mse_compare.m

channel estimation using Ls and MMSE algorithms also calculates the Mean square error and SER

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%   Author:      Vinay Uday Prabhu
%   E-mail:      [e-mail]
%   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 Mean square error
%  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
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clc;
clear all;
%Generation of a naive training sequence..
%Assuming BPSK modulation ...symbols:+1/-1
X=zeros(64,64);
dd=randint(64,1);% can be replaced by randint(yasser)
%       for i=1:64
%        if(d(i)>=0.5)
%            d(i)=+1;
%        else
%            d(i)=-1;
%        end
%     end
d=2*dd-1;
 for i=1:64
     X(i,i)=d(i);
 end%convert it do a diagonal matrix(yasser)
%Calculation of G[The channel Matrix]
 %The channnel is... 
  tau=[0.5 3.5];%The fractionally spaced taps..(question 1 of 4 what are these ????????????? why two values for taum)
%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..%question 2 of 4 ?????????????(why did he get the inverse transpose????????)in the paper without inverse
H=fft(G);% In the freq domain..
u=rand(64,64);
F=fft(u)*inv(u);% 'F' is the twiddle factor matrix..(checked and working(yasser))

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% Evaluation of the autocovariance matrix of G-Rgg
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gg=zeros(64,64);
for i=1:64
    gg(i,i)=G(i);
end
gg_myu = sum(gg, 1)/64;    %question 3 of 4??????????????????????????????????????????????????  %%(to get the diagonals and put them in a matrix yasser)              
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);

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%Running for a dozen trials to try and average out the results..
for m=1:12
    
for n=1:5

SNR_send=5*n;
XFG=X*H;
n1=ones(64,1);
n1=n1*0.000000000000000001i;
%n1=n1*0.000000000000000001;%Just to ensure that the function awgn adds 'complex gaussian noise'..
noise=awgn(n1,SNR_send);%question 4 of 4 why did he add comples noise???????????????????
variance=var(noise);
N=fft(noise);
Y=XFG+N;
%Evaluating the mean squared error for the LS estimator..
mean_squared_error_ls=LS_MSE_calc(X,H,Y);
%Evaluating the mean squared error for the MMSE estimator..
mean_squared_error_mmse=MMSE_MSE_calc(X,H,Y,Rgg,variance);
SNR(n)=SNR_send;
mmse_mse(m,n)=mean_squared_error_mmse;
ls_mse(m,n)=mean_squared_error_ls;
end;

end;
ls_mse
mmse_mse
mmse_mse_ave=mean(mmse_mse);%to get the mean of the 12 trials
ls_mse_ave=mean(ls_mse);%to get the mean of the 12 trials
%Now just the display part.....
semilogy(SNR,mmse_mse_ave,'k-');
grid on;
xlabel('SNR in DB');
ylabel('mean squared error');
title('PLOT OF SNR V/S MSE FOR AN OFDM SYSTEM WITH MMSE/LS ESTIMATOR BASED RECEIVERS');

hold on;
semilogy(SNR,ls_mse_ave,'b*');
semilogy(SNR,ls_mse_ave,'b-');
semilogy(SNR,mmse_mse_ave,'kv');
grid on;
xlabel('SNR in DB');
ylabel('mean squared error');
title('PLOT OF SNR V/S MSE FOR AN OFDM SYSTEM WITH MMSE/LS ESTIMATOR BASED RECEIVERS');