Variable Step LMS Decision Feedback Equalizer

Equalize using decision feedback equalizer that updates weights with variable-step-size LMS algorithm

Library

Equalizers

Description

The Variable Step LMS Decision Feedback Equalizer block uses a decision feedback equalizer and the variable-step-size LMS algorithm to equalize a linearly modulated baseband signal through a dispersive channel. During the simulation, the block uses the variable-step-size 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 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 Nth sample, for a 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 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, as described in Reference Signal and Operation Modes 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 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.

Initial step size

The step size that the variable-step-size LMS algorithm uses at the beginning of the simulation.

Increment step size

The increment by which the step size changes from iteration to iteration

Minimum step size

The smallest value that the step size can assume.

Maximum step size

The largest value that the step size can assume.

Leakage factor

The leakage factor of the variable-step-size 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 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 enables you to toggle between training and decision-directed mode. For training, the mode input must be 1, for decision directed, the mode should be 0. The equalizer will train for the length of the Desired signal. If the mode input is not present, the equalizer will train at the beginning of every 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.

References

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

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