(To be removed) Equalize using decision feedback equalizer that updates weights with RLS algorithm

**
RLS Decision Feedback Equalizer will be removed in a future release. Use Decision Feedback
Equalizer instead.**

Equalizers

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

, the block implements a symbol-spaced equalizer and
updates the filter weights once for each symbol. When you set the **Number of
samples per symbol** parameter to a value greater than
`1`

, the weights are updated once every
*N*^{th} sample, for a fractionally 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 forward taps**
parameter.

The port labeled `Equalized`

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 of the forward filter.

**Number of forward taps**The number of taps in the forward filter of the decision feedback equalizer.

**Number of feedback taps**The number of taps in the feedback filter of the decision feedback 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 modulation.

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

**Forgetting factor**The forgetting factor of the RLS algorithm, a number between 0 and 1.

**Inverse correlation matrix**The initial value for the inverse correlation matrix. The matrix must be N-by-N, where N is the total number of forward and feedback taps.

**Initial weights**A vector that concatenates the initial weights for the forward and feedback taps.

**Mode input port**When 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**When 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**When you select this check box, the block outputs the current forward and feedback weights, concatenated into one vector.

[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.