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RLS Decision Feedback Equalizer - Equalize using decision feedback equalizer that updates weights with RLS algorithm

Library

Equalizers

Description

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. If the Number of samples per symbol parameter is 1, then the block implements a symbol-spaced equalizer; otherwise, the block implements a fractionally spaced equalizer.

Input and Output Signals

The port labeled Input receives the signal you want to equalize, as a scalar or a frame-based column vector. The port labeled Desired receives a training sequence whose length is less than or equal to the number of symbols in the Input signal. Valid training symbols are those listed in the Signal constellation vector.

This block accepts only frame-based signals. If the value of Reference tap is equal to or greater than the frame size, the block will not work properly.

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 Controlling the Use of Training or Decision-Directed Mode in Communications BlocksetUser'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 Retrieving the Weights and Error Signal in Communications BlocksetUser's Guide.

Decision-Directed Mode and Training Mode

To learn the conditions under which the equalizer operates in training or decision-directed mode, see Using Adaptive Equalizers in Communications Blockset 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 of the forward filter.

Dialog Box

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: If you check this box, the block has an input port that enables you to toggle between training and decision-directed mode.
Output error: If you check this box, the block outputs the error signal, which is the difference between the equalized signal and the reference signal.
Output weights: If you check this box, the block outputs the current forward and feedback weights, concatenated into one vector.

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.