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

**normlms will be removed in a future release. Use comm.LinearEqualizer or comm.DecisionFeedback instead.**

`alg = normlms(stepsize)`

alg = normlms(stepsize,bias)

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 Equalization.

`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.

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 Equalization.

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 |

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

$$(\text{LeakageFactor})w+\frac{(\text{StepSize}){u}^{*}e}{{u}^{H}u+\text{Bias}}$$

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

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