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RLS Linear Equalizer

Equalize using linear equalizer that updates weights using RLS algorithm

Library

Equalizers

Description

The RLS Linear Equalizer block uses a linear 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, then the block implements a symbol-spaced (i.e. T-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 block updates the weights once every Nth sample, for a fractionally spaced (i.e. T/N-spaced) equalizer.

Input and Output Signals

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 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, as described in Adaptive Algorithms in Communications System Toolbox™ User's Guide.

  • 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, as described in Adaptive Algorithms in Communications System Toolbox User's Guide.

Decision-Directed Mode and Training Mode

To learn the conditions under which the equalizer operates in training or decision-directed mode, see Adaptive Algorithms in Communications System Toolbox User's Guide.

Equalizer Delay

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.

Dialog Box

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 modulation.

Reference tap

A positive integer less than or equal to the number of 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 number of taps.

Initial weights

A vector that lists the initial weights for the 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 weights.

Examples

See the Adaptive Equalization example.

References

[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.

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