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⛄ 内容介绍
OFDM通信链路中的信道估计是为了在接收端正确还原发送信号而对信道进行建模和估计的过程。常用的两种信道估计方法是最小二乘法（LS）和最小均方误差（MMSE）。下面是使用这两种方法实现OFDM通信链路信道估计的基本步骤：
- 发送端：
- 将原始数据分为子载波，并应用傅里叶变换得到频域符号。
- 插入导频符号，在OFDM符号中安排导频位置。
- 信号传输：
- 将频域符号转换为时域信号并加上循环前缀。
- 将待传输的信号通过信道传输。
- 接收端：
- 接收并去除循环前缀。
- 将接收到的信号进行傅里叶变换，转换为频域表示。
- 导频信号提取：
- 从接收到的信号中提取出导频符，即已知的已发送符号。
- LS信道估计：
- 使用导频符号计算信道的估计值。
- 对于每个子载波，计算导频符号在频域上与接收到的导频符号的比率。
- 根据信道估计的比率，得到各个子载波的信道估计。
- MMSE信道估计：
- 使用导频符号和噪声方差计算信道的估计值。
- 对于每个号以及噪声方差的比率。
- 根据信道估计的比率，得到各个子载波的信道估计。
⛄ 运行结果
⛄ 部分代码
clc;
clear all;
close all;
Nfft=2048;
Ng=512;
Nofdm=2560;
Nsym=100;
Nps=4; %Pilot Spacing
Np=Nfft/Nps; %Number of pilots per OFDM symbol
Nbps=4;
itr=10;
nn=11; %No. of SNR observations
%Initialising MSE arrays for different SNR observations:
z_linin=zeros(1,nn);
z_splin=zeros(1,nn);
z_lindft=zeros(1,nn);
z_spldft=zeros(1,nn);
zmmse=zeros(1,nn);
zmmse_dft=zeros(1,nn);
for t=1:itr
z=[];
z1=[];
z2=[];
z3=[];
zm=[];
zms=[];
snr1=[];
% 16 - QAM - Modulation Scheme
M=16;
hmod = modem.qammod('M',M, 'SymbolOrder','gray');
Es=1;
A=sqrt(3/2/(M-1)*Es); % Signal energy and QAM normalization factor
for nsym=1:Nsym
Xp = 2*(randn(1,Np)>0)-1; % Pilot sequence generation
msgint=randi(1,Nfft-Np,M); % bit generation
dat_ser = A*modulate(hmod,msgint);
end
% serial to parllel conversion
dat_par=dat_ser.';
% Pilot Insertion - Comb Type Arrangement
counter = 0;
loc = [];
for i=1:Nfft
if mod(i,Nps)==1
X(i)=Xp(floor(i/Nps)+1);
loc=[loc i];
counter = counter+1;
else
X(i) = dat_par(i-counter);
end
end
% inverse discret Fourier transform (IFFT)
X_ifft=ifft(X,Nfft);
% Adding Cyclic Prefix - Guard interval
guard=X_ifft(:,end-511:end); % this is the Cyclic Prefix part to be appended.
ofdm_par=[guard X_ifft];
% parallel to serial - Generation of the OFDM Signal
ofdm=ofdm_par.';
% Channel code
dopjakes = doppler.jakes;
dopgauss1 = doppler.bigaussian;
dopgauss1.CenterFreqGaussian1 = -0.8;
dopgauss1.CenterFreqGaussian2 = 0.4;
dopgauss1.SigmaGaussian1 = 0.05;
dopgauss1.SigmaGaussian2 = 0.1;
dopgauss1.GainGaussian1 = sqrt(2*pi*(dopgauss1.SigmaGaussian1)^2);
dopgauss1.GainGaussian2 = 1/10 * sqrt(2*pi*(dopgauss1.SigmaGaussian2)^2);
dopgauss2 = doppler.bigaussian;
dopgauss2.CenterFreqGaussian1 = 0.7;
dopgauss2.CenterFreqGaussian2 = -0.4;
dopgauss2.SigmaGaussian1 = 0.1;
dopgauss2.SigmaGaussian2 = 0.15;
dopgauss2.GainGaussian1 = sqrt(2*pi*(dopgauss1.SigmaGaussian1)^2);
dopgauss2.GainGaussian2 = 1/10^1.5 * sqrt(2*pi*(dopgauss1.SigmaGaussian2)^2);
fd=130; %Maximum Doppler Shift
ts=(7/64)*10^-6; %Sampling Time
chan = rayleighchan(ts, fd); %Rayleigh channel - Multifading Channel
% Assign profile-specific properties to channel object.
chan.PathDelays = [0.0 0.2 0.5 1.6 2.3 5.0] * 1e-6;
chan.AvgPathGaindB = [-3 0 -2 -6 -8 -10];
chan.DopplerSpectrum = [dopjakes dopjakes dopjakes dopgauss1 dopgauss2 dopgauss2];
chan.StoreHistory = 1;
chan.ResetBeforeFiltering = 0;
chan.NormalizePathGains = 1;
%Passing OFDM Signal through the created Channel
chan_op = filter(chan,ofdm);
XFG=fft(chan_op);
%Channel Covariance Matrix for MMSE estimation
x_test=randn(1,6);
X_test=fft(x_test,Nfft);
y_test=filter(chan,x_test);
Y_test=fft(y_test,Nfft);
H1=Y_test/X_test;
h=ifft(H1,6);
H=fft(h,Nfft);
ch_length=length(h);
%Reception at the receiver end for various SNR ranging from 5dB - 25dB:
for SNR =5:2:25
%AWGN Modelling
snr1=[snr1 SNR];
n1=ones(2560,1);
n1=n1*0.000000000000000001i;%Just to ensure that the function awgn adds 'complex gaussian noise'..
noise=awgn(n1,SNR);
variance=var(noise);
N=fft(noise);
Y_rec=XFG+N;
y_ser=ifft(Y_rec);
% serial to parallel conversion
y_par=y_ser.';
% guard interval
y = y_par(Ng+1:Nofdm);
% FFT
Y = fft(y);
% channel estimation
%LS Estimator with Linear Interpolator
H_est = LS_CE(Y,Xp,loc,Nfft,Nps,'linear');
err=(H-H_est)*(H-H_est)';
z=[z err/(Nfft*Nsym)];
%LS Estimator with Linear Interpolator - DFT Based
h_est = ifft(H_est);
h_DFT = h_est(1:ch_length);
H_DFT = fft(h_DFT,Nfft);
err=(H-H_DFT)*(H-H_DFT)';
z3=[z3 err/(Nfft*Nsym)];
%LS Estimator with Spline Cubic Interpolator
H_est = LS_CE(Y,Xp,loc,Nfft,Nps,'spline');
err=(H-H_est)*(H-H_est)';
z1=[z1 err/(Nfft*Nsym)];
%LS Estimator with Spline Cubic Interpolator - DFT Based
h_est = ifft(H_est);
h_DFT = h_est(1:ch_length);
H_DFT = fft(h_DFT,Nfft);
err=(H-H_DFT)*(H-H_DFT)';
z2=[z2 err/(Nfft*Nsym)];
% MMSE Estimator
H_est = MMSE_CE(Y,Xp,loc,Nfft,Nps,h,SNR);
err=(H-H_est)*(H-H_est)';
zm=[zm err/(Nfft*Nsym)];
% MMSE Estimator - DFT Based
h_est = ifft(H_est);
h_DFT = h_est(1:ch_length);
H_DFT = fft(h_DFT,Nfft);
err=(H-H_DFT)*(H-H_DFT)';
zms=[zms err/(Nfft*Nsym)];
end
z_linin=z_linin+z;
z_splin=z_splin+z1;
z_lindft=z_lindft+z2;
z_spldft=z_spldft+z2;
zmmse=zmmse+zm;
zmmse_dft=zmmse_dft+zms;
end
figure(1)
semilogy(snr1,(1/itr)*z_linin,'r+:', snr1,(1/itr)*z_splin,'bo:', snr1,(1/itr)*z_lindft,'--xg', snr1,(1/itr)*z_spldft,'--sc');
legend('LS - Linear Interpolation','LS - Spline Cubic Interpolation','LS - Linear Interpolation(DFT)','LS - Spline Cubic Interpolation(DFT)');
xlabel('SNR');
ylabel('MSE');
grid on
hold on
figure(2)
semilogy(snr1,(1/itr)*zmmse,'r+:',snr1,(1/itr)*zmmse_dft,'bo:');
xlabel('SNR');
ylabel('MSE');
legend('MMSE','MMSE - DFT Based');
hold on
grid on
figure(3)
semilogy(snr1,(1/itr)*z_linin,'r+:', snr1,(1/itr)*z_splin,'bo:', snr1, (1/itr)*zmmse,'--xg');
xlabel('SNR');
ylabel('MSE');
legend('LS - Linear Interpolation','LS - Spline Cubic Interpolation','MMSE');
hold on
grid on
⛄ 参考文献
[1] 童圣洁,李红信,邓晓燕.OFDM系统LS与MMSE信道估计算法仿真分析[J].微计算机信息, 2008, 24(34):2.DOI:10.3969/j.issn.1008-0570.2008.34.092.
[2] 曹文魁.基于OFDM协作通信系统中的信道估计技术研究[D].解放军信息工程大学[2023-06-22].DOI:CNKI:CDMD:2.1013.161304.
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