Communications Blockset™

LMS Linear Equalizer - Equalize using linear equalizer that updates weights with LMS algorithm

Library

Equalizers

Description

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. 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 inControlling the Use of Training or Decision-Directed Mode in Communications Blockset 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 Retrieving the Weights and Error Signal in Communications Blockset 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 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.

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 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 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 weights.

Examples

See Example: LMS Linear Equalizer and the Adaptive Equalization demo.

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.