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 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 (1972) 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(S) 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 ISI canceller and a Viterbi detector due to Ungerboeck and MacKechnie (1973), is shown to result in poor restricted-delay properties. Implications of these results are illustrated by means of examples