%channel_estimation.m
% for LS/DFT Channel Estimation with linear/spline interpolation
%MIMO-OFDM Wireless Communications with MATLAB
clear all; close all; figure(1), clf, figure(2), clf %清除
Nfft=32; %FFT长度
Ng=Nfft/8; %保护间隔长度
Nofdm=Nfft+Ng; %OFDM长度
Nsym=100; %OFDM符号个数，包括导频OFDM符号和数据OFDM符号
Nps=4; %导频间隔Pilot spacing 一个训练序列到另一个训练序列的间隔
Np=Nfft/Nps; %每个OFDM符号的导频数
Nd=Nfft-Np; %每个OFDM符号的数据数 Numbers of pilots and data per OFDM symbol
Nbps=4; %四进制
M=2^Nbps; %每个（调制）符号的比特数 Number of bits per (modulated) symbol
mod_object = modem.qammod('M',M, 'SymbolOrder','gray'); %QAM调制函数
demod_object = modem.qamdemod('M',M, 'SymbolOrder','gray'); %QAM解调函数
Es=1; A=sqrt(3/2/(M-1)*Es); % 信号能量及QAM归一化因子 Signal energy and QAM normalization factor
%fs = 10e6; ts = 1/fs; %采样频率及周期 Sampling frequency and Sampling period
SNRs = [30]; %信噪比30 SNRs=30即可
sq2=sqrt(2); %导频符号的幅度
for i=1:length(SNRs)
SNR = SNRs(i);
rand('seed',1); randn('seed',1);
MSE = zeros(1,6); nose = 0;
for nsym=1:Nsym
Xp = 2*(randn(1,Np)>0)-1; %生成导频序列 （随机产生-1,1） Pilot sequence generation
%Data = ((2*(randn(1,Nd)>0)-1) + j*(2*(randn(1,Nd)>0)-1))/sq2; % QPSK modulation
msgint=randint(1,Nfft-Np,M); % 比特生成bit generation
Data = modulate(mod_object,msgint)*A;%QAM调制函数
%Data = modulate(mod_object, msgint); Data = modnorm(Data,'avpow',1)*Data; % normalization
ip = 0; pilot_loc = [];
for k=1:Nfft
if mod(k,Nps)==1
X(k) = Xp(floor(k/Nps)+1); pilot_loc = [pilot_loc k]; ip = ip+1;
else X(k) = Data(k-ip);
end
end
x = ifft(X,Nfft); % 快速傅里叶逆变换IFFT
xt = [x(Nfft-Ng+1:Nfft) x]; % 加CP Add CP
h = [(randn+j*randn) (randn+j*randn)/2]; % 产生一个二抽头信道 generates a (2-tap) channel
H = fft(h,Nfft); channel_length = length(h); % 实际信道及长度 True channel and its time-domain length
H_power_dB = 10*log10(abs(H.*conj(H))); % 实际信道功率 True channel power in dB
y_channel = conv(xt, h); % 信道路径（卷积）Channel path (convolution)
sig_pow = mean(y_channel.*conj(y_channel)); %计算信号能量
%y_aw(1,1:Nofdm) = y(1,1:Nofdm) + ...
% sqrt((10.^(-SNR/10))*sig_pow/2)*(randn(1,Nofdm)+j*randn(1,Nofdm)); % Add noise(AWGN)
yt = awgn(y_channel,SNR,'measured'); %加入噪声
y = yt(Ng+1:Nofdm); % 去CP Remove CP
Y = fft(y); % FFT
for m=1:3
if m==1, H_est = LS_CE(Y,Xp,pilot_loc,Nfft,Nps,'linear'); method='LS-linear'; % LS estimation with linear interpolation
elseif m==2, H_est = LS_CE(Y,Xp,pilot_loc,Nfft,Nps,'spline'); method='LS-spline'; % LS estimation with spline interpolation
else H_est = MMSE_CE(Y,Xp,pilot_loc,Nfft,Nps,h,SNR); method='MMSE'; % MMSE estimation
end %三种估计方法
H_est_power_dB = 10*log10(abs(H_est.*conj(H_est)));
h_est = ifft(H_est); %IFFT
h_DFT = h_est(1:channel_length);
H_DFT = fft(h_DFT,Nfft); % 基于DFT的信道估计 DFT-based channel estimation
H_DFT_power_dB = 10*log10(abs(H_DFT.*conj(H_DFT)));
if nsym==1
figure(1), subplot(319+2*m), plot(H_power_dB,'b','linewidth',1); grid on; hold on;
plot(H_est_power_dB,'r:+','Markersize',4,'linewidth',1); axis([0 32 -6 10])
title(method); xlabel('Subcarrier Index'); ylabel('Power[dB]');
legend('True Channel',method,4); set(gca,'fontsize',9)
subplot(320+2*m), plot(H_power_dB,'b','linewidth',1); grid on; hold on;
plot(H_DFT_power_dB,'r:+','Markersize',4,'linewidth',1); axis([0 32 -6 10])
title([method ' with DFT']); xlabel('Subcarrier Index'); ylabel('Power[dB]');
legend('True Channel',[method ' with DFT'],4); set(gca,'fontsize',9)
end
MSE(m) = MSE(m) + (H-H_est)*(H-H_est)';
MSE(m+3) = MSE(m+3) + (H-H_DFT)*(H-H_DFT)';
end
Y_eq = Y./H_est;
if nsym>=Nsym-10
figure(2), subplot(221), plot(Y,'.','Markersize',5), axis([-1.5 1.5 -1.5 1.5])
axis('equal'), set(gca,'fontsize',9), hold on,
subplot(222), plot(Y_eq,'.','Markersize',5), axis([-1.5 1.5 -1.5 1.5])
axis('equal'), set(gca,'fontsize',9), hold on,
end
ip = 0;
for k=1:Nfft
if mod(k,Nps)==1, ip=ip+1; else Data_extracted(k-ip)=Y_eq(k); end
end
msg_detected = demodulate(demod_object,Data_extracted/A);
nose = nose + sum(msg_detected~=msgint);
end
MSEs(i,:) = MSE/(Nfft*Nsym);
end
Number_of_symbol_errors=nose
figure(3), clf, semilogy(SNRs',MSEs(:,1),'-x', SNRs',MSEs(:,3),'-o')
legend('LS-linear','MMSE')
fprintf('MSE of LS-linear/LS-spline/MMSE Channel Estimation = %6.4e/%6.4e/%6.4e\n',MSEs(end,1:3));
fprintf('MSE of LS-linear/LS-spline/MMSE Channel Estimation with DFT = %6.4e/%6.4e/%6.4e\n',MSEs(end,4:6));
