seq_nlms.m

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

function [e,w] = seq_nlms(x,d,N,M,w0,mu,epsilon)
%[e,w] = seq_lms(x,d,N,M,w0,mu) implements the sequential partial update LMS
%algorithm. 
%   ----------------
%   input parameters
%   ----------------
%   x : Lx1 input signal
%   d : Lx1 desired response 
%   N : filter length
%   M : number of coefficients to be updated
%   w0 : Nx1 initialization
%   mu : step-size parameter
%   ----------------
%   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);

B = N/M;
if B == floor(B),
    for i = 1:B
        J(i,1:M) = (i-1)*M+1:i*M;
    end
else
    B = ceil(B);
    for i = 1:B-1
        J(i,1:M) = (i-1)*M+1:i*M;
    end
    J(B,1:N-(B-1)*M) = (B-1)*M+1:N;
end

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;

    de = zeros(1,N);
    ix = mod(i-1,B)+1;
    Ix = J(ix,:);
    de(Ix(find(Ix))) = 1;
    IM = diag(de);

    upd = mu*e(i)*IM*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;