(To be removed) Equalize using linear equalizer that updates weights with LMS algorithm

Equalizers

**
LMS Linear Equalizer will be removed in a future release. Use Linear Equalizer
instead.**

The LMS Linear Equalizer block uses a linear equalizer and the LMS algorithm to equalize a
linearly modulated baseband signal through a dispersive channel. During the simulation, the
block uses the LMS algorithm to update the weights, once per symbol. When you set the
**Number of samples per symbol** parameter to `1`

, then
the block implements a symbol-spaced (i.e. T-spaced) equalizer. When you set the
**Number of samples per symbol** parameter to a value greater than one, the
block updates the weights once every *N*^{th} sample
for a T/N-spaced equalizer.

The `Input`

port accepts a column vector input signal. The
`Desired`

port receives a training sequence with a length that is less
than or equal to the number of symbols in the `Input`

signal. Valid
training symbols are those symbols listed in the **Signal constellation**
vector.

Set the **Reference tap** parameter so it is greater than zero and less
than the value for the **Number of taps** parameter.

The `Equalized`

port outputs the result of the equalization
process.

You can configure the block to have one or more of these extra ports:

`Mode`

input.`Err`

output for the error signal, which is the difference between the`Equalized`

output and the reference signal. The reference signal consists of training symbols in training mode, and detected symbols otherwise.`Weights`

output.

To learn the conditions under which the equalizer operates in training or decision-directed mode, see Equalization.

For proper equalization, you should set the **Reference tap** parameter
so that it exceeds the delay, in symbols, between the transmitter's modulator output and the
equalizer input. When this condition is satisfied, the total delay, in symbols, between the
modulator output and the equalizer *output* is equal to

1+(**Reference tap**-1)/(**Number of samples per
symbol**)

Because the channel delay is typically unknown, a common practice is to set the reference tap to the center tap.

**Number of taps**The number of taps in the filter of the linear equalizer.

**Number of samples per symbol**The number of input samples for each symbol.

**Signal constellation**A vector of complex numbers that specifies the constellation for the modulated signal, as determined by the modulator in your model

**Reference tap**A positive integer less than or equal to the number of taps in the equalizer.

**Step size**The step size of the LMS algorithm.

**Leakage factor**The leakage factor of the LMS algorithm, a number 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.

**Initial weights**A vector that lists the initial weights for the taps.

**Mode input port**If you select this check box, the block has an input port that allows you to toggle between training and decision-directed mode. For training, the mode input must be 1, and for decision directed, the mode must be 0. For every frame in which the mode input is 1 or not present, the equalizer trains at the beginning of the frame for the length of the desired signal.

**Output error**If you select this check box, the block outputs the error signal, which is the difference between the equalized signal and the reference signal.

**Output weights**If you select this check box, the block outputs the current weights.

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

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

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

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