%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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 : [email protected]
% Version : 1.0
% Date : 09 Novemeber 2008
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Script for computing the BER for BPSK modulation in a
% Rayleigh fading channel with 2 Tx, 2Rx MIMO channel
% Zero Forcing Equalization with Successive Interference
% Cancellation (ZF-SIC)
clear
N = 10^6; % number of bits or symbols
Eb_N0_dB = [0:50]; % multiple Eb/N0 values
nTx = 2;
nRx = 2;
for ii = 1:length(Eb_N0_dB)
% Transmitter
ip = rand(1,N)>0.5; % generating 0,1 with equal probability
s = 2*ip-1; % BPSK modulation 0 -> -1; 1 -> 0
sMod = kron(s,ones(nRx,1)); %
sMod = reshape(sMod,[nRx,nTx,N/nTx]); % grouping in [nRx,nTx,N/NTx ] matrix
h = 1/sqrt(2)*[randn(nRx,nTx,N/nTx) + j*randn(nRx,nTx,N/nTx)]; % Rayleigh channel
n = 1/sqrt(2)*[randn(nRx,N/nTx) + j*randn(nRx,N/nTx)]; % white gaussian noise, 0dB variance
% Channel and noise Noise addition
y = squeeze(sum(h.*sMod,2)) + 10^(-Eb_N0_dB(ii)/20)*n;
% Receiver
% Forming the ZF equalization matrix W = inv(H^H*H)*H^H
% H^H*H is of dimension [nTx x nTx]. In this case [2 x 2]
% Inverse of a [2x2] matrix [a b; c d] = 1/(ad-bc)[d -b;-c a]
hCof = zeros(2,2,N/nTx) ;
hCof(1,1,:) = sum(h(:,2,:).*conj(h(:,2,:)),1) ; % d term
hCof(2,2,:) = sum(h(:,1,:).*conj(h(:,1,:)),1) ; % a term
hCof(2,1,:) = -sum(h(:,2,:).*conj(h(:,1,:)),1); % c term
hCof(1,2,:) = -sum(h(:,1,:).*conj(h(:,2,:)),1); % b term
hDen = ((hCof(1,1,:).*hCof(2,2,:)) - (hCof(1,2,:).*hCof(2,1,:))); % ad-bc term
hDen = reshape(kron(reshape(hDen,1,N/nTx),ones(2,2)),2,2,N/nTx); % formatting for division
hInv = hCof./hDen; % inv(H^H*H)
hMod = reshape(conj(h),nRx,N); % H^H operation
yMod = kron(y,ones(1,2)); % formatting the received symbol for equalization
yMod = sum(hMod.*yMod,1); % H^H * y
yMod = kron(reshape(yMod,2,N/nTx),ones(1,2)); % formatting
yHat = sum(reshape(hInv,2,N).*yMod,1); % inv(H^H*H)*H^H*y
% receiver - hard decision decoding on second spatial dimension
ipHat2SS = real(yHat(2:2:end))>0;
ipHatMod2SS = 2*ipHat2SS-1;
ipHatMod2SS = kron(ipHatMod2SS,ones(nRx,1));
ipHatMod2SS = reshape(ipHatMod2SS,[nRx,1,N/nTx]);
% new received symbol - removing the effect from second spatial dimension
h2SS = h(:,2,:); % channel in the second spatial dimension
r = y - squeeze(h2SS.*ipHatMod2SS);
% maximal ratio combining - for symbol in the first spatial dimension
h1SS = squeeze(h(:,1,:));
yHat1SS = sum(conj(h1SS).*r,1)./sum(h1SS.*conj(h1SS),1);
yHat(1:2:end) = yHat1SS;
% receiver - hard decision decoding
ipHat = real(yHat)>0;
% counting the errors
nErr(ii) = size(find([ip- ipHat]),2);
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);
theoryBerMRC_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,theoryBerMRC_nRx2,'kd-','LineWidth',2);
semilogy(Eb_N0_dB,simBer,'mo-','LineWidth',2);
axis([0 25 10^-5 0.5])
grid on
legend('theory (nTx=2,nRx=2, ZF)', 'theory (nTx=1,nRx=2, MRC)', 'sim (nTx=2, nRx=2, ZF-SIC)');
xlabel('Average Eb/No,dB');
ylabel('Bit Error Rate');
title('BER for BPSK modulation with 2x2 MIMO and ZF-SIC equalizer (Rayleigh channel)');