lms_algorithm.m

This program simulates plant identification least mean square (NLMS) alogrithm reference: 《LMS算法的

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%                                                                                       %
%  This program simulates plant identification  least  mean square (NLMS) alogrithm     %
%  reference: 《LMS算法的频域快速实现》                                                  %                                                                    %
%  Created originally by Ni Min,Chen Zuo and Mao Xinsheng on Nov 11,2007                %
%                                                                                       %
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function [w1,lms_mse] = LMS_algorithm(x,d,u,N,num);
%generator1: [lms_mse] = LMS_algorithm(x,d,0.0002,64,num);
%generator2: [lms_mse] = LMS_algorithm(x,d,0.01,64,num);

% Input parameters:
%            u:   step size
%            N:   number of weights
%            x:   input signal
%            d:   output signal
%            y:   expectation output sequence of the AF
%            e:   the difference sequence
%            K:   experiment time
%            w:   weight
%            #:   edit up to user
%----------------------------------------------------%

% ---------------initialization----------------------%
K=length(x);                                               %  length of input signal
y=zeros(1,K);                                              %  the practical output of the idetification plant
w1=zeros(1,N);                                             %  the weight vector
wk=zeros((K-N+1),N);                                       %  store each weight value 
e=zeros(1,K);                                              %  the error signal of d and y
lms_mse=zeros(1,K);                                        %  the mean square error
block=11;                                                  %  the size used to smooth the mse
%-------------lms algorithm begin--------------------%
x=[zeros(1,N-1),x];
for n=N:K+N-1
    xb=x(n:-1:n-N+1);                                      %  input signal is delayed by the N weights
    y(n-N+1)=w1*xb';
    e(n-N+1)=d(n-N+1)-y(n-N+1);
    w1=w1+2*u*e(n-N+1)*xb;
    wk((n-N+1),:)=w1;                                      %  store weight every time
end;
%-------------lms algorithm end----------------------%

%----------compute the mean square error-------------%     %  compute the mean square error 
E=e.^2;
E1=[zeros(1,fix(block/2)),E,zeros(1,fix(block/2)+1)];
for i=1:K
    sum_E=0;                                                         
    for j=1:block
    sum_E=sum_E+E1(j+i);
    end
    lms_mse(i)=sum_E/block;
end

%-----------plot the weight comparison---------------%     %  plot the weight comparison
figure(1);
stem(1:N,num,'r');
hold on;
stem(1:N,w1(1:N),'b');
title('weight comparison'); 
xlabel('weight index');
ylabel('weight value');

%-----------plot the mse-----------------------------%     %  plot the mse
figure(2);
plot(1:K,lms_mse);
title('mean square error');
xlabel('iteration n');
ylabel('mse');

%-------display the mismatch--------------------------%       %  display the mismatch
MIS=10*log10(norm(num-w1(1:N))/(norm(num)));
disp('LMS_MIS=');
disp(MIS);