On the performance of data receivers with a restricted detection delay

is well known that the performance of a data receiver for an intersymbol interference (ISI) channel can depend strongly on the detection delay δ. For a discrete-time communication system, this paper derives a lower bound on the bit-error probability as a function of δ. This “restricted delay bound” is governed by a “restricted-delay distance” d(δ). 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(δ) does not converge to d
_min
even as δ-∝. For channels without spectral zeros, a finite detection delay suffices for d(δ) to coincide with d
_min
. For all finite δ, d(δ) is determined by a finite number of error patterns and may be computed in a straightforward manner. Unlike d
_min
, d(δ) depends on the phase characteristics of the channel. Minimum phase is proved to maximize d(δ). 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 IS1 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.