channeleqlizer.m

channel equalizer for wireless communication system

clear all
close all

%simulation length
N = 1000;

%channel length
M = 5;

%number of independent trials
T = 100;

cascade_impulse_response = zeros(1,2*M-1);
for j = 1 : T    
    %training signal
    u = randn(1,N);

    %channel to be equalized    
    c = randn(M,1);
    c = c / norm(c);

    %channel output
    z = filter(c,1,u);

    %additive noise to the channel output
    SNR = 30;
    var_v = var(z) * 10^(-SNR/10);
    v = var_v^0.5 * randn(1,N);

    %input to the equalizer
    x = z + v;

    %NLMS channel equalization
    w = zeros(M,1);
    x_regressor = zeros(1,M);
    step = 0.1;
    epsilon = 10^(-6);
    for k = 4 : N
        x_regressor = [x(k) x_regressor(1:M-1)];
        e = u(k-3) - x_regressor * w;
        w = w + (((step * x_regressor') * e )/ ((x_regressor * x_regressor')+epsilon));
    end
    cascade_impulse_response = cascade_impulse_response + conv(w,c)';
    display(j);
end
figure;
stem(cascade_impulse_response/T);
title('cascade channel-equalizer impulse response');
xlabel('taps');