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% Author: Vinay Uday Prabhu
% E-mail: vinay_u_prabhu@yahoo.co.uk
% Function: Comparison of the performances of the LS and the MMSE channel estimators
% for a 64 sub carrier OFDM system based on the parameter of Mean square error
% Assumptions: The channel is assumed to be g(t)=delta(t-0.5 Ts)+delta(t-3.5 Ts)
% {Fractionally spaced}
%For more information on the theory and formulae used , please do refer to the paper On
%"Channel Estimation In OFDM systems" By Jan-Jaap van de Beek, Ove Edfors, Magnus Sandell
% Sarah Kate wilson and Petr Ola Borjesson In proceedings Of VTC'95 Vol 2 pg.815-819
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clc;
clear all;
%Generation of a naive training sequence..
%Assuming BPSK modulation ...symbols:+1/-1
X=zeros(64,64);
d=rand(64,1);
for i=1:64
if(d(i)>=0.5)
d(i)=+1;
else
d(i)=-1;
end
end
for i=1:64
X(i,i)=d(i);
end
%Calculation of G[The channel Matrix]
%The channnel is...
tau=[0.5 3.5];%The fractionally spaced taps..
%Generation of the G matrix...
for k=1:64
s=0;
for m=1:2
s=s+(exp(-1i*pi*(1/64)*(k+63*tau(m))) * (( sin(pi*tau(m)) / sin(pi*(1/64)*(tau(m)-k)))));
%Go through the above cited paper for the theory behind the formula
end
g(k)=s/sqrt(64);
end
G=g';%Thus, the channel vector is evaluated..
H=fft(G);% In the freq domain..
u=rand(64,64);
F=fft(u)*inv(u);% 'F' is the twiddle factor matrix..
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% Evaluation of the autocovariance matrix of G-Rgg
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gg=zeros(64,64);
for i=1:64
gg(i,i)=G(i);
end
% gg_myu = sum(gg, 1)/64;
% gg_mid = gg - gg_myu(ones(64,1),:);
% sum_gg_mid= sum(gg_mid, 1);
% Rgg = (gg_mid' * gg_mid- (sum_gg_mid' * sum_gg_mid) / 64) / (64 - 1);
Rgg = cov(gg);
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%Running for a dozen trials to try and average out the results..
for m=1:12
for n=1:5
SNR_send=5*n;
XFG=X*H;
n1=ones(64,1);
n1=n1*0.000000000000000001i;%Just to ensure that the function awgn adds 'complex gaussian noise'..
noise=awgn(n1,SNR_send);
variance=var(noise);
N=fft(noise);
Y=XFG+N;
%Evaluating the mean squared error for the LS estimator..
mean_squared_error_ls=LS_MSE_calc(X,H,Y);
%Evaluating the mean squared error for the MMSE estimator..
mean_squared_error_mmse=MMSE_MSE_calc(X,H,Y,Rgg,variance);
SNR(n)=SNR_send;
mmse_mse(m,n)=mean_squared_error_mmse;
ls_mse(m,n)=mean_squared_error_ls;
end;
end;
ls_mse;
mmse_mse;
mmse_mse_ave=mean(mmse_mse);
ls_mse_ave=mean(ls_mse);
%Now just the display part.....
semilogy(SNR,mmse_mse_ave,'k-');
grid on;
xlabel('SNR in DB');
ylabel('mean squared error');
title('PLOT OF SNR V/S MSE FOR AN OFDM SYSTEM WITH MMSE/LS ESTIMATOR BASED RECEIVERS');
hold on;
semilogy(SNR,ls_mse_ave,'b*');
semilogy(SNR,ls_mse_ave,'b-');
semilogy(SNR,mmse_mse_ave,'kv');
grid on;
xlabel('SNR in DB');
ylabel('mean squared error');
title('PLOT OF SNR V/S MSE FOR AN OFDM SYSTEM WITH MMSE/LS ESTIMATOR BASED RECEIVERS');
就像这段函数中，那个函数g是根据什么来的？是对信道环境的一种预先判定吗？然后根据这个信道模型进一步估计得到修正的真正的信道信息？
2、梳状适用于时变信道，块状适用于准静态信道。梳状导频估计时，有三种方法(1)先估计导频处的冲击响应，然后1维插值(2）ML估计(3)PCMB。第一种方法中的第一步，得到导频处的冲击响应，是不是只能用LS？看了很多文献，梳状导频时，第一步都是用LS，为什么不用MMSE？