Adaptive Filtering

9.10  THE NORMALIZED SIGN–SIGN LMS ALGORITHM

The sign–sign LMS algorithm is defined by

$w\left(n+1\right)=w\left(n\right)+\text{μ}\frac{\text{sign}\left[e\left(n\right)\right]\text{sign}\left[x\left(n\right)\right]}{\epsilon +{\Vert x\left(n\right)\Vert }^2}{\Vert x\left(n\right)\Vert }^2=x\prime \left(n\right)x\left(n\right)$

(9.18)

Book m-Function for Normalized Sign–Sign LMS Algorithm

function[w,y,e,J,w1]=lms_normalized_sign_sign(x,dn,mu,M)

%function[w,y,e,J,w1]=lms_normalized_sign_sign(x,dn,mu,M)

%all quantities are real valued;

%x=input data to the adaptive filter;

%dn=desired signal;

%M=order of the filter;

%mu=step-size parameter;x and dn must be of

%the same length;

N=length(x);

y=zeros(1,N);

w=zeros(1,M);%initialized filter coefficient vector;

for n=M:N

x1=x(n:−1:n−M+1);%for each n the vector x1 is produced

 %of length M with elements from x in reverse order;

y(n)=w*x1';

e(n)=dn(n)−y(n);

w=w+2*mu*sign(e(n))*sign(x1)./(0.0001+x1*x1'); ...