THE ADAPTIVE EQUALIZER

The task of a receiver is to retrieve the information send by the transmitter. In order to do that it has to determine what has been send. To accomplish this task, it tries to extract from the receive signal the parameters related to the transmitted information. However there are some parameters that are not the actual part of the transmit data, but are included by the medium which is used for transmission of the signal.

One of such parameters is the channel. The transmit signal passes through the channel before reaching the receiver, or in other words the transmit signal convolves with the channel. This convolution bring distortion in the transmit signal called the inter-symbol interference. The effect of the channel can be nullified by a de-convolution operation. A simple deconvolution can be realized in Fourier domain. 

But, the problem here is that neither the transmit signal nor the channel are known. Therefore, a training signal is required which is known at the receiver. But, the problem with the Fourier domain approach is that it is for deterministic signal and deterministic system, while the input signal here is stochastic in nature plus the channel is time varying, and there is also channel noise. The extraction of channel parameters from the retrieved signal can therefore be done using Wiener solution.