LS_estimation.rar_OFDM estimation_matlab LS estimation_matlab es

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Author: Vinay Uday Prabhu % E-mail: vinay_u_prabhu@yahoo.co.uk % Function: Comparison of the performances of the LS and the MMSE channel estimators % for a 64 sub carrier OFDM system based on the parameter of Symbol Error Rate % Assumptions: The channel is assumed to be g(t)=delta(t-0.5 Ts)+delta(t-3.5 Ts) % {Fractionally spaced} %For more information on the theory and formulae used , please do refer to the paper On %"Channel Estimation In OFDM systems" By Jan-Jaap van de Beek, Ove Edfors, Magnus Sandell % Sarah Kate wilson and Petr Ola Borjesson In proceedings Of VTC'95 Vol 2 pg.815-819 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clc; clear all; %Generation of a naive training sequence.. %Assuming BPSK modulation ...symbols:+1/-1 X=zeros(64,64); d=rand(64,1); for i=1:64 if(d(i)>=0.5) d(i)=+1; else d(i)=-1; end end for i=1:64 X(i,i)=d(i); end %Calculation of G[The channel Matrix] %The channnel is... tau=[0.5 3.5];%The fractionally spaced taps.. %Generation of the G matrix... for k=1:64 s=0; for m=1:2 s=s+(exp(-j*pi*(1/64)*(k+63*tau(m))) * (( sin(pi*tau(m)) / sin(pi*(1/64)*(tau(m)-k))))); %Go through the above cited paper for the theory behind the formula end g(k)=s/sqrt(64); end G=g';%Thus, the channel vector is evaluated.. H=fft(G);% In the freq domain.. XFG=X*H; % i.e. it is the input multiplied by the channel matrix. So it is the output pilot without the addition of awgn noise n1=ones(64,1); n1=n1*0.000000000000000001i;%Just to ensure that the function awgn adds 'complex gaussian noise'.. noise=awgn(n1,8);%Assuming the 'channel learning' is happening at 8db.. variance=var(noise); N=fft(noise); Y=XFG+N; % so it becomes the output pilot matrix of the channel. for the notation XFG see the above reffered paper %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Evaluation of the autocovariance matrix of G-Rgg %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% gg=zeros(64,64); for i=1:64 gg(i,i)=G(i); end gg_myu = sum(gg, 1)/64; gg_mid = gg - gg_myu(ones(64,1),:); sum_gg_mid= sum(gg_mid,1); Rgg = (gg_mid' * gg_mid- (sum_gg_mid' * sum_gg_mid) / 64) / (64 - 1); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %OK..Now that we have the ingredients ready,lets move on and evaluate the estimated channels by the %use of the LS and the MMSE algorithms.. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %EVALUATION OF Hls %Hls=inv(X)*Y; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% H_ls=(inv(X)) * Y; % i.e. x-1y i.e. x inverse y , v r basically implementing LS estimation technique which is equivalent to zero forcing technique Hls=zeros(64,64); for i=1:64 Hls(i,i)=H_ls(i); end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %EVALUATION OF Hmmse %Hmmse=F*Rgy*inv(Ryy)*Y; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% u=rand(64,64); F=fft(u)*inv(u);%The 64 X 64 twiddle factor matrix.(twiddle factor in FFT algo is a trignometric constt coefficient which is when multiplied with a number produces it FFT). I=eye(64,64); Rgy=Rgg * F'* X'; % see paper Ryy=X * F * Rgg * F' *X' + variance * I; % see paper for i=1:64 yy(i,i)=Y(i); end Gmmse=Rgy * inv(Ryy)* Y; % see paper H_mmse=fft(Gmmse); % see paper for i=1:64 Hmmse(i,i)=H_mmse(i); end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Fine..the channels have been estimated , now is the time for real time simulations.. for n=1:6 SNR_send=5*n; error_count_ls=0;%Clear the error_count.. error_count_mmse=0;%Clear the error_count.. %Sending around 1000 data vectors through the channel %Roughly like 1000 simulations per SNR reading.. for c=1:1000 %Generate Random Data[i/p matrix..] X=zeros(64,64); d=rand(64,1); for i=1:64 if(d(i)>=0.5) d(i)=+1; else d(i)=-1; end end for i=1:64 X(i,i)=d(i); end XFG=X*H;%Let it go through the actual channel... n1=ones(64,1); n1=n1*0.000000000000000001i;%Just to ensure that the function awgn adds 'complex gaussian noise'.. noise=awgn(n1,SNR_send); variance=var(noise); N=fft(noise); Y=XFG+N;%o/p got by the receiver... %The receiver begins.... %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % I:LS ESTIMATOR BASED RECEIVER: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %I(k) represents the decision matrix.. I=inv(Hls)* Y; for k=1:64 if(real(I(k))>0)%Putting it through a slicer(decision maker, perhapes) I(k)=1; else I(k)=-1; end end for k=1:64 if(I(k)~=d(k)) error_count_ls=error_count_ls+1; end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % I:MMSE ESTIMATOR BASED RECEIVER: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %I(k) represents the decision matrix.. I=inv(Hmmse)* Y; for k=1:64 if(real(I(k))>0)%Putting it through a slicer I(k)=1; else I(k)=-1; end end for k=1:64 if(I(k)~=d(k)) error_count_mmse=error_count_mmse+1; end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% end%End of the 1000 run simulation.. ser_ls(n)=error_count_ls/64000; ser_mmse(n)=error_count_mmse/64000; ser_ls ser_mmse SNR(n)=SNR_send; end; %Now just the display part..... semilogy(SNR,ser_mmse,'k-'); grid on; xlabel('SNR in DB'); ylabel('Symbol Error Rate'); title('PLOT OF SNR V/S SER FOR AN OFDM SYSTEM WITH MMSE/LS ESTIMATOR BASED RECEIVERS'); hold on; % hold on draws the next figure on the same graph semilogy(SNR,ser_ls,'b*'); semilogy(SNR,ser_ls,'b-'); semilogy(SNR,ser_mmse,'kv'); grid on; xlabel('SNR in DB'); ylabel('Symbol Error Rate'); title('PLOT OF SNR V/S SER FOR AN OFDM SYSTEM WITH MMSE/LS ESTIMATOR BASED RECEIVERS');