MRC.m

% Script for computing the BER for BPSK modulation in a
% Rayleigh fading channel with Maximal Ratio 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 maximal ratio combining 
        yHat =  sum(conj(h).*y,1)./sum(h.*conj(h),1); 

        % 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)); 
p = 1/2 - 1/2*(1+1./EbN0Lin).^(-1/2);
theoryBer_nRx2 = p.^2.*(1+2*(1-p)); 

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 Maximal Ratio Combining in Rayleigh channel');