lms.rar_LMS adaptive_adaptive equalizer_adaptive filter_lms_tran

%********************************************************************************* % LMS ADAPTIVE TRANSVERSAL FILTER EQUALIZER % % % % This is MATLAB code for a variable order LMS Adaptive % Transversal Filter Equalizer. The model includes: % % (1) Variable length (seqlen) Pseudorandom symbol generator with % binary-to-real symbol conversion % (2) Variable-order Transversal filter channel model % synthesized via shift register ak and channel % coefficient vector pk % (3) Additive gaussian noise component z1 with S/N % compensation (SNR) % (4) Variable-order Transversal filter equalizer model % synthesized via shift register rk and equalizer % coefficient vector ck % (5) Output symbol delay compensation (delay1:channel, % delay2:equalizer) % (6) Ensemble averaging option,M (limits iteration size) % % This code was generated using the student edition of MATLAB version 4 % and therefore the number of iterations was limited due primarily % to storage vector size limitations. But the number of availble iterations % appears sufficient to model the characterized channel and equalizer % The following plots are generated: % % (1) plot of channel input vs. channel output % (2) plot of channel input vs. equalizer output % (3) plot of mean squared error (ensemble averaged) % (4) plot showing the evolution of equalizer coefficients %********************************************************************************* clear seqlen=500; % length of ensemble sequence M=10; % number of ensembles (2 to 32) pk=[0.25,1,0.3]; % channel coefficient vector (ISI) SNR=500; % symbol to noise ratio desired (5,50,120) comments='pk=[0.25,1,0.3], High SNR'; %--------------------------------------------------------------------------------- % SYMBOL SEQUENCE GENERATOR SR=ones(size(1:14)); SR(9)=0; Xn=zeros(size(1:seqlen)); Ak=zeros(size(1:seqlen)); for n=1:seqlen Xn(n)=xor(SR(14),xor(SR(13),xor(SR(9),SR(11)))); SR(2:14)=SR(1:13); SR(1)=Xn(n); if Xn(n)==0 Ak(n)=-1; else Ak(n)=1; end end %--------------------------------------------------------------------------------- % INITIALIZATION ak=zeros(size(1:length(pk))); % channel shift register ak=ak-1; ck=[1,0,1,1,0,0,1,0,0]; % equalizer coefficient vector (initial) rk=zeros(size(1:length(ck))); % equalizer shift register rk=rk-1; delay1=round(length(ak)/2)-1; % channel delay delay2=round(length(rk)/2)-1; % equalizer delay R2=zeros(size(length(seqlen))); Q2=zeros(size(length(seqlen))); %--------------------------------------------------------------------------------- % LMS MODEL for m=1:M m for k=1:seqlen A=Ak(k); % retrieve symbol ak(2:length(ak))=ak(1:length(ak)-1); ak(1)=A; % shift symbol into channel register r1=conv(ak,pk); % convolve data with channel model r2=r1(round(length(r1)/2)); % correlate channel delay z1=exp(-SNR/20)*randn(1); % compute random noise sample at proper SNR r3=r2+z1; % add noise to channel output R2(k)=r3; % composite channel output R=r3; if k>delay1 past=k-delay1; ER(k)=Ak(past)-r2; % calculate channel error end rk(2:length(rk))=rk(1:length(rk)-1); rk(1)=R; % shift channel output into equalizer register q1=conv(rk,ck); % convolve with equalizer model q2=q1(round(length(q1)/2)); % correlate equalizer delay if q2<0 % slicer q3=-1; else q3=1; end Q2(k)=q2; % equalizer output estimate if k>(delay1+delay2) % calculate delay compensated mean-squared-error past2=k-(delay1+delay2); EQ(k)=Ak(past2)-q2; Q3(k)=Ak(past2)-q3; MSE(k)=EQ(k)^2; Q4(k)=mean(abs(Q3(k)^2)); CC(k,:)=ck; egn=eig(rk.'*rk); % compute gradient, stepsize, and new equalizer emax=max(egn); % coefficient vector beta=2/(10*emax); cnxt=((eye(length(rk))-beta*rk.'*rk)*ck.')'+beta*Ak(past2)*rk; chng=abs(cnxt-ck); ck=cnxt; % update equalizer coefficient vector end end MSEE(m,:)=MSE; end MSEEE=mean(MSEE); % PLOTS figure; subplot(1,2,1); orient landscape; plot(R2,Ak); grid on; axis([-10,10,-2,2]); xlabel('Channel Output'); ylabel('Channel Input'); title('Channel Input vs. Channel Output'); gtext(comments); subplot(1,2,2); orient landscape; plot(Q2,Ak); grid on; axis([-10,10,-2,2]); xlabel('Equalizer Output'); ylabel('Channel Input'); title('Channel Input vs. Equalizer Output'); figure; orient landscape; plot(MSEEE); grid on; axis auto; xlabel('Iteration Index'); ylabel('Mean Squared Error'); title('Mean Squared Error vs. Iteration'); gtext(comments); figure; orient landscape; plot(CC); grid on; xlabel('Iteration Index'); ylabel('Equalizer Coefficient Values'); title('Evolution of Equalizer Coefficients'); gtext(comments);