Accurate error-rate calculations through the inversion of mixed characteristic functions

This article presents a new computational tool for use in general fading channel analysis when the detection scheme can be expressed as a quadratic form in zero-mean complex Gaussian random variables. We develop a simple numerical algorithm which is capable of inverting a characteristic function consisting of both simple and multiple poles. The approach benefits from the inherent symmetry in the residue calculations and uses the wellknown Vandermonde matrix in order to take advantage of this symmetry. It is numerically stable, eliminates singularities, and circumvents the need for differentiation.