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

This letter presents a new computational tool for use in general fading channel analyses 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 well-known Vandermonde matrix in order to take advantage of this symmetry. It is numerically stable, eliminates singularities, and circumvents the need for differentiation.