normlms - Construct normalized least mean square (LMS) adaptive algorithm object

Syntax

alg = normlms(stepsize) alg = normlms(stepsize,bias)

Description

The normlms function creates an adaptive algorithm object that you can use with the lineareq function or 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 Using Adaptive Equalizer Functions and Objects.

alg = normlms(stepsize) constructs an adaptive algorithm object based on the normalized least mean square (LMS) algorithm with a step size of stepsize and a bias parameter of zero.

alg = normlms(stepsize,bias) sets the bias parameter of the normalized LMS algorithm. bias must be between 0 and 1. The algorithm uses the bias parameter to overcome difficulties when the algorithm's input signal is small.

Properties

The table below describes the properties of the normalized LMS adaptive algorithm object. To learn how to view or change the values of an adaptive algorithm object, see Accessing Properties of an Adaptive Algorithm.

Property	Description
`AlgType`	Fixed value, `'Normalized LMS'`
`StepSize`	LMS step size parameter, a nonnegative real number
`LeakageFactor`	LMS leakage factor, a real number between 0 and 1. A value of 1 corresponds to a conventional weight update algorithm, while a value of 0 corresponds to a memoryless update algorithm.
`Bias`	Normalized LMS bias parameter, a nonnegative real number

Examples

For an example that uses this function, see Delays from Equalization.

Algorithm

Referring to the schematics presented in Overview of Adaptive Equalizer Classes, define w as the vector of all weights w_i and define u as the vector of all inputs u_i. Based on the current set of weights, w, this adaptive algorithm creates the new set of weights given by

where the * operator denotes the complex conjugate and H denotes the Hermitian transpose.

References

[1] Farhang-Boroujeny, B., Adaptive Filters: Theory and Applications, Chichester, England, John Wiley & Sons, 1998.

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