简单16-QAM传输系统（Matlab实现）

这是一个简单的16-QAM传输系统设计，包含发射机，信道和接收机。此项目的目标是学习在数字传输系统中一些基本模块的功能。通过仿真，我们需要掌握发送滤波器、接受滤波器以及均衡器等模块是如何被使用、为什么被使用以及使用了这些模块之后对通信系统产生了怎么样的影响。通信系统仿真的设计框图如图所示。

代码缺陷

（1）眼图不对，可能是错误使用了eyediagram()函数
（2）信道均衡时，训练测试使用同一个数据集，考虑使用另一个随机样本集合会更好
（3）误码率曲线有问题，（代码为误符号率）最后结果没有转换为误码率，需要添加一个符号-比特映射模块

注意：
实验平台：MatlabR2018a，若使用低版本的Matlab，可能会使某些函数出错，例如：sprintf(),equalize()等
可改进之处：
（1）16QAM直接生成星座图点，可能经过IQ映射生成QAM信号会更好。
（2）信道均衡训练测试使用同一个数据集，考虑使用另一个随机样本会更好
（3）可以尝试更多的信道模型模拟不同的场景
equalize的使用： 均衡时使用了信号前2000个对均衡器权系数进行训练，模仿训练集和测试集的划分。当使用较少信号对权系数训练时，最后结果明显不如较多信号训练结果。

完整代码

clc
clear%% 发送机 要求滚降0.25，FS=4M,FS*T=4,1/T=1M,M = 16;aqam = [-3, -1, 1, 3];A = repmat(aqam, 4, 1);B = flipud(A');konst_qam = A+i*B;konst_qam = konst_qam(:); % 产生所有星座点qam = konst_qam(randi([0,15], 10000, 1)+1);figure()plot(qam, 'o');title('Ordinary Signal Contellation');axis([-4 4 -4 4]);xlabel('Re');ylabel('Im')FS = 3000000;   %采样频率N = length(qam);T = 1/1000000;RS = 1/T;FS_T = 3;t = -5*T:1/FS:5*T;t = t+1e-10;alfa = 0.35;%发送滤波器的时域表达式以及过采样因子缩放cositem = cos((1+alfa)*pi*t/T);sinitem = sin((1-alfa)*pi*t/T);extra = 4*alfa*t/T;below = (1-(4*alfa*t/T).^2).*(pi*t/T);p = (extra.*cositem+sinitem)./below; %发送滤波器的时域表达p = p./(sqrt(FS*T)); %过采样% 下面是加零和滤波qams = zeros(size(1:FS_T*N));qams(1:FS_T:FS_T*N) = qam;symbols = filter(p, 1, qams);%下面是滤波器和实际传输信号的幅度谱Nfft = 2048;P = fftshift(fft(p,Nfft));X0 = fftshift(fft(symbols,Nfft));f = -FS/2:FS/Nfft:FS/2-FS/Nfft;figure()subplot(211);plot(f, 20*log10(abs(P)));grid;title('Pulse Spectrum in dB');xlabel('Freq');subplot(212);plot(f, 20*log10(abs(X0)));grid;title('Signal Spectrum in dB')xlabel('Freq');figure();plot(symbols,'.');  % 信号星座图title('Trans Signal Contellation')eyediagram(symbols, 2); % 实际发送信号的眼图
%% 通过信道传输% 通过线性滤波器Fcut = 500000;wn_lpf = Fcut*2/FS;b_lpf = fir1(4, wn_lpf);lpf_symbols = filter(b_lpf, 1, symbols);figure()X1 = fftshift(fft(lpf_symbols, Nfft));plot(f, 20*log10(abs(X1)));grid;title('After Channel Filter Signal Spectrum in dB')xlabel('Freq');% SNR加噪noise = randn(size(lpf_symbols))+i*randn(size(lpf_symbols)); % 产生复数噪声svsymbol = std(lpf_symbols)^2; nv = std(noise)^2;figure()Ps = [];for SNR = 5:5:20p1 = std(lpf_symbols)/(std(noise)*10^(SNR/20));sign_withnoise(SNR/5,:) = lpf_symbols+noise*p1;Ps(SNR/5,:) = fftshift(fft(sign_withnoise(SNR/5,:),Nfft));subplot(2,2,SNR/5)plot(f, 20*log10(abs(Ps(SNR/5,:))));grid;title(sprintf("Signal Spectrum in dB in SNR %d",SNR))xlabel('Freq');end
%% 接收机for i = 1:4rvfilter(i,:) = filter(p,1,sign_withnoise(i,:));end% 下面是接受信号的星座图for i = 1:4eyediagram(rvfilter(i,:),2)end% 找到相位差,并且重采样impulse = [1,zeros(1,100)];TxImpOut = filter(p,1,impulse);ChannelImpOut = filter(b_lpf, 1, TxImpOut);RxImpOut = filter(p,1,ChannelImpOut);[Trash, Pos] = max(abs(RxImpOut));%RXSAMPOUT能恢复出qamfigure()for i = 1:4temp = rvfilter(i,:);subplot(4,3,3*i-2)plot(rvfilter(i,:), '.')title(sprintf("Recieved signal Contellation in SNR %d", i*5))subplot(4,3,3*i-1)RxSampOut(i,:) = temp(Pos:FS*T:end);plot(RxSampOut(i,:),'.')title(sprintf("Resampled Signal Contellation in SNR %d", i*5))end
%% 信道均衡%使用均衡函数进行均衡操作sigconst = step(comm.RectangularQAMModulator(M),(0:M-1)');eqlms = lineareq(6, lms(0.0008)); % Create an LMS equalizer object.eqlms.SigConst = sigconst'; % Set signal constellation.eqlms.ResetBeforeFiltering = 0; % Maintain continuity between iterations.eq_current = eqlms;msglen = length(RxSampOut(1,:));modmsg = qam(1:msglen);itr = 2000;trainsig = modmsg(1:itr);%取其中1/5训练均衡器抽头系数for i = 1:4msg = RxSampOut(i,:).';y = equalize(eq_current, msg, trainsig);subplot(4,3,3*i)plot(y(itr+1:end),'.')z(i,:) = y;title(sprintf("Equalized Signal Contellation in SNR %d", i*5))end%% 误码率曲线
for i = 1:4sn_block = repmat(z(i,:),16,1);konst_block = repmat(konst_qam,1,msglen);distance = abs(sn_block-konst_block);[dmin,ind_2] = min(distance);qam_det = konst_qam(ind_2);qamlen = length(qam_det);d = 2;SNR =5*i;p2 = std(qam)/(std(noise)*10^(SNR/20));sigma = std(real(noise*p2));Q = 0.5*erfc(d/(sqrt(2)*2*sigma));sep_theo(i) = 3.5*Q - 3.0625*Q^2;number_of_errors = sum(qam(1:qamlen) ~= qam_det);sep_simu(i) = number_of_errors/qamlen;
endfigure()A2_over_sigma2_dB=5:5:20;%仿真信噪比范围(dB)A2_over_sigma2=10.^(A2_over_sigma2_dB./10);%仿真信号信噪比（倍数）hold on; semilogy(A2_over_sigma2_dB,sep_theo,'b');semilogy(A2_over_sigma2_dB,sep_simu,'r');legend('理论误码率','实际仿真结果')title('Bit Error Rate (BER) in SNR')xlabel('SNR');ylabel('Bit Error Rate (BER)');grid on;hold off;