36 init_ rls

Purpose

Creates and initializes the variables required for the Recursive Least Squares (RLS) adaptive algorithm.

Syntax

[w,x,d,y,e,R]=init_rls(L,b)
[w,x,d,y,e,R]=init_rls(L,b,w0,x0,d0)

Description

The variables of the RLS are summarized below (see Fig. 2.6).

Input Parameters:: 
   L  : Adaptive filter length
   b  : a small +ve constant to initialize R 
   w0 : initial coefficient vector  
   x0 : initial input samples vector 
   d0 : initial desired sample
Output parameters [default]::
   w  : Initialized filter coefficients [zeros]
   x  : Initialized input vector [zeros]
   d  : Initialized desired sample [white noise]
   y  : Initialized filter output [y = w' * x]
   e  : Initialized error sample [e = d - y]
   R  : Initialized inverse of the weighted 
        auto correlation matrix of x, [R=b*eye(L)]

Example

L  = 5;           % Number of coefficients 
w0 = [0;0;1;0;0]; % initial filter coefficients 
x0 = rand(5,1);   % initial delay line
d0 = 0;           % desired sample

% Create and initialize the RLS FIR filter
[w,x,d,y,e,R]=init_rls(L,0.1,w0,x0,d0);

Remarks

• Supports both real and complex signals and filters.
• Use input parameters 3 through 5 to initialize the algorithm storage. This is helpful when the adaptation process is required to start from a known operation point calculated off-line or from previous simulations.

See Also

ASPTRLS, EQUALIZER_ RLS.