A new approach for evaluating the error probability in the presence of intersymbol interference and additive Gaussian noise

TLDR: A new method is developed which yields the error probability in terms of the first 2k moments of the intersymbol interference, which is compared with the Chernoff bound technique in three representative cases and an order of magnitude improvement in accuracy is obtained.

Abstract: The determination of the error probability of a data transmission system in the presence of intersymbol interference and additive gaussian noise is a major goal in the analysis of such systems. The exhaustive method for finding the error probability calculates all the possible states of the received signal using an N-sample approximation of the true channel impulse response. This method is too time-consuming because the computation involved grows exponentially with N. The worst-case sequence bound avoids the lengthy computation problem but is generally too loose. In this paper, we have developed a new method∗ which yields the error probability in terms of the first 2k moments of the intersymbol interference. A recurrence relation for the moments is derived. Therefore, a good approximation to the error probability of the true channel can be obtained by choosing N large enough, and the amount of computation involved increases only linearly with N. The series expansion is shown to be absolutely convergent, and an upper bound on the series truncation error is given. In order to show the improvement provided in this new method, it is compared with the Chernoff bound technique in three representative cases. An order of magnitude improvement in accuracy is obtained.