SQJHC.rar_LMS MATLAB_nlms

%FQRRLS3T Problem 3.4 % % 'ifile.mat' - input file containing: % I - members of ensemble % K - iterations % s - deterministic part of signal to predict % sigman - standard deviation of noise in signal to predict % ND - delayer order % N - filter order % lambda - forgetting factor % % 'ofile.mat' - output file containing: % ind - sample indexes % MSE - mean-square error clear all % clear memory load ifile; % read input variables LD=ND+1; % delayer length L=N+1; % filter length LD1=LD+1; L1=L+1; L2=L1+1; % auxiliary constants MSE=zeros(K,1); % prepare to accumulate MSE*I for i=1:I, % ensemble D=zeros(LD,1); % initial delayer memory X=zeros(L,1); % initial memory n=randn(K,1)*sigman; % noise in signal to predict xq2=zeros(L,1); dq2=zeros(L,1); Qthetaf=sparse(eye(L2)); for l=1:L, Qthetabp(:,((1:L1)+(l-1)*L1))=sparse(eye(L1)); Qtheta(:,((1:L1)+(l-1)*L1))=sparse(eye(L1)); end d=s(1)+n(1); D=[d D(1:ND)]; % initial values normef=abs(D(LD)); for k=1:LD, % iterations d=s(k+1)+n(k+1); % sample of signal to predict D=[d D(1:ND)]; % new delay vector x=D(LD); % new input sample AUX=[x lambda^(1/2)*xq2]; for l=1:L, AUX=Qtheta(:,((1:L1)+(l-1)*L1))*AUX; end efq1=AUX(1); xq2=AUX(2:L1); aux=normef; normef=sqrt(lambda*aux^2+efq1^2); Qthetaf(1,1)=1; Qthetaf(1,L2)=0; Qthetaf(L2,1)=0; Qthetaf(L2,L2)=1; c=[1 zeros(L,1)]; for l=L:-1:1, c=Qthetabp(:,((1:L1)+(l-1)*L1))*c; end ce=[0 c]; for l=1:L, ce(1:L1)=Qtheta(:,((1:L1)+(l-1)*L1))*ce(1:L1); end ce=Qthetaf*ce; c=ce(2:L2); alpha=c(1); for l=1:L, aux=alpha; alpha=sqrt(aux^2+(c(l+1))^2); Qthetabp(1,1+(l-1)*L1)=1; Qthetabp(1,l+1+(l-1)*L1)=0; Qthetabp(l+1,1+(l-1)*L1)=0; Qthetabp(l+1,l+1+(l-1)*L1)=1; end AUX=[1 zeros(L1,1)]; for l=1:L, AUX(1:L1)=Qtheta(:,((1:L1)+(l-1)*L1))*AUX(1:L1); end AUX=Qthetaf*AUX; re=AUX(2:L2); for l=1:L, re=(Qthetabp(:,((1:L1)+(l-1)*L1)))'*re; end r=re(2:L1); gammap=1; for l=1:L, aux=gammap; gammap=sqrt(aux^2-(r(l))^2); Qtheta(1,1+(l-1)*L1)=1; Qtheta(1,l+1+(l-1)*L1)=0; Qtheta(l+1,1+(l-1)*L1)=0; Qtheta(l+1,l+1+(l-1)*L1)=1; end X=[x X(1:N)]; % new input vector AUX=[d lambda^(1/2)*dq2]; for l=1:L, AUX=Qtheta(:,((1:L1)+(l-1)*L1))*AUX; end eq1=AUX(1); dq2=AUX(2:L1); ep=eq1/gammap; % error sample MSE(k+1)=MSE(k+1)+ep^2; % accumulate MSE*I end for k=LD1:(K-1), % iterations d=s(k+1)+n(k+1); % sample of signal to predict D=[d D(1:ND)]; % new delay vector x=D(LD); % new input sample AUX=[x lambda^(1/2)*xq2]; for l=1:L, AUX=Qtheta(:,((1:L1)+(l-1)*L1))*AUX; end efq1=AUX(1); xq2=AUX(2:L1); aux=normef; normef=sqrt(lambda*aux^2+efq1^2); costhetaf=lambda^(1/2)*aux/normef; sinthetaf=efq1/normef; Qthetaf(1,1)=costhetaf; Qthetaf(1,L2)=-sinthetaf; Qthetaf(L2,1)=sinthetaf; Qthetaf(L2,L2)=costhetaf; c=[1 zeros(L,1)]; for l=L:-1:1, c=Qthetabp(:,((1:L1)+(l-1)*L1))*c; end ce=[0 c]; for l=1:L, ce(1:L1)=Qtheta(:,((1:L1)+(l-1)*L1))*ce(1:L1); end ce=Qthetaf*ce; c=ce(2:L2); alpha=c(1); for l=1:L, aux=alpha; alpha=sqrt(aux^2+(c(l+1))^2); costhetabp=aux/alpha; sinthetabp=-c(l+1)/alpha; Qthetabp(1,1+(l-1)*L1)=costhetabp; Qthetabp(1,l+1+(l-1)*L1)=sinthetabp; Qthetabp(l+1,1+(l-1)*L1)=-sinthetabp; Qthetabp(l+1,l+1+(l-1)*L1)=costhetabp; end AUX=[1 zeros(L1,1)]; for l=1:L, AUX(1:L1)=Qtheta(:,((1:L1)+(l-1)*L1))*AUX(1:L1); end AUX=Qthetaf*AUX; re=AUX(2:L2); for l=1:L, re=(Qthetabp(:,((1:L1)+(l-1)*L1)))'*re; end r=re(2:L1); gammap=1; for l=1:L, aux=gammap; gammap=sqrt(aux^2-(r(l))^2); costheta=gammap/aux; sintheta=r(l)/aux; Qtheta(1,1+(l-1)*L1)=costheta; Qtheta(1,l+1+(l-1)*L1)=-sintheta; Qtheta(l+1,1+(l-1)*L1)=sintheta; Qtheta(l+1,l+1+(l-1)*L1)=costheta; end X=[x X(1:N)]; % new input vector AUX=[d lambda^(1/2)*dq2]; for l=1:L, AUX=Qtheta(:,((1:L1)+(l-1)*L1))*AUX; end eq1=AUX(1); dq2=AUX(2:L1); ep=eq1/gammap; % error sample MSE(k+1)=MSE(k+1)+ep^2; % accumulate MSE*I end end ind=0:(K-1); % sample indexes MSE=MSE/I; % calculate MSE save ofile ind MSE; % write output variables