Construct recursive least squares (RLS) adaptive algorithm object
alg = rls(forgetfactor)
alg = rls(forgetfactor,invcorr0)
rls function creates an adaptive algorithm
object that you can use with the
dfe function to create an
equalizer object. You can then use the equalizer object with the
equalize function to equalize a signal.
To learn more about the process for equalizing a signal, see Adaptive Algorithms.
alg = rls(forgetfactor) constructs
an adaptive algorithm object based on the recursive least squares
(RLS) algorithm. The forgetting factor is
a real number between 0 and 1. The inverse correlation matrix is initialized
to a scalar value.
alg = rls(forgetfactor,invcorr0) sets
the initialization parameter for the inverse correlation matrix. This
scalar value is used to initialize or reset the diagonal elements
of the inverse correlation matrix.
The table below describes the properties of the RLS adaptive algorithm object. To learn how to view or change the values of an adaptive algorithm object, see Access Properties of an Adaptive Algorithm.
|Fixed value, |
|Scalar value used to initialize or reset the diagonal elements of the inverse correlation matrix|
Also, when you use this adaptive algorithm object to create
an equalizer object (via the
dfe function), the equalizer
object has an
InvCorrMatrix property that represents
the inverse correlation matrix for the RLS algorithm. The initial
N is the total number of equalizer weights.
Referring to the schematics presented in Equalizer Structure, define w as the vector of all weights wi and define u as the vector of all inputs ui. Based on the current set of inputs, u, and the current inverse correlation matrix, P, this adaptive algorithm first computes the Kalman gain vector, K
where H denotes the Hermitian transpose.
Then the new inverse correlation matrix is given by
and the new set of weights is given by
w + K*e
where the * operator denotes the complex conjugate.
 Farhang-Boroujeny, B., Adaptive Filters: Theory and Applications, Chichester, England, John Wiley & Sons, 1998.
 Haykin, S., Adaptive Filter Theory, Third Ed., Upper Saddle River, NJ, Prentice-Hall, 1996.
 Kurzweil, J., An Introduction to Digital Communications, New York, John Wiley & Sons, 2000.
 Proakis, John G., Digital Communications, Fourth Ed., New York, McGraw-Hill, 2001.