Polynomial approximations for average error rate evaluations over slowly fading channels

A semi-numerical polynomial approximation method to evaluate the average probability of error of digital modulations over slowly flat fading channels is investigated. This method requires knowledge of the incomplete moment generating function of the signal-to-noise ratio at the detector input. For a given accuracy, the number of required approximation sub-intervals and the order of approximation polynomial is smaller than in the case of trapezoidal rule and other piecewise polynomial numerical integration methods. Numerical examples for single channel and multichannel reception with diversity combining are used to show that the polynomial approximation method achieves accuracy better than 5%, for the quadratic polynomial approximation and the number of sub-intervals, 30, over all practical values of the signal-to-noise ratio.