefilteringalgorithm[J].DataCollectingandProcessing,1997,12(3):171-194.[2]SHaykin.Adaptivefilteringtheory(3rdEdition)[M].Prentice-Hall,1985.[3]GitlinRD,WeinsteinSD.Onthedesignofgradientalgorithmsfordigitallyimplementedadaptivefilters[J].IEEETransonCT,1973(2):125-136.[4]YasukawaH,ShimadaS,FurukrawaI,etal.Acousticechocancellerwithhighspeechquality[J].ICASSP87:2125-2128.[5]GitlinRD,WeinsteinSD.Theeffectsoflargeinterferenceonthetrackingcapabilityofdigitallyimplementedechocancellers[J].IEEETransonCOM,1978(6):833-839.[6],.[J].,1990,18(4):63-69.YEHua,WUBai-xiu.Astudyofvariablestepsizeadaptivefilteringalgorithms[J].ACTAElectronicaSinica,1990,18(4):63-69.[7],.LMS[J].,1994,22(1):55-60.WUGuang-bi,ZHULing-yu.AvariablestepsizeLMSadaptivefilteringalgorithm[J].ACTAElectronicaSinica,1994,22(1):55-60.[8],.LMS[J].,2001,29(8):1094-1097.GAOYing,XIESheng-li.AvariablestepsizeLMSadaptivefilteringalgorithmanditsanalyses[J].ACTAElectronicaSinica,2001,29(8):1094-1097.[9]JMCioffi,TKailath.Windowedfasttransversalfiltersforrecursiveleastsquaresadaptivefiltering[J].IEEETrans.onASSP.1985,33(3):607-625.[10]GCarayannis,DGManolakis,NKalouptsidis.Afastsequentialalgorithmforleast-squaresfilteringandprediction[J].IEEETrans.ASSP,1983,31(6):1394-1402.[11].[J].,2001,15(2):32-34.GAOYing.Anadaptivefilteringalgorithmbasedonleastsquarescriterion[J].JournalofGuangzhouUniversity,2001,15(2):32-84()1©1995-2006TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.