Main Content

(To be removed) Construct least mean square (LMS) adaptive algorithm object

**lms will be removed in a future release. Use comm.LinearEqualizer or comm.DecisionFeedbackEqualizer instead.**

`alg = lms(stepsize)`

alg = lms(stepsize,leakagefactor)

The `lms`

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 Equalization.

`alg = lms(stepsize)`

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

.

`alg = lms(stepsize,leakagefactor)`

sets the
leakage factor of the LMS algorithm. `leakagefactor`

must be between 0
and 1. A value of 1 corresponds to a conventional weight update algorithm, and a value
of 0 corresponds to a memoryless update algorithm.

The table below describes the properties of the LMS adaptive algorithm object. To learn how to view or change the values of an adaptive algorithm object, see Equalization.

Property | Description |
---|---|

`AlgType` | Fixed value, `'LMS'` |

`StepSize` | LMS step size parameter, a nonnegative real number |

`LeakageFactor` | LMS leakage factor, a real number between 0 and 1 |

Referring to the schematics presented in Equalization,
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

(`LeakageFactor`

) w + (`StepSize`

)
u^{*}e

where the * operator denotes the complex conjugate.

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

[2] Haykin, Simon, *Adaptive Filter
Theory*, Third Ed., Upper Saddle River, NJ, Prentice-Hall,
1996.

[3] Kurzweil, Jack, *An Introduction to
Digital Communications*, New York, John Wiley & Sons,
2000.

[4] Proakis, John G., *Digital
Communications*, Fourth Ed., New York, McGraw-Hill, 2001.