%------------------------------------------% EE359 final project, Fall 2002% Channel estimation for a MIMO-OFDM system% By Shahriyar Matloub               %------------------------------------------clear all;%close all;i=sqrt(-1);Rayleigh=1;AWGN=0;                             % for AWGN channel 加性高斯白噪聲 AWGN(Additive White Gaussion Noise) MMSE=0;% estimation technique最小均方誤差（MMSE）準測是求所接受到的信號和所發(fā)送的信號之差的平方最小，所以有時會在接收信號前先加一個接受濾波器以使得誤差的平方最小，相應(yīng)就得到接受濾波器的最優(yōu)值Nsc=64;                             % Number of subcarriers載波數(shù)Ng=16;                              % Cyclic prefix length 循環(huán)前綴長度SNR_dB=[0 5 10 15 20 25 30 35 40];  % Signal to noise ratio信噪比Mt=2;                               % Number of Tx antennas發(fā)射天線數(shù)Mr=2;                               % Number of Rx antennas接收天線數(shù)pilots=[1:Nsc/Ng:Nsc];              % pilot subcarriers 導(dǎo)頻載波DS=5;                              % Delay spread of channel 信道時延?iteration_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);