matlabrandomsignal-processingtelecommunicationmodulation

Calculating Error Rates for QPSK(for AWGN channel) in MATLAB


I want to simulate the QPSK for AWGN Channel and compare the errors I get with the theoritical ones on a plot. I want to do this on MATLAB for different SNR values from 1 to 10. When I plot this I get a huge difference between simulated and theoritical errors. I suspect I might have done with the demodulation part. I used atan function there but I am not %100 sure that it works. Can you help me?

M=100000;
snrdB=1:10;
snr=10.^(snrdB/10);
sError = zeros(1,10);%simulated error
tError = zeros(1,10);%theoritical error
for i=1:10
    symbols = randi([1,4],1,M);
    symbols(symbols == 1) = 1;
    symbols(symbols == 2) = 1i;
    symbols(symbols == 3) = -1;
    symbols(symbols == 4) = -1i;

    %calculating total energy
    Eb = 0;
    for k=1:M
        Eb = Eb + abs(symbols(k).^2);
    end
    Eb = Eb/2;

    var = abs(sqrt(Eb/(2*snr(i))));%variance
    noise = var*rand(1,M) + var*1i*rand(1,M);%noise

    r=symbols+noise;%adding noise

    symbols1 = atan(r);%demodulation

    error = abs((symbols - symbols1)./abs(symbols));%error
    sError(i) = mean(error);
    tError(i) = 2*qfunc(sqrt(2*snr(i)));%theoritical error
end
%comparison
semilogy(snrdB, tError,'x-')  
hold on
semilogy(snrdB, sError,'o-')                                 
xlabel('snr(dB)')                                    
ylabel('error')                                         
grid on 

Solution

  • Something like this should work;

    M=100000;
    snrdB=1:10;
    snr=10.^(snrdB/10);
    sError = zeros(1,10);%simulated error
    tError = zeros(1,10);%theoritical error
    
    
    for i=1:10
        symbols = randi([1,4],1,M);
    
        symbols(symbols == 1) = 1;
        symbols(symbols == 2) = 1i;
        symbols(symbols == 3) = -1;
        symbols(symbols == 4) = -1i;
    
        var = 1/(2*sqrt(snr(i)));%variance
    
        noise = var*(randn(1,M)) + var*j*(randn(1,M));
    
        r=symbols+noise;%adding noise
    
        c1 = exp(j*pi/4);
        c2 = exp(-j*pi/4);
    
        symbols1 = sign(real(symbols .* c1));
        symbols2 = sign(imag(symbols .* c1));
    
        symbols3 = sign(real(symbols .* c2));
        symbols4 = sign(imag(symbols .* c2));
    
        symbols1r = sign(real(r .* c1));
        symbols2r = sign(imag(r .* c1));
    
        symbols3r = sign(real(r .* c2));
        symbols4r = sign(imag(r .* c2));
    
    
        ind = find(symbols1==symbols1r & symbols2==symbols2r & symbols3==symbols3r & symbols4==symbols4r);
    
        sError(i) = (M-length(ind))/M;
        tError(i) = 2*qfunc(sqrt(2*snr(i)));%theoritical error
    end
    %comparison
    
    semilogy(snrdB, tError,'x-')  
    hold on
    semilogy(snrdB, sError,'o-')                                 
    xlabel('snr(dB)')                                    
    ylabel('error')                                         
    grid on