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The Constant-Modulus Algorithm and the Property-Restoral Principle

Module by: Douglas L. Jones. E-mail the author

The adaptive filter configurations that we have examined so far require a "desired signal" d k d k . There are many clever ways to obtain such a signal, but in some potential applications a desired signal is simply not available. However, a "property-restoral algorithm" can sometimes circumvent this problem.

If the uncorrupted signal has special properties that are characteristic of the signal and not of the distortion or interference, an algorithm can be constructed which attempts to cause the output of the adaptive filter to exhibit that property. Hopefully, the adapting filter will restore that property by removing the distortion or interference!

Example 1: the Constant-Modulus Algorithm (CMA)

Certain communication modulation schemes, such as PSK and FSK, transmit a sinusoid of a constant analytic magnitude. Only the frequency or phase change with time. The constant modulus algorithm tries to drive the output signal to one having a constant amplitude: ε k =| y k |2A2 ε k y k 2 A 2 One can derive an LMS (or other) algorithm that seeks a Wiener filter minimizing this error. In practice, this works very well for equalization of PSK and FSK communication channels.

Figure 1
Figure 1 (fig1Constant-Modulus.png)
CMA is simpler than decision-directed feedback, and can work for high initial error rates!

This property-restoral idea can be used in any context in which a property-related error can be defined.

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