%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% All rights reserved by Krishna Pillai, http://www.dsplog.com
% The file may not be re-distributed without explicit authorization
% from Krishna Pillai.
% Checked for proper operation with Octave Version 3.0.0
% Author : Krishna Pillai
% Email : krishna@dsplog.com
% Version : 1.0
% Date : 6th September 2008
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Script for computing the BER for BPSK modulation in a
% Rayleigh fading channel with equal gain combining
clear
N = 10^6; % number of bits or symbols
% Transmitter
ip = rand(1,N)>0.5; % generating 0,1 with equal probability
s = 2*ip-1; % BPSK modulation 0 -> -1; 1 -> 0
nRx = [1 2];
Eb_N0_dB = [0:35]; % multiple Eb/N0 values
for jj = 1:length(nRx)
for ii = 1:length(Eb_N0_dB)
n = 1/sqrt(2)*[randn(nRx(jj),N) + j*randn(nRx(jj),N)]; % white gaussian noise, 0dB variance
h = 1/sqrt(2)*[randn(nRx(jj),N) + j*randn(nRx(jj),N)]; % Rayleigh channel
% Channel and noise Noise addition
sD = kron(ones(nRx(jj),1),s);
y = h.*sD + 10^(-Eb_N0_dB(ii)/20)*n;
% equalization with equal gain combining
yHat = y.*exp(-j*angle(h)); % removing the phase of the channel
yHat = sum(yHat,1); % adding values from all the receive chains
% receiver - hard decision decoding
ipHat = real(yHat)>0;
% counting the errors
nErr(jj,ii) = size(find([ip- ipHat]),2);
end
end
simBer = nErr/N; % simulated ber
EbN0Lin = 10.^(Eb_N0_dB/10);
theoryBer_nRx1 = 0.5.*(1-1*(1+1./EbN0Lin).^(-0.5));
theoryBer_nRx2 = 0.5*(1 - sqrt(EbN0Lin.*(EbN0Lin+2))./(EbN0Lin+1) );
% plot
close all
figure
semilogy(Eb_N0_dB,theoryBer_nRx1,'bp-','LineWidth',2);
hold on
semilogy(Eb_N0_dB,simBer(1,:),'mo-','LineWidth',2);
semilogy(Eb_N0_dB,theoryBer_nRx2,'rd-','LineWidth',2);
semilogy(Eb_N0_dB,simBer(2,:),'ks-','LineWidth',2);
axis([0 35 10^-5 0.5])
grid on
legend('nRx=1 (theory)', 'nRx=1 (sim)', 'nRx=2 (theory)', 'nRx=2 (sim)');
xlabel('Eb/No, dB');
ylabel('Bit Error Rate');
title('BER for BPSK modulation with Equal Gain Combining in Rayleigh channel');