# Adaptive equalizer

Adaptive equalizer

An adaptive equalizer is a filter that adaptively updates its coefficients in order to track a time-varying communication channel. It is frequently used with coherent modulations such as phase shift keying in wireless communications, mitigating the effects of multipath propagation and Doppler spreading. Many varieties exist. A well-known example is the decision feedback equalizer, a filter that uses feedback of detected symbols in addition to conventional equalization of future symbols.

An adaptive equalizer is an example of a time variant system.

What is a Time Variant system ?

It's a system whose characteristics change with time.If we assume that the input of a certain system is x(t) and the output is y(t),and if we assume that the relation between both is y(t)=ʎ(t)*x(t)

Given that ʎ is a function of time [ ʎ(t)] ,and since the value of ʎ changes..then the gain of the above relation changes with time.

Example

Assume that at time ( t=0 ) ,ʎ(0)=10 ,x(t)=50 accordingly y(t)=50*10=500 at time (t=10s) ,ʎ(10)=30 ,x(t)=50 accordingly y(t)=50*30=1500

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"What do we notice from this example ?"

For the same input [x(t)=50] ;the output [y(t)] changed.

a system of this nature is called Time Variant. So in case of Adaptive Equalizer the gain of the circuit changes with time so as to adjust the value of the output to a certain level.

To make this clearer..the gain [ʎ(t)] changes to adjust the output [y(t)] to a preset level,so any change in the input [x(t)] has no effect on the output.

Example

The output [y(t)] of an adaptive equalizer must be set to 100. 1. x(10s)=10 then ʎ(t)=100/10 = 10 2. x(50s)=25 then ʎ(t)=100/25 = 4 and so on So that it's clear now that the value of ʎ changes to set the value of the output to its preset value.

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