Error Rate Estimates in Digital Communication Over a Nonlinear Channel with Memory

The principal representations of Krein are known to provide very tight upper and lower bounds on the error probability in digital communication over a linear channel with intersymbol interference. These bounds depend on the signal-to-noise ratio, the amount of intersymbol interference, and the number of moments of the random interference variable. The same technique can be applied to a nonlinear channel with memory. However, it is difficult to calculate these moments when the channel is nonlinear and has memory. In this paper, we describe a method for computing the moments for the case of an arbitrary nonlinear channel with finite memory. The method of Krein is then used to evaluate the error probability from the moments obtained. We demonstrate the technique with two examples. The model of the nonlinear channel consists of a linear filter in cascade with a memoryless nonlinearity followed by another linear filter. If a sufficient number of moments are used, we obtain accurate estimates of the true error probability.