Improved Intersymbol Interference Error Bounds in Digital Systems

Abstract

A thorough solution to the problem of determining the error rate of a digital communication system with intersymbol interference and additive Gaussian noise is presented in this paper. The solution achieves for the first time a combination of computational simplicity and a high degree of accuracy, and is obtained by deriving tight upper and lower bounds on the error rate. It is shown that, for a system with a normalized peak distortion less than unity, these bounds can be made to differ by an arbitrarily small amount. The numerical evaluation of the bounds takes less than one second on the GE-Mark II time-sharing system for almost all the cases. Examples are given for 2M-ary digital systems to demonstrate the accuracy and computational efficiency of our method. The results show that our estimates of error rate are generally orders of magnitude better than the Chernoff bound. For example, in the case of an ideal bandlimited system [(sin t)/t pulse shape] with a signal-to-noise ratio of 16 dB and a sampling instant deviation of 0.05 from the optimum value, the lower and upper bounds on the error rate are 1.1 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−8</sup> and 1.2 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−8</sup> , respectively. This method can also be applied to the calculation of the performance of certain phase-shift-keyed systems and certain systems with co-channel interference.