A new class of automatic equalizers with very fast convergence is discussed in this paper. This fast convergence is accomplished by means of an iterative procedure which successively makes higher-order approximations on the desired equalizer function.The iterative procedure can be conveniently realized in the form of transversal filter stages in casSflde. For a given distortion D < 1, the residual distortion at the equalizer output after I'! iterations can be reduced to no more than D 2 in the noise-free cases. When this approach is applied to the feed-forward part of a recursive structure, the front distortion (due to precursors) can be reduced in a similar fashion without unduly increasing the overall distortion. The resulting distortion, mainly in the rear end, can then be cancelled out via feedback paths. Other topics treated include certain generalizations, the truncation error due to limited length in cascaded equalizer sections, and the effect of noise. Several numerical examples are also presented to illustrate the effectiveness of the approach. 556
IntroductionOne of the significant developments in recent years in digital data transmission has been the use of transversal filters as time-domain equalizers. Various algorithms have been developed to automatically adjust the tap-gain settings in such an equalizer during a training period in which a train of isolated reference pulses is transmitted [I -3]. Adaptiveness can be achieved during actual data transmission by adjusting the tap-gain settings as a function of estimated channel response [4][5][6][7]. It is clear that, for high-speed data transmission systems, fast convergence in automatic equalization is important to keep the turn-around time small. In this paper, we describe a new equalization technique with very fast convergence time. The technique is based on an iterative procedure that makes successively higher-order approximations on the desired equalizer transfer function. This procedure can be conveniently implemented in the form of cascaded transversal filter stages. We also describe how this technique can be applied to the feed-forward part of a recursive structure, resulting in the suppression of the front distortion without unduly increasing the overall distortion. Other topics treated include certain generalizations of this technique, the effect of truncation (limiting the number of delay units in an equalizer stage), and the effect of noise. Several examples with numerical results obtained via an APL simulation program are also included