%DEMO of ADAPTIVE EQUALIZATION USING THE LMS ALGORITHM

%------- Define equalizer parameters

N = 4;          % number of equalizer coefficients
mu = 0.005;     % equalizer step size

%------- Define modulation parameters

alphabet = [-3 -1 1 3];
K = 400;        % number of symbols to transmit

%------- Define channel parameters

h = [1 -0.5];   % channel impulse response
sig = 0.1;      % noise standard deviation

%------- Generate channel output r

a = alphabet(ceil((length(alphabet)*rand(1,K))));
r = conv(a,h) + sig * randn(1, K + length(h)-1);

%------------------------------------

C = zeros(N,1);
R = zeros(N,1);
for k=1:K,
        R(2:N) = R(1:N-1);              
        R(1) = r(k);
        z(k) = C.' * R;
        e(k) = z(k) - a(k);             % LMS
        C = C - mu * e(k) * conj(R);    % algorithm

        Cs(k,:) = C';
end;

subplot(211); plot(z,'o');
xlabel('Time (in symbol periods)'); ylabel('Equalizer output');
subplot(212); plot(Cs);
xlabel('Time (in symbol periods)'); ylabel('Equalizer coefficients');