%------------------------------------------
% 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
MMSE=0; % estimation technique
Nsc=64; % Number of subcarriers
Ng=16; % Cyclic prefix length
SNR_dB=[0 5 10 15 20 25 30 35 40]; % Signal to noise ratio
Mt=2; % Number of Tx antennas
Mr=2; % Number of Rx antennas
pilots=[1:Nsc/Ng:Nsc]; % pilot subcarriers
DS=5; % Delay spread of channel
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);
end
MEE1=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);
end
%plot(SNR_dB,10*log10(MEE1),'b');
%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=5;
% i=1;
figure(1);
plot([0:length(H_act)-1],abs(H_act)),grid;
figure(2);
plot([0:length(H_est1)-1],abs(H_est1)),grid;
figure(3);
plot([0:length(H_est2)-1],abs(H_est2));grid;
figure(4);
plot([0:length(error1)-1],error1),grid;
figure(5);
plot([0:length(error2)-1],error2),grid;
%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);
