Adaptive equalizer

[1] It is frequently used with coherent modulations such as phase-shift keying, mitigating the effects of multipath propagation and Doppler spreading.

For example, in case of linear discrete-time filters, the following equation can be used:[2] where

In practice, the last quantities are not known and, if necessary, must be estimated during the equalization procedure either explicitly or implicitly.

They include, e.g.: A well-known example is the decision feedback equalizer,[4][5] a filter that uses feedback of detected symbols in addition to conventional equalization of future symbols.

[6] Some systems use predefined training sequences to provide reference points for the adaptation process.

The mean square error performance of LMS , SG and RLS in dependence of training symbols. Parameter denotes step size, and means forgetting factor.
The mean square error performance of LMS , SG and RLS in dependence of training symbols in case of changed during the training procedure channel. Signal power is 1 W, noise power is 0.01 W.