Intersymbol interference error bounds with application to ideal bandlimited signaling

An upper bound is derived for the probability of error of a digital communication system subject to intersymbol interference and Gaussian noise. The bound is applicable to multilevel as well as binary signals and to all types of intersymbol interference. The bound agrees with the exponential portion of a normal distribution in which the larger intersymbol interference components subtract from the signal amplitude, and the smaller components add to the noise power. The results are applied to the case of random binary signaling with sin x/x pulses. It is shown that such signals are not so sensitive to timing error as is commonly believed, nor does the total signal amplitude become very large with significant probability. However, the error probability does grow very rapidly as the system bandwidth is reduced below the Nyquist band.