【信道估计】LS/MMSE信道估计,CS信道估计的MATLAB仿真

1.软件版本

MATLAB2021a

2.本算法理论知识

构造测量矩阵是压缩感知技术中关键的研究方向之一, 在实现压缩的过程中需要构建一个满足RIP法则的特殊矩阵来保证较高的重构精度.在这篇文章中,我们通过一个简单的方式利用混沌序列构造测量矩阵,并证明在大多数情况下这种矩阵满足RIP法则.同时,在基于压缩感知的OFDM系统信道估计中应用这种观测矩阵,与基于最小二乘法的信道估计方法进行比较,通过实验仿真说明基于压缩感知的信道估计算法和利用混沌序列构造测量矩阵的优势.
3.核心代码

function [cs_mse_ave,ls_mse_ave,mmse_mse_ave]=MSE_com(N,L,K,h,N1)
W_h=1/sqrt(N)*fft(eye(N,L));
H=W_h*h;
H1=H(1:N1,:);
H2=H((N1+1):N,:);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%-----------------------------training sequence----------------------%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
d=randn(1,N);
d=d/std(d);
d=d-mean(d);
X=diag(d);
X1=X(1:N1,1:N1);
X2=X((N1+1):N,(N1+1):N);
XH=X*H;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --------------------求h的自协方差矩阵-Rhh-------------------------%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
gg=diag(h);
gg_myu = sum(gg, 1)/L;
gg_mid = gg - gg_myu(ones(L,1),:);
sum_gg_mid= sum(gg_mid, 1);
Rgg = (gg_mid' * gg_mid- (sum_gg_mid' * sum_gg_mid) / L) / (L- 1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%---------------------------添加高斯白噪声，得Y-----------------------%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
n1=ones(N,1);
for m=1:20%多组实验取平均
for n=0:6
SNR(n+1)=5*n;%比较不同SNR
clear j;
n1=n1*0.01j;%保证下面的awgn函数输入的是复高斯噪声
No=awgn(n1,SNR(n+1));%white Gaussian noise
%variance=var(noise);
SNR_log=10^(SNR(n+1)/10);
variance=var(XH)/SNR_log;
No=variance/var(No)*No;
var_No=var(No);
%No=fft(noise);
%Y = AWGN(X,SNR) adds to X. The SNR is in dB.The power of X is assumed to be 0 dBW. If X is complex, then AWGN adds complex noise.
%No=fft(noise);
Y=XH+No;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%-----------------------LS/MMSE信道估计，得MSE-------------------------%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
mean_squared_error_ls=LS_MSE_calc(X,H,Y,N);
%Evaluating the mean squared error for the MMSE estimator..
mean_squared_error_mmse=MMSE_MSE_calc(X,H,Y,Rgg,var_No,N,L);
mmse_mse(m,n+1)=mean_squared_error_mmse;
ls_mse(m,n+1)=mean_squared_error_ls;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%--------------------------CS信道估计H，得MSE--------------------------%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%CS evaluate H
s=Y;
Phi=X;
T=Phi*W_h; % 恢复矩阵(测量矩阵*正交反变换矩阵
re_H=zeros(1,N); % 待重构的谱域(变换域)向量
re_y=zeros(1,L);
[pos_arry,aug_y]=omp(K,s,T); % pos_arry:最大投影系数对应的位置,
[cos_pos_arry,aug_y]=omp(K,s,T); % pos_arry:最大投影系数对应的位置,
re_y(pos_arry)=aug_y;
re_H=W_h*re_y.'; % 做傅里叶变换重构得到原信号
diff_value=abs((re_H) -(H));
re_error=mean((diff_value./abs(H)).^2);
cs_mse(m,n+1)=re_error;
end
end
mmse_mse_ave=mean(mmse_mse);
ls_mse_ave=mean(ls_mse);
cs_mse_ave=mean(cs_mse);

4.操作步骤与仿真结论

 

 D200