An adaptive equalizer is an equalizer

Equalizer (communications)

In telecommunication, the equalizer is a device that attempts to reverse the distortion incurred by a signal transmitted through a channel.- Digital communications :...

 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

Fading

In wireless communications, fading is deviation of the attenuation that a carrier-modulated telecommunication signal experiences over certain propagation media. The fading may vary with time, geographical position and/or radio frequency, and is often modelled as a random process. A fading channel...

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Many adaptation strategies exist. They include:

• LMS
  Least mean squares filter
  Least mean squares algorithms are a class of adaptive filter used to mimic a desired filter by finding the filter coefficients that relate to producing the least mean squares of the error signal . It is a stochastic gradient descent method in that the filter is only adapted based on the error at...
  
   Note that the receiver does not have access to the transmitted signal when it is not in training mode. If the probability that the equalizer makes a mistake is sufficiently small, the symbol decisions made by the equalizer may be substituted for .
• RLS
  Recursive least squares filter
  The Recursive least squares adaptive filter is an algorithm which recursively finds the filter coefficients that minimize a weighted linear least squares cost function relating to the input signals. This is in contrast to other algorithms such as the least mean squares that aim to reduce the...
  
  

A well-known example is the decision feedback equalizer , a filter that uses feedback of detected symbols

Modulation

In electronics and telecommunications, modulation is the process of varying one or more properties of a high-frequency periodic waveform, called the carrier signal, with a modulating signal which typically contains information to be transmitted...

in addition to conventional equalization of future symbols. Some systems use predefined training sequences to provide reference points for the adaptation process.