ON THE PERFORMANCE OF DATA RECEIVERS WITH A RESTRICTED DETECTION DELAY

It is well known that the performance of a data receiver for an intersymbol interference (ISI) channel can depend strongly on the detection delay delta. For a discrete-time communication system, this paper derives a lower bound on the bit-error probability as a function of delta. This ''restricted delay bound'' is governed by a ''restricted-delay distance'' d(delta). In many instances, it improves upon Forney's bound, which is governed by the minimum distance d(min). For instance, for partial-response channels, d(delta) does not converge to d(min) even as delta --> infinity. For channels without spectral zeros, a finite detection delay suffices for d(delta) to coincide with d(min). For all finite delta, d(delta) is determined by a finite number of error patterns and may be computed in a straightforward manner. Unlike d(min), d(delta) depends on the phase characteristics of the channel. Minimum phase is proved to maximize d(delta). The lower bound is generalized to discrete-time channels with colored noise and to continuous-time channels. The effect of transforming a continuous-time channel into a discrete-time channel is discussed. Transformation via a matched filter, as in the ISI canceller and a Viterbi detector due to Ungerboeck and MacKechnie, is shown to result in poor restricted-delay properties. Implications of these results are illustrated by means of examples.