MPSK载波信号在awgn信道下的误码率

@MPSK载波信号在awgn信道下的误码率

一、M-PSK误码率理论计算公式

  在awgn信道，相干解调的条件下可得到M-PSK载波信号的误码率$P_e$理论计算公式为：
$$P_e=efrc(sin(\frac{\pi }{M})\sqrt{r})$$
  其中，M为多进制,$r=\frac{E_s}{N_0}$,$E_s=E_{b}lo{g}_{2}M$。

二、Matlab仿真

1.代码

%------Function:Estimate M-PSK Symbol Error Rate------------
%------Remark:----------------------------------------------
%------Time:2025.03.26--------------------------------------
%------Author:Clemence--------------------------------------

clc;
clear all;
close all;


M = [2 4 8];
k = log2(M); 
EsN0 = 0:15; 
snrdB = 10.^(EsN0/10);
symbNum = 1e5;  

for j=1:length(M)
    %---theory Value-------------------------
    ser1(j,:) = erfc(sin(pi/M(j))*sqrt(snrdB));
    %-----produce  symbol--------------------
    msg = randi([0 M(j)-1],1,symbNum); 
    %-----M PSK modulate---------------------
    msgmod = pskmod(msg,M(j));
    %-----calculate signal pow---------------
    spow = norm(msgmod).^2/symbNum;
   
    for n =1:length(EsN0)
        
        %---calculte noise coefficent by snr---
        sigma = sqrt(spow/(2*snrdB(n)));
        noise = sigma*(randn(1,length(msgmod))+1i*randn(1,length(msgmod)));
        
        %----add noise to signal--------------
        rxSig = msgmod + noise;     
        %----M PSK demodulate-----------------
        y1 = pskdemod(rxSig,M(j));
        %----calculte error bit---------------
        [err,berEst(j,n)] = biterr(msg(2:end),y1(2:end),k(j));
         %----calculte error symbol---------------
        [err,serEst(j,n)] = symerr(msg(2:end),y1(2:end));
    end
end
 
%----------plot theoretical and simulation symbol error rate under awgn----
hold on;  
semilogy(EsN0, serEst(1,:), 'c--', 'LineWidth', 1.5, 'MarkerSize', 3, 'MarkerFaceColor', 'c');
semilogy(EsN0, serEst(2,:), 'm--', 'LineWidth', 1.5, 'MarkerSize', 3, 'MarkerFaceColor', 'm');
semilogy(EsN0, serEst(3,:), 'g--', 'LineWidth', 1.5, 'MarkerSize', 3, 'MarkerFaceColor', 'k');
semilogy(EsN0, ser1(1,:), 'c-s', 'LineWidth', 1.5, 'MarkerSize', 3, 'MarkerFaceColor', 'none');
semilogy(EsN0, ser1(2,:), 'm-d', 'LineWidth', 1.5, 'MarkerSize', 3, 'MarkerFaceColor', 'none');
semilogy(EsN0, ser1(3,:), 'g-p', 'LineWidth', 1.5, 'MarkerSize', 3, 'MarkerFaceColor', 'none');
hold off;


title('M-PSK载波信号在awgn信道下的性能');
legend('BPSK误码率','QPSK误码率','8PSK误码率','BPSK理论误码率','QPSK理论误码率','8PSK理论误码率');

2.仿真结果

三、总结

  由仿真结果可以看出，载波信号的误码率BPSK<QPSK<8PSK,随着信噪比的增加，MPSK载波信号的误码率理论值与仿真值越来约接近