# Documentation

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# signlms

Construct signed least mean square (LMS) adaptive algorithm object

## Syntax

```alg = signlms(stepsize) alg = signlms(stepsize,algtype) ```

## Description

The `signlms` 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 = signlms(stepsize)` constructs an adaptive algorithm object based on the signed least mean square (LMS) algorithm with a step size of `stepsize`.

`alg = signlms(stepsize,algtype)` constructs an adaptive algorithm object of type `algtype` from the family of signed LMS algorithms. The table below lists the possible values of `algtype`.

Value of `algtype`Type of Signed LMS Algorithm
`'Sign LMS'`Sign LMS (default)
```'Signed Regressor LMS'```Signed regressor LMS
`'Sign Sign LMS'`Sign-sign LMS

### Properties

The table below describes the properties of the signed 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
`AlgType`Type of signed LMS algorithm, corresponding to the `algtype` input argument. You cannot change the value of this property after creating the object.
`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.

## Examples

collapse all

This example shows to use a signed least mean square (LMS) algorithm to create an adaptive equalizer object.

Set the number of weights and the step size for the equalizer.

```nWeights = 2; stepSize = 0.05;```

Create the adaptive algorithm object using the signed regressor LMS algorithm type.

`alg = signlms(stepSize,'Signed Regressor LMS');`

Construct a linear equalizer using the algorithm object.

`eqObj = lineareq(nWeights,alg)`
```eqObj = EqType: 'Linear Equalizer' AlgType: 'Signed Regressor LMS' nWeights: 2 nSampPerSym: 1 RefTap: 1 SigConst: [-1 1] StepSize: 0.0500 LeakageFactor: 1 Weights: [0 0] WeightInputs: [0 0] ResetBeforeFiltering: 1 NumSamplesProcessed: 0 ```

## Algorithms

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 weights, w, this adaptive algorithm creates the new set of weights given by

• `(LeakageFactor) w + (StepSize) u*sgn(Re(e))`, for sign LMS

• ```(LeakageFactor) w + (StepSize) sgn(Re(u)) Re(e)```, for signed regressor LMS

• ```(LeakageFactor) w + (StepSize) sgn(Re(u)) sgn(Re(e))```, for sign-sign LMS

where the `*` operator denotes the complex conjugate and `sgn` denotes the signum function (`sign` in MATLAB® technical computing software).

## References

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

[2] Kurzweil, J., An Introduction to Digital Communications, New York, John Wiley & Sons, 2000.