5.12 Adaptive equalization

Important application

Channel equalization in a digital communication system.

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

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 $s_k$ is known.
• Decision-directed feedback: If the overall system is working well, then the output $(s_{k-{}_0})$ should almost always equal $s_{k-{}_0}$ . 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 $(s_k)$ is not too high (say $75\%$ ), this method works. Otherwise, $d_k$ 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.