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
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