GENERAL CODE OF MQAM TO GENERATE BER VS SNR PLOT

clc;
clear all;
close all;
N = 4*10^3; % number of symbols
M = 16; % size
k = log2(M); % bits/symbol

% for 16-QAM
Re = [-(2*sqrt(M)/2-1):2:-1 1:2:2*sqrt(M)/2-1];

Im = [-(2*sqrt(M)/2-1):2:-1 1:2:2*sqrt(M)/2-1];

k_QAM = 1/sqrt(10);

bdB = 3:1:13; % SNR range

sdB = bdB + 10*log10(k);

% binary to gray code

a = [0:k-1];

map = bitxor(a,floor(a/2));

[tt ind] = sort(map);

for i = 1:length(bdB)

c = rand(1,N*k,1)>0.5; % random 1's and 0's
d = reshape(c,k,N).';
bd = ones(N,1)*(2.^((k/2-1):-1:0)) ; % conversion from binary to decimal

% real

cRe = d(:,(1:k/2));
e = sum(cRe.*bd,2);
f = bitxor(e,floor(e/2));

% imaginary
cIm = d(:,(k/2+1:k));
g = sum(cIm.*bd,2);
h = bitxor(g,floor(g/2));

% mapping the Gray coded symbols into constellation
modRe = Re(f+1);
modIm = Im(h+1);

% constellation

mod = modRe + 1i*modIm;
s = k_QAM*mod;

% noise

n = 1/sqrt(2)*[randn(1,N) + 1i*randn(1,N)];

% reciever
r = s + 10^(-sdB(i)/20)*n;

% demodulation

r_re = real(r)/k_QAM;
r_im = imag(r)/k_QAM;

% rounding off


m = 2*floor(r_re/2)+1;
m(m>max(Re)) = max(Re);
m(m<min(Re)) = min(Re);

n= 2*floor(r_im/2)+1;
n(n>max(Im)) = max(Im);
n(n<min(Im)) = min(Im);

% To Decimal conversion

oRe = ind(floor((m+4)/2+1))-1;
oIm = ind(floor((n+4)/2+1))-1;

% To binary string
pRe = dec2bin(oRe,k/2);
pIm = dec2bin(oIm,k/2);

% binary string to number
pRe = pRe.';
pRe = pRe(1:end).';
pRe = reshape(str2num(pRe).',k/2,N).' ;

pIm = pIm.';
pIm = pIm(1:end).';
pIm = reshape(str2num(pIm).',k/2,N).' ;

% counting errors for real and imaginary
Err(i) = size(find([cRe- pRe]),1) + size(find([cIm - pIm]),1) ;

end
sBer = Err/(N*k);
tBer = (1/k)*3/2*erfc(sqrt(k*0.05*(10.^(bdB/10))));

% plot
figure
semilogy(bdB,tBer,'rs-','LineWidth',2);
hold on
semilogy(bdB,sBer,'kx-','LineWidth',2);
grid on
legend('theory', 'simulation');
xlabel('SNR dB')
ylabel('Bit Error Rate')
title('BER VS SNR')