%------------------------------------------% Channel estimation for a MIMO-OFDM system          %------------------------------------------clear all;%close all;i=sqrt(-1);Rayleigh=1;AWGN=0;                             % for AWGN channel MMSE=0;                             % estimation techniqueNsc=64;                             % Number of subcarriersNg=16;                              % Cyclic prefix lengthSNR_dB=[0 5 10 15 20 25 30 35 40];  % Signal to noise ratioMt=2;                               % Number of Tx antennasMr=2;                               % Number of Rx antennaspilots=[1:Nsc/Ng:Nsc];              % pilot subcarriers DS=5;                              % Delay spread of channeliteration_max=200;%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Channel impulse response %%%%%%%%%%%%%%%%%%%%%%%%%%%%%if (Rayleigh)    N=50;    fm=100;    B=20e3;    fd=(rand(1,N)-0.5)*2*fm;    theta=randn(1,N)*2*pi;    c=randn(1,N);    c=c/sum(c.^2);    t=0:fm/B:10000*fm/B;    Tc=zeros(size(t));        Ts=zeros(size(t));    for k=1:N       Tc=c(k)*cos(2*pi*fd(k)*t+theta(k))+Tc;       Ts=c(k)*sin(2*pi*fd(k)*t+theta(k))+Ts;    end    r=ones(Mt*Mr,1)*(Tc.^2+Ts.^2).^0.5;    index=floor(rand(Mt*Mr,DS)*5000+1);endMEE1=zeros(1,length(SNR_dB));MEE2=zeros(1,length(SNR_dB));for snrl=1:length(SNR_dB)    snrl    estimation_error1=zeros(Mt*Mr,Nsc);    estimation_error2=zeros(Mt*Mr,Nsc);    R1=besselj(0,2*pi*fm*(Nsc+Ng)/B);    sigma2=10^(-SNR_dB(snrl)/10);    aa=(1-R1^2)/(1-R1^2+sigma2);    bb=sigma2*R1/(1-R1^2+sigma2);    for iteration=1:iteration_max        %iteration            if AWGN==1            h=ones(Mt*Mr,1);        else            phi=rand*2*pi;            h=r(index+iteration)*exp(j*phi);            %h=rand(Mt*Mr,DS);            h=h.*(ones(Mt*Mr,1)*(exp(-0.5).^[1:DS]));            h=h./(sqrt(sum(abs(h).^2,2))*ones(1,DS));        end        CL=size(h,2);                                               % channel length        data_time=zeros(Mt,Nsc+Ng);        data_qam=zeros(Mt,Nsc);        data_out=zeros(Mr,Nsc);        output=zeros(Mr,Nsc);        for tx=1:Mt            data_b=0*round(rand(4,Nsc));                                  % data            data_qam(tx,:)=j*(2*(mod(data_b(1,:)+data_b(2,:),2)+2*data_b(1,:))-3)+...            2*(mod(data_b(3,:)+data_b(4,:),2)+2*data_b(3,:))-3;            for loop=1:Mt                 data_qam(tx,pilots+loop-1)=(1+j)*(loop==tx);              % pilots            end            data_time_temp=ifft(data_qam(tx,:));            data_time(tx,:)=[data_time_temp(end-Ng+1:end) data_time_temp];        end            for rx=1:Mr            for tx=1:Mt                output_temp=conv(data_time(tx,:),h((rx-1)*Mt+tx,:));                output(rx,:)=output_temp(Ng+1:Ng+Nsc)+output(rx,:);            end            np=(sum(abs(output(rx,:)).^2)/length(output(rx,:)))*sigma2;            noise=(randn(size(output(rx,:)))+i*randn(size(output(rx,:))))*sqrt(np);            output(rx,:)=output(rx,:)+noise;            data_out(rx,:)=fft(output(rx,:));        end%%%%%%%%%%%%%%%%%%%%%%% Channel estimation %%%%%%%%%%%%%%%%%%%%%%%            H_act=zeros(Mt*Mr,Nsc);        H_est1=zeros(Mt*Mr,Nsc);        H_est2=zeros(Mt*Mr,Nsc);        i=1;        for tx=1:Mt            for rx=1:Mr                H_est_temp=data_out(rx,pilots+tx-1)./data_qam(tx,pilots+tx-1);                %H_est_temp2=aa*abs(H_est_temp1)+bb*abs(H_est2((rx-1)*Mt+tx,:));                h_time=ifft(H_est_temp);                h_time=[h_time zeros(1,Nsc-length(h_time))];                H_est1((rx-1)*Mt+tx,:)=fft(h_time);                H_est2((rx-1)*Mt+tx,:)=((aa*abs(H_est1((rx-1)*Mt+tx,:))+bb*abs(H_est2((rx-1)*Mt+tx,:)))...                    .*H_est1((rx-1)*Mt+tx,:))./abs(H_est1((rx-1)*Mt+tx,:));                if (tx>1)                    H_est1((rx-1)*Mt+tx,:)=[H_est1((rx-1)*Mt+tx,Nsc-tx+2:Nsc) H_est1((rx-1)*Mt+tx,1:Nsc-tx+1)];                    H_est2((rx-1)*Mt+tx,:)=[H_est2((rx-1)*Mt+tx,Nsc-tx+2:Nsc) H_est2((rx-1)*Mt+tx,1:Nsc-tx+1)];                    end                H_act((rx-1)*Mt+tx,:)=fft([h((rx-1)*Mt+tx,:) zeros(1,Nsc-CL)]);                error1=(abs(H_act((rx-1)*Mt+tx,:)-H_est1((rx-1)*Mt+tx,:)).^2);                error2=(abs(H_act((rx-1)*Mt+tx,:)-H_est2((rx-1)*Mt+tx,:)).^2);                %error=(abs(H_act((rx-1)*Mt+tx,:)-H_est((rx-1)*Mt+tx,:)).^2)./(abs(H_act((rx-1)*Mt+tx,:)).^2);                estimation_error1((rx-1)*Mt+tx,:)=estimation_error1((rx-1)*Mt+tx,:)+error1;                                 estimation_error2((rx-1)*Mt+tx,:)=estimation_error2((rx-1)*Mt+tx,:)+error2;                 %subplot(Mt*Mr,3,i),plot([0:Nsc-1],abs(H_act((rx-1)*Mt+tx,:))); i=i+1;                %subplot(Mt*Mr,3,i),plot([0:Nsc-1],abs(H_est((rx-1)*Mt+tx,:))); i=i+1;                %subplot(Mt*Mr,3,i),plot([0:Nsc-1],abs(error)); i=i+1;            end        end      end    estimation_error1=estimation_error1/iteration_max;    estimation_error2=estimation_error2/iteration_max;    %estimation_error=min(estimation_error,10*iteration_max*ones(size(estimation_error)));    %for i=1:Mt*Mr    %    subplot(Mt*Mr,2,2*i-1),plot([0:Nsc-1],estimation_error1(i,:));        %    subplot(Mt*Mr,2,2*i),plot([0:Nsc-1],estimation_error2(i,:));    %end    MEE1(snrl)=sum(sum(estimation_error1))/(Mt*Mr*Nsc);    MEE2(snrl)=sum(sum(estimation_error2))/(Mt*Mr*Nsc);endplot(SNR_dB,10*log10(MEE1));    hold on;plot(SNR_dB,10*log10(MEE2),'r');%H_act=fft([h_zeros(1,Nsc-CL)]).';error1=(abs(H_act-H_est1).^2)./(abs(H_act).^2);error2=(abs(H_act-H_est2).^2)./(abs(H_act).^2);%%%%%%%%%% Plots %%%%%%%%%%fig=4;i=1;subplot(fig,1,i),plot([0:length(H_act)-1],abs(H_act));    i=i+1;subplot(fig,1,i),plot([0:length(H_est1)-1],abs(H_est1));  i=i+1;subplot(fig,1,i),plot([0:length(H_est2)-1],abs(H_est2));  i=i+1;subplot(fig,1,i),plot([0:length(error1)-1],error1);       i=i+1;%subplot(fig,1,i),plot([0:length(error2)-1],error2);