Direct Transmission - BPSK - Rayleigh Fading

MATLAB PROGRAM

clc;

clear all;

N = 10^5; % number of symbols

ip0 = randi([0,1], 1,N); % random symbol generation

s = 2*ip0-1; % BPSK mapping

snr_dB = 0:2:20; % SNR in dB

fad_chan = 1/sqrt(2)*(randn(1,N)+1i*randn(1,N)); % complex channel gain

noise = 1/sqrt(2)*(randn(1,N)+1i*randn(1,N)); % AWGN

for ii = 1:length(snr_dB) % iteration for each SNR

%% simulation

snr = 10^(snr_dB(ii)/10);

rxd = sqrt(snr)*s.*fad_chan + noise; % received signal

r1 = conj(fad_chan).*rxd; % compensation for fading (equalization)

s_hat = real(r1)>0; % decision making

n_err = size(find(s_hat-ip0),2); % number of errors for given SNR

err_sim(ii) = n_err/N; % error for given SNR

%% analytical

err_ana(ii) = 0.5*(1-sqrt(snr/(1+snr)));

end

figure;

semilogy(snr_dB, err_sim,'--+k');

hold on; grid on;

semilogy(snr_dB, err_ana,'-ok');

title('Direct Transmission - BPSK - Rayleigh Fading')

xlabel('SNR (dB)');

ylabel('Error rate');

legend('simulation', 'analytical');

SIMULATED OUTPUT