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This module is included inLens: richb's DSP resources
By: Richard BaraniukAs a part of collection:"Adaptive Filters"
Comments:
"A good introduction in adaptive filters, a major DSP application."
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LMS feedback signal processing echo filter wiener digital adaptive cancellation

Adaptive Equalization

Module by: Douglas L. Jones

goal: Design an approximate inverse filter to cancel out as much distortion as possible.

Figure 1

In principle, WH≈ z - Δ

W H z - Δ

, or W≈ z - Δ H

W z - Δ H

, so that the overall response of the top path is approximately δn-Δ

δ n Δ

. However, limitations on the form of W

(FIR) and the presence of noise cause the equalization to be imperfect.

Important Application

Channel equalization in a digital communication system.

Figure 2

If the channel distorts the pulse shape, the matched filter will no longer be matched, intersymbol interference may increase, and the system performance will degrade.

An adaptive filter is often inserted in front of the matched filter to compensate for the channel.

Figure 3

This is, of course, unrealizable, since we do not have access to the original transmitted signal, s k

s k

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 s k s k is known.
Decision-directed feedback: If the overall system is working well, then the output ŝ k - Δ 0 s k - Δ 0 should almost always equal s k - Δ 0 s k - Δ 0 . We can thus use our received digital communication signal as the desired signal, since it has been cleaned of noise (we hope) by the nonlinear threshold device!
Decision-directed equalizer
Figure 4
As long as the error rate in ŝk s k is not too high (say <75% 75% ), this method works. Otherwise, d k d k is so inaccurate that the adaptive filter can never find the Wiener solution. This method is widely used in the telephone system and other digital communication networks.