%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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..
u=rand(64,64);
F=fft(u)*inv(u);% 'F' is the twiddle factor matrix..

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%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;%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;
%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);
ls_mse_ave=mean(ls_mse);
%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');