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7Â¥2014-05-22 23:16:16
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mvpyqz

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% CRB_final

%CRB CALCULATION

clear all
nFFT        = 64; % fft size
MSym        = 64; % lenght of each OFDM block
nb      = 150; % number of symbols
montcarlo=10;
EsN0dB      = [-10:5:25]; % bit to noise ratio



% Discrete Fourier Transform Matrix F
for iii=1:nFFT;
    for jjj=1:nFFT;
        F(iii,jjj)=(1/sqrt(nFFT))*exp(j*(2*pi*(iii-1)*(jjj-1))/nFFT);
    end;
end;
  
% multipath channel
nTap = 3;
k=0:2;
multipath=exp(-(k)/10);
multipath=multipath/sum(multipath);

for k=1:3
    ht(:,k)=(randn(1,1)+ sqrt(-1)*randn(1,1))*sqrt(0.5)*sqrt(multipath(k)); %% rayleigh fading  
end
   
% computing and storing the frequency response of the channel, for use at recevier
hF =sqrt(nFFT)*F(:,1:nTap)*(ht.');
hF_diag=diag(hF);
  
% producing matrix Hh , circulant channel matrix
htt=[ht(1, zeros(1,nFFT-nTap)];
for i=1:nFFT
    for j=1:nFFT
        H_cir(i,j)=htt(mod((i-j),nFFT)+1);
    end
end


nt = (1/sqrt(2))*[randn(MSym,nb)+ sqrt(-1)*randn(MSym,nb)];
         

%Precoding
     
t=nFFT/4;
for m=1:nFFT
    for q=1:nFFT
        if (m==q)&(m==t)
            W(m,q)=2;
        elseif m==q
               W(m,q)=1;
        elseif q==t
                W(m,q)=1;
        else
                W(m,q)=0;
        end
     end
end
     
P=W*(W');
% noise production

  b =(1/sqrt(2))*[randn(1,MSym)+ sqrt(-1)*randn(1,MSym)];
         moy=mean(b);
         bc = b - moy;
         varb = (1/(MSym))*trace((diag(bc)*(diag(bc))'));
%%%%%%%%%%%%%%%%%%%%%%         
         
Rs=1;     
for ii = 1:length(EsN0dB)  
        
         noise = sqrt(((0.5*10^(-EsN0dB(ii)/10))/varb))* conj(bc');
         Var = std(noise)^2;         
         
    Rx=Rs* H_cir*(F')*P*F*( H_cir')+Var*eye(nFFT);
    for l=1:nTap  
        for i=1:nFFT
            for j=1:nFFT
                if (mod((i-j),nFFT))==(l-1)
                    Hl(i,j)=1;
                else
                    Hl(i,j)=0;
                end
            end
        end
        Al=Rs*(Rx^(-.5))*Hl*(F')*P*F*(hF_diag')*(Rx^(-.5));
        G1(:,l)=reshape((Al+(Al')),[],1);
        G2(:,l)=reshape((sqrt(-1)*Al-sqrt(-1)*(Al')),[],1);  
        
    end
   
    v=reshape(((Rx^(-.5))*H_cir*(F')*P*F*(H_cir')*(Rx^(-.5))),[],1);
    u=reshape((Rx^(-1)),[],1);
    G=[G1 G2];
    delta=[u v];
    P_delta=eye(nFFT*nFFT)-delta*(((delta')*delta)^(-1))*(delta');
    CRB=(1/150)*pinv((G')*P_delta*G);
    CRB_plot(ii)=(trace(CRB));
      
end

plot(EsN0dB,CRB_plot)
axis([-10 25 10^(-5) 10^(-1)]);

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27Â¥2014-05-22 23:23:39
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pjstang

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