Tracking speed requirements for time-varying adaptive channel equalizers

This paper addresses the problem of adaptively equalizing a slowly time-varying linearly dispersive propagation channel. Owing to the time variation, the adaptive filter rarely has exactly the proper impulse response, and the quality of the output signal will almost always be poorer than that of a time-invariant, adaptively equalized channel. In order to gain a fundamental understanding of the underlying mechanisms, this paper examines the signal degradation introduced by the time-varying combination of a propagation channel with a single complex pole and an equalizer with a single adaptable complex zero. The effects on transmission mean squared error (and hence NPR and BER) are quantified in terms of the type of variation in the pole´s position and the updating strategy of the zero. A set of curves is developed which quantifies the intuitive concept that more rapid updating produces progressively better matching between the channel and the equalizer and hence progressively better signal quality.