Further Results on Prony Approximation for Evaluation of the Average Probability of Error

Further results on a Prony approximation for efficient evaluation of the average probability of error over fading channels are presented. A generic definition of the average probability of error for a communication system is given. The Prony approximation method is shown to be an extension of the Chernoff bound and the MGF method. An improved algorithm for obtaining the parameters of the Prony approximation is developed. New, simple and highly accurate Prony approximations for the conditional probability of bit-error of M-ary modulations assuming parameter quantization to only 3 significant figures are presented. Furthermore, the rank and determinant design criteria for space-time block codes in Gaussian channels are shown to be valid for the exact pairwise error probability. Numerical results indicate that the relative approximation error using the Prony approximation method is less than 5% of the exact average probability of error for all practical values of the signal-to-noise ratio.