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# varlms

Construct variable-step-size least mean square (LMS) adaptive algorithm object

## Syntax

alg = varlms(initstep,incstep,minstep,maxstep)

## Description

The varlms 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 Adaptive Algorithms.

alg = varlms(initstep,incstep,minstep,maxstep) constructs an adaptive algorithm object based on the variable-step-size least mean square (LMS) algorithm. initstep is the initial value of the step size parameter. incstep is the increment by which the step size changes from iteration to iteration. minstep and maxstep are the limits between which the step size can vary.

### Properties

The table below describes the properties of the variable-step-size LMS adaptive algorithm object. To learn how to view or change the values of an adaptive algorithm object, see Access Properties of an Adaptive Algorithm.

PropertyDescription
AlgTypeFixed value, 'Variable Step Size LMS'
LeakageFactorLMS 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.
InitStepInitial value of step size when the algorithm starts
IncStepIncrement by which the step size changes from iteration to iteration
MinStepMinimum value of step size
MaxStepMaximum value of step size

Also, when you use this adaptive algorithm object to create an equalizer object (via the lineareq or dfe function), the equalizer object has a StepSize property. The property value is a vector that lists the current step size for each weight in the equalizer.

## Examples

For an example that uses this function, see Linked Properties of an Equalizer Object.

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### Algorithms

Referring to the schematics presented in Equalizer Structure, define w as the vector of all current weights wi and define u as the vector of all inputs ui. Based on the current step size, μ, this adaptive algorithm first computes the quantity

μ0 = μ + (IncStep) Re(ggprev)

where g = ue*, gprev is the analogous expression from the previous iteration, and the * operator denotes the complex conjugate.

Then the new step size is given by

• μ0, if it is between MinStep and MaxStep

• MinStep, if μ0 < MinStep

• MaxStep, if μ0 > MaxStep

The new set of weights is given by

(LeakageFactor) w + 2 μ g*

## References

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