Adaptive equalizer
An adaptive equalizer is an equalizer that automatically adapts to time-varying properties of the communication channel. It is frequently used with coherent modulations such as phase-shift keying, mitigating the effects of multipath propagation and Doppler spreading. Adaptive equalizers are a subclass of adaptive filters. The central idea is altering the filter's coefficients to optimize a filter characteristic. For example, in case of linear discrete-time filters, the following equation can be used: where formula_2 is the vector of the filter's coefficients, formula_3 is the received signal covariance matrix and formula_4 is the cross-correlation  vector between the tap-input vector and the desired response. In practice, the last quantities are not known and, if necessary, must be estimated during the equalization procedure either explicitly or implicitly. Many adaptation strategies exist. They include, e.g.: A well-known example is the decision feedback equalizer, a filter that uses feedback of detected symbols in addition to conventional equalization of future symbols. Some systems use predefined training sequences to provide reference points for the adaptation process.