full_nlms.m

System identification with adaptive filter using full and partial-update Normalised-Least-Mean-Squar

function [e,w] = full_nlms(x,d,N,w0,mu,epsilon)
%[e,w] = full_nlms(x,d,N,w0,mu,epsilon) implements the NLMS algorithm. 
%   ----------------
%   input parameters
%   ----------------
%   x : Lx1 input signal
%   d : Lx1 desired response 
%   N : filter length
%   w0 : Nx1 initialization
%   mu : step-size parameter
%   epsilon: regularization parameter (to avoid divide by zero)
%   ----------------
%   function outputs
%   ----------------
%   w : LxN evolution of coefficients
%   e : Lx1 error vector

x = x(:);
d = d(:);
w0 = w0(:);

L = length(x);
w = zeros(L,N);
e = zeros(L,1);

w(1,:) = w0';
xvec = zeros(N,1);

for i = 1:L-1
    xvec = [x(i);xvec(1:N-1)];
    e(i) = d(i)-w(i,:)*xvec;
    upd = mu*e(i)*xvec/(norm(xvec)^2+epsilon);
    w(i+1,:) = w(i,:) + upd';
end
xvec = [x(L);xvec(1:N-1)];
e(L) = d(L)-w(L,:)*xvec;