Estimating the performance of signaling over non-linear channels using the PDF of inter-signal distance

This paper presents a general method to estimate the performance of various signaling schemes over mildly non-linear channels. The approach is an extension of an established method used to estimate the performance of complex signaling schemes over linear channels which relies on the distance spectrum. The non-linear channel is first approximated by a linear channel with finite memory. A distance spectrum is obtained using all possible combinations of symbols contained in the linear channel´s memory. The effect of channel non-linearities is modeled by a random variable (RV) having a probability density function (pdf) conditioned on the symbols contained within the channel´s memory. Since the effect of a non-linearity can be accounted for by the form of the pdf itself, the effect on communication performance can be estimated by adding the RV as a perturbation factor to the inter-signal distance in the expression for the probability of symbol error over the linear channel. The expected value of the resultant expression is then numerically evaluated over the range of values which the RV can reasonably assume to obtain the probability of error for signaling over the non-linear channel. This approach provides a useful abstraction of non-linear channel behavior that enables an efficient evaluation of alternative signaling schemes without having to resort to implementation-specific simulation or importance sampling