Selective DF - 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

h1= 1/sqrt(2)*(randn(1,N)+1i*randn(1,N)); % complex channel gain

h2= 1/sqrt(2)*(randn(1,N)+1i*randn(1,N)); % complex channel gain

h3= 1/sqrt(2)*(randn(1,N)+1i*randn(1,N)); % complex channel gain

n1 = 1/sqrt(2)*(randn(1,N)+1i*randn(1,N)); % AWGN

n2 = 1/sqrt(2)*(randn(1,N)+1i*randn(1,N)); % AWGN

n3 = 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);

r_u1bs = sqrt(snr/2)*s.*h1 + n1; % received signal

r_u1u2 = sqrt(snr/2)*s.*h2 + n2; % received signal

r_u2bs = sqrt(snr/2)*s.*h3 + n3; % received signal

r1 = conj(h1).*r_u1bs; % compensation for fading (equalization)

r2 = conj(h2).*r_u1u2; % compensation for fading (equalization)

r3 = conj(h1).*r_u1bs + conj(h3).*r_u2bs; % compensation for fading (equalization)

s1_hat = real(r1)>0; % decision making

s2_hat = real(r2)>0; % decision making

s3_hat = real(r3)>0; % decision making

n_err1 = size(find(s1_hat-ip0),2); % number of errors for given SNR

n_err2 = size(find(s2_hat-ip0),2); % number of errors for given SNR

n_err3 = size(find(s3_hat-ip0),2); % number of errors for given SNR

err1 = n_err1/N; % error for given SNR

err2 = n_err2/N; % error for given SNR

err3 = n_err3/N; % error for given SNR

err_sim(ii) = err1*err2 +(1-err1)*err3;

%% analytical

Pe = 0.5*(1-sqrt(snr/2/(1+snr/2)));

err_ana(ii) = Pe^2 + (1-Pe)*Pe^2*(3-2*Pe);

end

figure;

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

hold on; grid on;

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

xlabel('SNR (dB)');

ylabel('Error rate');

legend('simulation', 'analytical');

title('Selective DF - BPSK - Rayleigh Fading')

SIMULATED OUTPUT