Average error rate evaluation of digital modulations in slow fading by Prony approximation

A novel, remarkably simple semianalytical method for average error-rate evaluation over slowly fading channels is presented. Assume that an error-rate curve conditioned on the instantaneous signal-to-noise ratio at the detector input is known either analytically or can be estimated at a few points by a computer simulation. In the first step, a sum of the first-order exponentials is fitted to the conditional error-rate curve. The curve fitting by a sum of exponentials is well-known in many areas of data processing as Prony approximation. A universal numerical algorithm to find the parameters of Prony approximation is developed. In the second step, knowledge of the moment generating function of the signal-to-noise ratio is required to obtain an average error-rate. Hence, the proposed method can be shown to be an extension of the moment generating function method. The method is illustrated on an example of average bit-error rate evaluation for M-ary phase-shift keying over a generalized Ricean fading and over correlated multichannel Rayleigh fading with maximum ratio combining.