% *************** Simulation BER of QPSK transmission over noise *********%
% with using Monte Carlo simulation
% ********************* Initialization ***********************************%
clc;
clear all;
close all;
loop=1; % Monte Carlo
M=1000000; % Frame length (x_1 x_2 ... x_M)
SNRdB=-10:10; % SNR in dB
SNR=10.^(SNRdB/10);
Rate= zeros(1, length(SNRdB)); %
% ********************* Transmitter **************************************%
for dB= 1: length(SNRdB) % start looping by SNR
dB
for lp= 1: loop, % start looping of frame data
% ********************* QPSK signal generation ***************************%
x_inp_I=sign(rand(M,1)- 0.5); % 1 or -1 for inphase signal
x_inp_Q=sign(rand(M,1)- 0.5); % 1 or -1 for guadrature signal
x_inp=x_inp_I+i*x_inp_Q; % 1+j=00, -1+j=01, -1-j=10, 1-j=11
x_inp=(1/sqrt(2))*x_inp; % normalization
% ********************* Channel ******************************************%
N0=1./SNR(dB);
sigma(dB)=sqrt(N0/2);
noise=(1/sqrt(2))*(sigma(dB)*randn(M,1)+i*sigma(dB)*randn(M,1));
y_channel=x_inp+noise; % Additive White Guassiann Noise (AWGN)
% ********************* Receiver *****************************************%
y=y_channel;
x_out_I= sign(real(y)); %
x_out_Q= sign(imag(y)); %
x_out=x_out_I+i*x_out_Q;
% ********************* Bit Error Rate (BER) calulation ******************%
[err, rate]= symerr([x_inp_I;x_inp_Q], [x_out_I;x_out_Q]);
Rate(dB)= Rate(dB) + rate;
end % end for loop
Rate(dB)= Rate(dB)/loop; % Average value over Monte Carlo simulation
% loop
end % end Monte Carlo
% ********************* Plot the simulation result ***********************%
f1 = figure(1);
set(f1,'color',[1 1 1]);
semilogy(SNRdB,Rate, 'b')
hold on;
BER_th=(1/2)*erfc(sqrt(SNR)); % theoritical calculation for BER
semilogy(SNRdB,BER_th,'r-o');
hold on;
axis([-10 10 0.000001 1.2]);
xlabel( 'Signal-to-Noise Ratio (SNR)')
ylabel( 'Bit Error Rate (BER)')
title('Simulation QPSK transmission over noise');
legend('BER simulation','BER calculation')
grid on;
