cslmmse.asv

分别给出单天线和多天线下的MIMO－仿真

clc
clear all
Nt = 1; % the number of transmitted antennas
Nr = 1; % the number of transmitted antennas
T=2; % the number of symbol periods
Tp=Nt;
Td=T-Tp;

SNR = 0:5:70; % the system signal-to-noise ratio with dB
snr = 10.^(0.1*SNR); % the signal-to-noise with normal scale
snrp=snr; 

MM=100;    % 1000 channel
NN = 100;% using 10000 Monte-Carlo runs

hm=zeros(Nt*Nr,1);   % channel mean 
hh=eye(Nt*Nr);       % channel covariance
vv=eye(Tp*Nr);
nn=eye(Td*Nr);       % noise covariance
nn_ray=eye(T*Nr);     % rayleigh fading with perfect csi and without training symbol



capa_ray = zeros(1,length(SNR));  % rayleigh fading with perfect csi and without training symbol
A_ray=zeros(T*Nr,T*Nr);   % rayleigh fading with perfect csi and without training symbol

capa1 = zeros(1,length(SNR));  % perfect csi
A10=zeros(Td*Nr,Td*Nr);

capa2 = zeros(1,length(SNR));    % worst case noise lower bound
A20=zeros(Td*Nr,Td*Nr);
AA20=zeros(Td*Nr,Td*Nr);

capa3 = zeros(1,length(SNR));    % inequality lower bound
capa30=zeros(1,length(SNR));
capa300=zeros(1,length(SNR));
A30=zeros(Td*Nr,Td*Nr);
AA30=zeros(Td*Nr,Td*Nr);
aa300=0;

for ii = 1:length(SNR)
waitbar(ii/length(SNR));

      % LMMSE estimator
p=eye(Nt*Nr);       % training symbol
pp=inv(p'*p)*p';    % wei ni 
F=sqrt(snrp(ii))*hh*p'*inv(snrp(ii)*p*hh*p'+vv');
f0=(eye(size(F*pp))-sqrt(snrp(ii))*F*pp)*hm;

for jj=1:MM

Hw=sqrt(1/2)*(randn(Nr*Nt,1) + j*randn(Nr*Nt,1));         % channel 
v=sqrt(1/2)*(randn(Nr*Tp,1) + j*randn(Nr*Tp,1));          % training noise
z=sqrt(snrp(ii))*p*Hw+v;                                        % receive
g=F*z+f0;                                                   % estimation

B=eye(Nt*Nr);
C=inv(eye(Nt*Nr)+snrp(ii)*hh*p'*inv(vv)*p);
d=B*g+C*hm-B*f0;

for kk =1:NN
    
    X_ray =sqrt(1/(2*Nt))* (randn(Nt,T + j* randn(Nt,T));   % rayleigh fading with perfect csi and without training symbol
    XX_ray=kron(X_ray.',eye(Nr)); 
    
    X =sqrt(1/(2*Nt))* (randn(Nt,Td) + j* randn(Nt,Td)); 
    XX=kron(X.',eye(Nr)); 
    
    A_ray=A_ray+XX_ray*Hw*Hw'*XX_ray';   % rayleigh fading with perfect csi and without training symbol
    
    A10=A10+XX*Hw*Hw'*XX';   % perfect csi
    
    A20=A20+XX*d*d'*XX';    % worst case noise lower bound
    AA20=AA20+snrp(ii)*XX*C*hh*XX'+nn;
    
    A30=A30+XX*Hw*Hw'*XX';  % inequality lower bound
    aa300=aa300+1/T*log2(det(eye(Nt*Nr)+snr(ii)*XX'*inv(nn)*XX*C*hh));
   
end
    A_ray=1/NN*A_ray;   % rayleigh fading with perfect csi and without training symbol
    capa_ray(ii)=capa_ray(ii)+1/T(ii)*log2(det(eye(T*Nr)+snr*A_ray*inv(nn_ray)));

A10=1/NN*A10;     % perfect csi
capa1(ii)=capa1(ii)+1/T*log2(det(eye(Td*Nr)+snr(ii)*A10*inv(nn)));

A20=1/NN*A20;      % worst case noise lower bound
AA20=1/NN*AA20;
capa2(ii)=capa2(ii)+1/T*log2(det(eye(Td*Nr)+snr(ii)*A20*inv(AA20)));

A30=1/NN*A30;        % inequality lower bound
capa30(ii)=capa30(ii)+1/T*log2(det(eye(Td*Nr)+snr(ii)*A30*inv(nn)));
aa300=1/NN*aa300;
capa300(ii)=aa300+capa300(ii);


end
capa_ray(ii)=1/MM*capa_ray(ii);    % rayleigh fading with perfect csi and without training symbol 
capa1(ii)=1/MM*capa1(ii);
capa2(ii)=1/MM*capa2(ii); 
capa3(ii)=1/MM*(capa30(ii)-capa300(ii));   
 
 ww= waitbar(ii/length(SNR));
    end
    close(ww)
% figure
plot(SNR,capa_ray,'ko-')
hold on
plot(SNR,capa1,'ks-')
hold on
plot(SNR,capa2,'kv-')
hold on
plot(SNR,capa3,'k*-')
hold on
grid on
title('The Ergodic Capacity of MIMO Systems')
xlabel('SNR (dB)')
ylabel('Ergodic Capacity (bit/channel use)') 

legend('Rayleigh','perfect csi','worst case','inequality')