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Overview of Adaptive Equalizer Classes

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Section Overview Symbol-Spaced Equalizers Fractionally Spaced Equalizers Decision-Feedback Equalizers

Section Overview

This section gives some background information about the supported classes of adaptive equalizers:

For more detailed background material, see the works listed in Selected Bibliography for Equalizers. For more information about particular adaptive algorithms, see the reference pages for the corresponding functions: lms, signlms, normlms, varlms, rls, cma.

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Symbol-Spaced Equalizers

A symbol-spaced linear equalizer consists of a tapped delay line that stores samples from the input signal. Once per symbol period, the equalizer outputs a weighted sum of the values in the delay line and updates the weights to prepare for the next symbol period. This class of equalizer is called symbol-spaced because the sample rates of the input and output are equal.

Below is a schematic of a symbol-spaced linear equalizer with N weights, where the symbol period is T.

Updating the Set of Weights

The algorithms for the Weight Setting and Error Calculation blocks in the schematic are determined by the adaptive algorithm chosen from the list in Equalizer Features of Communications Toolbox Software. The new set of weights depends on these quantities:

• The current set of weights

• The input signal

• The output signal

• For adaptive algorithms other than CMA, a reference signal, d, whose characteristics depend on the operation mode of the equalizer

Reference Signal and Operation Modes

The table below briefly describes the nature of the reference signal for each of the two operation modes.

Operation Mode of Equalizer	Reference Signal
Training mode	Preset known transmitted sequence
Decision-directed mode	Detected version of the output signal, denoted by yd in the schematic

In typical applications, the equalizer begins in training mode to gather information about the channel, and later switches to decision-directed mode.

Error Calculation

The error calculation operation produces a signal given by the expression below, where R is a constant related to the signal constellation.

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Fractionally Spaced Equalizers

A fractionally spaced equalizer is a linear equalizer that is similar to a symbol-spaced linear equalizer, as described in Symbol-Spaced Equalizers. By contrast, however, a fractionally spaced equalizer receives K input samples before it produces one output sample and updates the weights, where K is an integer. In many applications, K is 2. The output sample rate is 1/T, while the input sample rate is K/T. The weight-updating occurs at the output rate, which is the slower rate.

Below is a schematic of a fractionally spaced equalizer.

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Decision-Feedback Equalizers

A decision-feedback equalizer is a nonlinear equalizer that contains a forward filter and a feedback filter. The forward filter is similar to the linear equalizer described in Symbol-Spaced Equalizers, while the feedback filter contains a tapped delay line whose inputs are the decisions made on the equalized signal. The purpose of a DFE is to cancel intersymbol interference while minimizing noise enhancement. By contrast, noise enhancement is a typical problem with the linear equalizers described earlier.

Below is a schematic of a fractionally spaced DFE with L forward weights and N-L feedback weights. The forward filter is at the top and the feedback filter is at the bottom. If K is 1, the result is a symbol-spaced DFE instead of a fractionally spaced DFE.

In each symbol period, the equalizer receives K input samples at the forward filter, as well as one decision or training sample at the feedback filter. The equalizer then outputs a weighted sum of the values in the forward and feedback delay lines, and updates the weights to prepare for the next symbol period.

Note   The algorithm for the Weight Setting block in the schematic jointly optimizes the forward and feedback weights. Joint optimization is especially important for the RLS algorithm.

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Equalizer Features of Communications Toolbox Software

Using Adaptive Equalizer Functions and Objects

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