%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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 Sankar M
% Email : krishna@dsplog.com
% Version : 1.0
% Date : 29 November 2009
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Script for computing the BER for BPSK modulation in 3 tap ISI
% channel. Zero Forcing equalization with 3/5/7/9 tap is performed
% and the BER computed
clear
N = 10^6; % number of bits or symbols
Eb_N0_dB = [0:10]; % multiple Eb/N0 values
K = 4;
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
% Channel model, multipath channel
nTap = 3;
ht = [0.2 0.9 0.3];
chanOut = conv(s,ht);
n = 1/sqrt(2)*[randn(1,N+length(ht)-1) + j*randn(1,N+length(ht)-1)]; % white gaussian noise, 0dB variance
% Noise addition
y = chanOut + 10^(-Eb_N0_dB(ii)/20)*n; % additive white gaussian noise
for kk = 1:K
L = length(ht);
hM = toeplitz([ht([2:end]) zeros(1,2*kk+1-L+1)], [ ht([2:-1:1]) zeros(1,2*kk+1-L+1) ]);
d = zeros(1,2*kk+1);
d(kk+1) = 1;
c = [inv(hM)*d.'].';
% mathched filter
yFilt = conv(y,c);
yFilt = yFilt(kk+2:end);
yFilt = conv(yFilt,ones(1,1)); % convolution
ySamp = yFilt(1:1:N); % sampling at time T
% receiver - hard decision decoding
ipHat = real(ySamp)>0;
% counting the errors
nErr(kk,ii) = size(find([ip- ipHat]),2);
end
end
simBer = nErr/N; % simulated ber
theoryBer = 0.5*erfc(sqrt(10.^(Eb_N0_dB/10))); % theoretical ber
% plot
close all
figure
semilogy(Eb_N0_dB,simBer(1,:),'bs-'),'Linewidth',2;
hold on
semilogy(Eb_N0_dB,simBer(2,:),'gd-'),'Linewidth',2;
semilogy(Eb_N0_dB,simBer(3,:),'ks-'),'Linewidth',2;
semilogy(Eb_N0_dB,simBer(4,:),'mx-'),'Linewidth',2;
axis([0 10 10^-3 0.5])
grid on
legend('sim-3tap', 'sim-5tap','sim-7tap','sim-9tap');
xlabel('Eb/No, dB');
ylabel('Bit Error Rate');
title('Bit error probability curve for BPSK in ISI with ZF equalizer');