This model shows the behavior of adaptive equalizer algorithms at a receiver for modulated data transmitted along a channel.
The example includes two equalizers, a reference equalizer that uses the LMS algorithm and a configurable equalizer whose algorithm you can select from these choices:
Least Mean Square (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.
This 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, or symbol constellation
The number of coefficients, or taps, in both equalizers
To access these parameters, double-click the Model Parameters block.
Cost Function and Initial Conditions. You can choose an initial set of weights for the equalizers when the Model Parameters block has Number of equalizer coefficients set to 2 and Symbol Constellation set to BPSK. To choose the initial set of weights, use this procedure:
1. Double-click the Plot Cost Function block to open a contour plot of the MSE cost function (as well as the constant modulus cost function, in case you selected CMA as the algorithm for the configurable equalizer).
2. Click in the plotting window to choose an initial set of weights for the equalizers in the model. Your choice takes effect the next time you run the simulation.
Equalizer Mode. During the simulation, each of the equalizers (except a CMA equalizer) is capable of operating in training mode or decision-directed mode. In training mode, the desired symbol sequence exactly matches the transmitted symbol sequence (i.e., 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.
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 blocks.
Scope Windows. During the simulation, the model creates plots that show
A scatter plot of the received signal, at the output of the channel
You can see how, under certain conditions, the equalizers' cost functions converge to the minimum MSE.
The real parts of the weights of the equalizers, on the same axes with the real parts of the optimal weights
The imaginary parts of the weights of the equalizers, on the same axes with the imaginary parts of the optimal weights
The frequency response of the channel, equalizer, and their combination. You can see how, under certain conditions, the frequency response of the combination of channel and equalizer becomes flat.
A scatter plot of the signal equalized by the reference equalizer
A scatter plot of the signal equalized by the configurable equalizer
The cost functions for the equalizers, on the same axes with the minimum MSE. Postsimulation Display of Trajectory: When the Number of equalizer coefficients parameter in the Model Parameters block is set to 2 and the Symbol Constellation parameter is set to BPSK, the model produces an additional plot at the end of a simulation. The new plot shows the trajectory of the two-element weight vector for each of the equalizers. On the same set of axes is a contour plot of the MSE cost function (or the constant modulus cost function, in case you selected CMA as the algorithm for the configurable equalizer). You can see from the plot how the adaptive algorithm causes the weights to change so as to minimize the cost function.
The simulation runs more slowly when it needs to update all the plots. To close the plotting windows and speed up the simulation, double-click the icon labeled Close Scopes.
To generate executable code for this model, you will need to comment out the Plot Results subsystem, as it does not support code generation. Use set_param('commeqsim/Plot Results','Commented', 'on') to do this and then generate code for the model.
 Haykin, S., Adaptive Filter Theory, Third Ed., Upper Saddle River, N.J., Prentice Hall, 1996.
 Farhang-Boroujeny, B., Adaptive Filters: Theory and Applications, Chichester, England, Wiley, 1998.
 Johnson, C.R., et al., "Blind Equalization Using the Constant Modulus Criterion: A Review," Proc. IEEE, Vol. 86, No. 10, Oct. 1998.