- See also
- References
An adaptive equalizer is an equalizer that automatically adapts to time-varying properties of the communication channel.[1] It is frequently used with coherent modulations such as phase shift keying, mitigating the effects of multipath propagation and Doppler spreading.
This topic belongs to the adaptive filters theory wich central idea can be formulated as an optimal altering of coefficients of the filter. For example, in case of linear discrete-time filters, the following equation can be used[2]:
where 
is the vector of the filter's coefficients, 
is the received signal covariance matrix and 
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.:
- LMS 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 .[3] - SG
- RLS
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.
See also
- Equalizer
- Intersymbol interference
References
2. ^Haykin, Simon S. Adaptive filter theory. Pearson Education India, 2008. - p.118
3. ^Tutorial on the LMS algorithm
4. ^Decision Feedback Equalizer
5. ^{{cite web|url=http://signal-integrity.blogs.keysight.com/2012/decision-feedback-equalizer-beauty-is-in-the-eye/|title=For Decision Feedback Equalizers, Beauty is in the Eye|last=Warwick|first=Colin|date=March 28, 2012|website=Signal Integrity|publisher=Agilent Technologies|archive-url=|archive-date=|dead-url=|access-date=}}
6. ^{{cite web|url=http://literature.cdn.keysight.com/litweb/pdf/5989-3777EN.pdf|title=Equalization: The Correction and Analysis of Degraded Signals|last=Stevens|first=Ransom|date=|website=Keysight.com|archive-url=|archive-date=|dead-url=|access-date=}}
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