An adaptive equalizer is an
equalizer that automatically adapts to time-varying properties of the
communication channel
A communication channel refers either to a physical transmission medium such as a wire, or to a logical connection over a multiplexed medium such as a radio channel in telecommunications and computer networking. A channel is used for informa ...
. It is frequently used with coherent modulations such as
phase-shift keying
Phase-shift keying (PSK) is a digital modulation process which conveys data by changing (modulating) the phase of a constant frequency reference signal (the carrier wave). The modulation is accomplished by varying the sine and cosine inputs at a ...
, mitigating the effects of
multipath propagation
In radio communication, multipath is the propagation phenomenon that results in radio signals reaching the receiving antenna by two or more paths. Causes of multipath include atmospheric ducting, ionospheric reflection and refraction, and reflec ...
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
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.:
*
Least mean squares filter
Least mean squares (LMS) 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 square of the error signal (difference between the desired and the actual ...
(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
.
*
Stochastic gradient descent
Stochastic gradient descent (often abbreviated SGD) is an iterative method for optimizing an objective function with suitable smoothness properties (e.g. differentiable or subdifferentiable). It can be regarded as a stochastic approximation of ...
(SG)
*
Recursive least squares filter Recursive least squares (RLS) is an adaptive filter algorithm that recursively finds the coefficients that minimize a weighted linear least squares cost function relating to the input signals. This approach is in contrast to other algorithms such ...
(RLS)
A well-known example is the
decision feedback equalizer
Decision may refer to:
Law and politics
*Judgment (law), as the outcome of a legal case
*Landmark decision, the outcome of a case that sets a legal precedent
* ''Per curiam'' decision, by a court with multiple judges
Books
* ''Decision'' (novel ...
, a filter that uses feedback of detected
symbols
A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different conc ...
in addition to conventional equalization of future symbols.
Some systems use predefined training sequences to provide reference points for the adaptation process.
See also
*
Equalizer
*
Intersymbol interference
In telecommunication, intersymbol interference (ISI) is a form of distortion of a signal in which one symbol interferes with subsequent symbols. This is an unwanted phenomenon as the previous symbols have a similar effect as noise, thus making ...
References
Data transmission
Digital signal processing
{{Telecomm-stub