Simple Closed-Form Approximations for the Error Performance of Digital Modulations in Generalized Fading Channels

This article derives several new and simple closed-form approximations for the average symbol error rate (ASER) and outage probability performance metrics of digital communication systems impaired by additive white Gaussian noise and fading. These approximations utilize the coefficients of the Poincare series expansion for the probability density function (PDF) of signal-to-noise ratio (SNR) random variable in conjunction with Mellin transform of the conditional error probability (CEP) and/or its auxiliary functions to generalize some of the known asymptotic ASER/outage probability expressions to a wider range of modulation schemes and different types of propagation environments (including κ-μ, η-μ, α-μ fading channels). Moreover, a new class of asymptotic approximations for the ASER/outage probability are also presented (based on a normalized asymptotic PDF of SNR) that is considerably better than the conventional high-SNR approximation, although both techniques need only the first non-zero term of the Maclaurin (if exists) or the Poincare series expansion of the channel PDF.