%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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 selection diversity

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;


        % finding the power of the channel on all rx chain
        hPower = h.*conj(h);
        
        % finding the maximum power
        [hMaxVal ind] = max(hPower,[],1);
        hMaxValMat = kron(ones(nRx(jj),1),hMaxVal);
        
        % selecting the chain with the maximum power
        ySel = y(hPower==hMaxValMat);
        hSel = h(hPower==hMaxValMat);

        % equalization with the selected rx chain
        yHat = ySel./hSel;
        yHat = reshape(yHat,1,N); % just to get the matrix dimension proper

        % 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.*(1-2*(1+1./EbN0Lin).^(-0.5) +   (1+2./EbN0Lin).^(-0.5));

% 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 Selection diveristy in Rayleigh channel');