% 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))
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)
function ms_error=MMSE_MSE_calc(X,H,Y,Rgg,variance)%This function generates mean squared error for the the MMSE estimator..
%EVALUATION OF Hmmse
%Hmmse=F*Rgg*inv(Rgy)*Y
u=rand(64,64)
F=fft(u)*inv(u)%The 64 X 64 twiddle factor matrix..
I=eye(64,64)
Rgy=Rgg * F'* X'
Ryy=X * F * Rgg * F' *X' + variance * I
for i=1:64
yy(i,i)=Y(i)
end
Gmmse=Rgy * inv(Ryy)* Y
Hmmse=fft(Gmmse)
ms_error_mat=mean(((abs(H)-abs(Hmmse))/abs(H)).^2)
for i=1:64
if(ms_error_mat(i)~=0)
ms_error=ms_error_mat(i)
end
end
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