Design an approximate inverse filter to cancel out as much
distortion as possible.
In principle,
, or
, so that the overall response of the top path is approximately
. However, limitations on the form of
(FIR) and the presence of noise
cause the equalization to be imperfect.
Important application
Channel equalization in a digital communication system.
If the channel distorts the pulse shape, the matched
filter will no longer be matched, intersymbol interference mayincrease, and the system performance will degrade.
An adaptive filter is often inserted in front of the matched
filter to compensate for the channel.
This is, of course, unrealizable, since we do not have access
to the original transmitted signal,
.
There are two common solutions to this problem:
Periodically broadcast a known
training
signal . The adaptation is switched on only when the
training signal is being broadcast and thus
is known.
Decision-directed feedback: If the overall system is
working well, then the output
should almost always equal
. We can thus use our received digital
communication signal as the desired signal, since it hasbeen cleaned of noise (we hope) by the nonlinear threshold
device!
Decision-directed equalizer
As long as the error rate in
is not too high
(say
), this method works. Otherwise,
is so inaccurate that the adaptive filter can never find
the Wiener solution. This method is widely used in thetelephone system and other digital communication networks.
