## Documentation Center |

`alg = rls(forgetfactor)alg = rls(forgetfactor,invcorr0)`

The `rls` 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 = rls(forgetfactor)` constructs
an adaptive algorithm object based on the recursive least squares
(RLS) algorithm. The forgetting factor is `forgetfactor`,
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.

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

AlgType | Fixed value, 'RLS' |

ForgetFactor | Forgetting factor |

InvCorrInit | 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 `lineareq` function
or `dfe` function), the equalizer
object has an `InvCorrMatrix` property that represents
the inverse correlation matrix for the RLS algorithm. The initial
value of `InvCorrMatrix` is `InvCorrInit*eye(N)`,
where `N` is the total number of equalizer weights.

For examples that use this function, see Defining an Equalizer Object and Example: Adaptive Equalization Within a Loop.

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

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

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

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

`dfe` | `equalize` | `lineareq` | `lms` | `normlms` | `signlms` | `varlms`

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