setmem_apa2.m

System identification with adaptive filter using full and partial-update Affine Projection Algorithm

function [e,w] = setmem_apa2(x,d,N,M,K,w0,gamma,epsilon)
%setmem_apa2(x,d,N,M,K,w0,gamma,epsilon) implements set-membership
%partial-update APA-2 adaptive filter
%   ----------------
%   input parameters
%   ----------------
%   x : Lx1 input signal
%   d : Lx1 desired response 
%   N : filter length
%   M : number of coefficients to be updated
%   K : APA order
%   w0 : Nx1 initialization
%   gamma : error bound for set membership filter
%   epsilon: regularization parameter (to avoid divide by zero)
%   ----------------
%   function outputs
%   ----------------
%   e : Lx1 output error vector
%   w : LxN adaptive coefficient vectors

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

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

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

X = zeros(K,N);
dvec = zeros(K,1);

for i = 1:L-1
    xvec = [x(i);xvec(1:N-1)];
    X = [xvec';X(1:K-1,:)];
    e(i) = d(i)-w(i,:)*xvec;
    dvec = [d(i);dvec(1:K-1)];
    if abs(e(i)) > gamma,
        evec = [e(i)*(1-gamma/abs(e(i))); zeros(K-1,1)];

        [xs,ix] = sort(-sum(X.^2,1));     %rank
        de = zeros(1,N);
        de(ix(1:M)) = 1;
        IM = diag(de);

        upd = IM*X'*inv(epsilon*eye(K)+X*IM*X')*evec;

        w(i+1,:) = w(i,:) + upd';
    else
        w(i+1,:) = w(i,:);
    end
end

xvec = [x(L);xvec(1:N-1)];
e(L) = d(L)-w(L,:)*xvec;