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THE ADAPTIVE EQUALIZER
ABSTRACT:
Non line-of-sight systems such as mobile communications are severely affected by the multi-path effect.
In non line-of-sight communication, there is no direct path for the signal from the Transmitter to Receiver. This results in signal undergoing multiple reflections, diffractions, scattering before reaching the receiver. As a result, multiple copies of the same signal arrive at the receiver at successive time intervals.
This multi-path propagation distorts the signal reception by introducing delay spread and inter-symbol-interference (ISI)
Equalization is a technique which is used to overcome the affects of multi-path and ISI in narrowband systems such as GSM.
It involves finding the channel response H(f) of the medium through which signal traversed. The received signal is then passed through an inverse filter (1/H(f)) which nullifies the effect of the channel.
H(f) can be estimated at the receiver by using methods like training sequence, pilot carrier etc., H(f) being a random function ( since channel condition is unpredictable) can be estimated from time-to-time using a feedback loop ( adaptive method)
This project aims at such an adaptive equalizer based upon the wiener solution using MATLAB.
goal:
Design an approximate inverse filter to cancel out as much
distortion as possible.

, so that the overall response of the top path is approximately
. However, limitations on the form of
WW (FIR) and the presence of noise
cause the equalization to be imperfect.


Important Application
Channel equalization in a digital communication system.


Figure 2Figure 2 (fig2AdaptiveEqual.png)
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 3Figure 3 (fig3AdaptiveEqual.png)

This is, of course, unrealizable, since we do not have access
to the original transmitted signal,
There are two common solutions to this problem:

1. Periodically broadcast a known training
signal. The adaptation is switched on only when the
training signal is being broadcast and thus

is known.

2. 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 has
been cleaned of noise (we hope) by the nonlinear threshold
device!


Figure4Decision-directed equalizer
Decision-directed equalizer (fig4AdaptiveEqual.png)