equalizer.m

自适应滤波器的实现：包括信号的产生,最优系数的求解等等。

clc;
clear;
a=[-3 -1 1 3];                   % 4-PAM alphabet
Ak=a(randint(1000,1,4)+1);       % 4-PAM sequence
figure(1); 
plot(a,[0 0 0 0],'o');
title('4-PAM constellation'); 
grid;
H=fir1(8,0.6); % Channel model, FIR-filter
figure(2); 
stem(H);                      % Impulse response of the channel
title('Impulse response of the channel')
 figure(3); 
freqz(H,1,256);                 % Frequency response of the channel
title('Frequency response of the channel')
Rk=filter(H,1,Ak);              % Received signal
figure(4);
plot(Rk,zeros(size(Rk)),'o') ;      % Constellation 
title(' Constellation of the received signal');
grid;

% Initialization
FII=zeros([31,31]);            % Autocorrelation Matrix
alfa=0;
% How to define FII and alfa
% The channel causes a delay. It can be seen from the maximum point of the impulse response.
% In this case, the delay is 5 (see channel impulse response).
for i=5:900,
rk=flipud(Rk(i:i+30).');         % received signal vector
FII=FII+rk*rk.';               % Autocorrelation matrix
alfa=alfa+Ak(i-4+15)*rk;
end
FII=FII/896;
alfa=alfa/896;
c=inv(FII)*alfa;               % Equalizer coefficients
figure(5);
freqz(c,1,256);                % Frequency response of equalizer
title('Frequency response of the equalizer')

H=fir1(8,0.8);         % new channel
Rk=filter(H,1,Ak);     % received signal
% close all;             % Close all figures
beta=0.01;            % step-size of the algorithm
c=zeros(size(1:31)).';    % equalizer coefficients, initializations
for i=5:900,
rk=flipud(Rk(i:i+30).');     % Received signal vector
Ek(i-4)=Ak(i-4+15)-c.'*rk;  % Error signal, we use the symbol sequence known in
% advance
c=c+beta*Ek(i-4)*rk;
end
figure(6);
plot(abs(Ek))   % Covergence behaviour of the LMS-algorithm. Should be zero or 
                % near zero (in the case of channel noise) after the convergence
title('Covergence behaviour');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
y=filter(c,1,Rk);
figure(7);
plot(y,zeros(size(Rk)),'o');grid;    % Constellation
title('Constellation of the received signal');
figure(8);
freqz(H,1,256);                      % Frequency response of the channel
title('Frequency response of the channel');
figure(9);
freqz(c,1,256);                      % Frequency response of equalizer
title('Frequency response of the equalizer');