基于OFDM的信道估计算法

本是古典何须时尚 2022-09-04 12:41 225阅读 0赞

% simulation for channel estimation techniequs using LS, LMMMSE, and  
% computationally efficient LMMMSE methods.  
% Prepared by: Hiren Gami

% Ref: J J Van de Beek, "Synchronization and Channel Estimation in OFDM  
% systems", Ph.D thesis,Sept. 1998

clc  
clear all

nCP = 8;%round(Tcp/Ts);  
nFFT = 64;  
NT = nFFT + nCP;  
F = dftmtx(nFFT)/sqrt(nFFT);

MC = 1500;

EsNodB = 0:5:40;  
snr = 10.^(EsNodB/10);  
beta = 17/9;  
M = 16;  
modObj = modem.qammod(M);  
demodObj = modem.qamdemod(M);  
L = 5;  
ChEstLS = zeros(1,length(EsNodB));  
ChEstMMSE = zeros(1,length(EsNodB));  
TD\_ChEstMMSE = zeros(1,length(EsNodB));  
TDD\_ChEstMMSE = zeros(1,length(EsNodB));  
TDQabs\_ChEstMMSE = zeros(1,length(EsNodB));

for ii = 1:length(EsNodB)  
disp('EsN0dB is :'); disp(EsNodB(ii));tic;  
ChMSE\_LS = 0;  
ChMSE\_LMMSE=0;  
TDMSE\_LMMSE =0;  
TDDMSE\_LMMSE=0;  
TDQabsMSE\_LMMSE =0;  
for mc = 1:MC  
% Random channel taps  
g = randn(L,1)+1i\*randn(L,1);  
g = g/norm(g);  
H = fft(g,nFFT);  
% generation of symbol  
X = randi(\[0 M-1\],nFFT,1); %BPSK symbols  
XD = modulate(modObj,X)/sqrt(10); % normalizing symbol power  
x = F'\*XD;  
xout = \[x(nFFT-nCP+1:nFFT);x\];  
% channel convolution and AWGN  
y = conv(xout,g);  
nt =randn(nFFT+nCP+L-1,1) + 1i\*randn(nFFT+nCP+L-1,1);  
No = 10^(-EsNodB(ii)/10);  
y = y + sqrt(No/2)\*nt;  
% Receiver processing  
y = y(nCP+1:NT);  
Y = F\*y;  
% frequency doimain LS channel estimation  
HhatLS = Y./XD;  
ChMSE\_LS = ChMSE\_LS + ((H -HhatLS)'\*(H-HhatLS))/nFFT;  
% Frequency domain LMMSE estimation  
Rhh = H\*H';  
W = Rhh/(Rhh+(beta/snr(ii))\*eye(nFFT));  
HhatLMMSE = W\*HhatLS;  
ChMSE\_LMMSE = ChMSE\_LMMSE + ((H -HhatLMMSE)'\*(H-HhatLMMSE))/nFFT;  
% Time domain LMMSE estimation  
ghatLS = ifft(HhatLS,nFFT);  
Rgg = g\*g';  
WW = Rgg/(Rgg+(beta/snr(ii))\*eye(L));  
ghat = WW\*ghatLS(1:L);  
TD\_HhatLMMSE = fft(ghat,nFFT);%  
TDMSE\_LMMSE = TDMSE\_LMMSE + ((H -TD\_HhatLMMSE)'\*(H-TD\_HhatLMMSE))/nFFT;

% Time domain LMMSE estimation - ignoring channel covariance  
ghatLS = ifft(HhatLS,nFFT);  
Rgg = diag(g.\*conj(g));  
WW = Rgg/(Rgg+(beta/snr(ii))\*eye(L));  
ghat = WW\*ghatLS(1:L);  
TDD\_HhatLMMSE = fft(ghat,nFFT);%  
TDDMSE\_LMMSE = TDDMSE\_LMMSE + ((H -TDD\_HhatLMMSE)'\*(H-TDD\_HhatLMMSE))/nFFT;  
  
% Time domain LMMSE estimation - ignoring smoothing matrix  
ghatLS = ifft(HhatLS,nFFT);  
TDQabs\_HhatLMMSE = fft(ghat,nFFT);%  
TDQabsMSE\_LMMSE = TDQabsMSE\_LMMSE + ((H -TDQabs\_HhatLMMSE)'\*(H-TDQabs\_HhatLMMSE))/nFFT;  
  
end  
ChEstLS(ii) = ChMSE\_LS/MC;  
ChEstMMSE(ii)=ChMSE\_LMMSE/MC;  
TD\_ChEstMMSE(ii)=TDMSE\_LMMSE/MC;  
TDD\_ChEstMMSE(ii)=TDMSE\_LMMSE/MC;  
TDQabs\_ChEstMMSE(ii)=TDQabsMSE\_LMMSE/MC;  
toc;  
end

% Channel estimation  
semilogy(EsNodB,ChEstLS,'r','LineWidth',2);  
hold on;grid on;xlabel('EsNodB'); ylabel('Channel MSE');  
semilogy(EsNodB,ChEstMMSE,'k','LineWidth',2);  
semilogy(EsNodB,TD\_ChEstMMSE,'g','LineWidth',2);  
semilogy(EsNodB,TDD\_ChEstMMSE,'m','LineWidth',2);  
semilogy(EsNodB,TDQabs\_ChEstMMSE,'b','LineWidth',2);

% Theoratical bound calculation  
semilogy(EsNodB,beta./snr,'-.r\*','LineWidth',2);  
ThLMMSE = (1/nFFT)\*(beta./snr).\*(1./(1+(beta./snr)));  
semilogy(EsNodB,ThLMMSE,'-.k\*','LineWidth',2);  
legend('LS','MMSE', 'TD LMMSE','TDD LMMSE','TD Qabs LMMSE','Theory-LS', 'Theory-LMMSE');

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