Intersymbol interference and probability of error in digital systems

Intersymbol interference and additive Gaussian noise are two important sources of distortion in digital systems, and a principal goal in the analysis of such systems is the determination of the resulting probability of error. Earlier related work has sought to estimate the error probability either by calculating an approximation based upon a truncated version of the random pulse train or by obtaining an upper bound which results from consideration of the worst case intersymbol interference. In this paper a new upper bound is derived for the probability of error which is computationally simpler than the truncated pulse-train approximation and which never exceeds the worst case bound. Moreover, the new bound is applicable in a number of cases where the worst case bound cannot be used. The bound is readily evaluated and depends upon three parameters: the usual signal-to-noise ratio; the ratio of intersymbol interference power to total distortion power; and the ratio of the maximum intersymbol interference amplitude to its rms value. To illustrate the utility of the bound, it is compared with the earlier methods in three cases which are representative of the most important situations occurring in practice.