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Equalization FilterAn equalization filter (also called simply an equalizer) is used to remove alarge part of the intersymbol interference introduced by channel filtering [8]. Achannel filter, as in Fig. 3.11, is used to remove the channel’s extraneous tonescaused by noise that may have escaped filtering prior to transmission.To illustrate the basic idea of an equalizer, consider a channel perturbingthe received signal, say yðtÞ, with white Gaussian noise with double-sidedpower spectral density ð1=2ÞN 0 . Let’s formulate the received signal aswhereyðtÞ ¼s d ðtÞþb c s d ðt t D ÞþnðtÞ ð3:26Þb c ¼ Attenuation due to intersymbol interference.t i ¼ Delay induced by intersymbol interference.s d ðtÞ ¼AdðtÞ cos o c t:dðtÞ ¼Data stream: a sequence of 1, each of which is T sec induration.A ¼ voltage level.If we take the Fourier transform of this expression and—although important—the noise component nðtÞ is neglected for simplicity, the transfer function ofthe channel isH c ð f Þ¼=½ yðtÞŠ=½s d ðtÞŠ ¼ 1 þ b ce j2pt Dfð3:27ÞIf b c and t D are known, the equalizer will have a transfer function ofH eq ð f Þ¼ 1H c ð f Þð3:28ÞThis expression leads to the concept of an inverse filter: a filter best matched tothe incoming signal to achieve optimal reception. This type of filter is called amatched filter. Since b c and t D will not be exact or may even change with time,we must allow for adjusting the parameters of the equalizer. If we restrictourselves to transversal or tapped delay-line structures for the purpose ofequalization, we can develop a simple algorithm for estimating the tap weightsa n using either a zero forcing or minimum mean-square error technique. Thesetechniques are described in the next subsections.Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.