Communications Blockset

Adaptive Equalization Demo

The Adaptive Equalization demo, eq_sim, demonstrates the behaviors of several algorithms that are commonly used in communications:

• Least Mean-Square (LMS)
• Recursive Least-Squares (RLS)
• Constant Modulus Algorithm (CMA)

To select any of these algorithms and to set up the parameters corresponding to each algorithm, double click the block in the model labeled "Initial Settings."

The Least Mean-Square (LMS) algorithm tries to minimize the mean square error (MSE) by using instantaneous values of the error.

Both the LMS and RLS algorithms use a sequence of symbol estimation errors to drive the equalizer weight adaptation. The error is given by the difference between the equalizer's output symbol and the so-called desired symbol. The algorithms operate in one of two modes:

• Training mode, in which the desired symbol sequence exactly matches the transmitted symbol sequence (i.e., the receiver has knowledge of the transmitted data in this mode).
• Decision-directed mode, in which the "desired" symbols are derived from the output of the decision device.

In the demo, a manual switch controls these modes of operation. To toggle the mode, double-click the block.

To overcome some of the disadvantages of the LMS algorithms, researchers have proposed different modifications of the algorithms that can be used under different scenarios. Several of these algorithms have been implemented in the model: Sign LMS, Normalized LMS (NLMS), Variable Step-size LMS (VSLMS), and Leaky LMS.

The Recursive Least-Squares (RLS) algorithm uses a deterministic approach instead of stochastic as in the case of the LMS to update the coefficients. By increasing the computational complexity and risk of instability, the RLS achieves faster convergence than the LMS.

Finally, the Constant Modulus Algorithm (CMA), or Godard Algorithm, belongs to the family of blind equalization. It is mainly used when no knowledge of the input sequence is available and only statistics of the source are known.

When the number of coefficients and the number of points in the constellation are equal to 2, the trajectory over the MSE and the CMA cost functions are presented when the simulation is stopped. To select the initial conditions over the cost function, double-click the block labeled "Plot Cost Function."

For more information on the LMS adaptive filter or channel equalization, see the following references:

[1]  Haykin, S., Adaptive Filter Theory, Third Ed., Prentice Hall, 1996.

[2]  Farhang-Boroujeny, B. Adaptive Filters - Theory and Applications, John Wiley & Sons, 1999.

[3]  Johnson, C. R., et al., "Blind Equalization Using the Constant Modulus Criterion: A Review," Proc. IEEE, Vol. 86, No. 10, Oct. 1998.

Bibliography

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