MATLAB Examples

This model shows the behavior of adaptive equalizer algorithms at a receiver for modulated data transmitted along a channel.

## Structure of the Example

The example includes two equalizers, a reference equalizer that uses the least means square (LMS) algorithm and a configurable equalizer whose algorithm you can select from these choices:

• Least Mean Square (LMS)
• Sign LMS
• Normalized LMS
• Variable Step-Size LMS
• Recursive Least Squares (RLS)
• Constant Modulus Algorithm (CMA)

The example also creates plots that can help you understand how different algorithms behave.

## Experimenting with the Example

The example provides several ways for you to change settings and observe the results.

Initial Settings

The Model Parameters block enables you to vary some parameters of the model, including

• The algorithm for the configurable equalizer
• The modulation scheme (symbol constellation)
• Channel coefficients
• The number of coefficients, or taps, in both equalizers
• To access these parameters, double-click the Model Parameters block

## Equalizer Mode

During the simulation, each of the equalizer types (other than CMA) is capable of operating in training mode or decision-directed mode. In training mode, the desired symbol sequence exactly matches the transmitted symbol sequence. The receiver has knowledge of the transmitted data in this mode. In decision-directed mode, the "desired" symbols are derived from the output of the decision device. You can toggle between training and decision-directed mode by double-clicking the Switch block in the model.

## Results and Displays

Plots shown here are for the CMA equalizer with 6 taps.

Error Statistics

When you run the simulation, the display labeled BER Results Reference LMS shows error statistics for the link with the reference equalizer, while the display labeled BER Results shows error statistics for the link with the configurable equalizer. In particular, each set of error statistics is a three-element vector containing the calculated bit error rate (BER), the number of errors observed, and the number of bits processed.

You can reset the BER statistics during the simulation by double-clicking the Switch block connected to the Rst port of the Error Rate Calculation block.

Scope Windows

During the simulation the model creates plots that show:

• A scatter plot of the received signal at the output of the channel.

• The real part of the weights for the reference, configurable, and optimum equalizers.

• The imaginary part of the weights for the reference, configurable, and optimum equalizers.

• The frequency responses of the channel, the channel after equalization (combined), and the equalizer itself. You can see that the frequency response of the equalizer is roughly the inverse of the channel response and that the post equalization or combined response is flatter.

• A scatter plot of the signal equalized by the reference equalizer.

• A scatter plot of the signal equalized by the configurable equalizer.