Asymptotic analysis of digital modulations in κ–μ , η–μ and α–μ fading channels

Abstract

This study derives several new and simple closed-form approximations for the average symbol error rate (ASER) and outage probability performance metrics of digital communication systems (with/without diversity receivers) impaired by additive white Gaussian noise and fading. These approximations utilise 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 and/or its auxiliary functions to generalise 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 and α–μ fading channels). A new class of asymptotic approximations for the ASER/outage probability is also derived (based on a normalised 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. The authors’ also investigate the utility/efficacy of Welch–Satterthwaite and Moschopoulos approximations for yielding accurate predictions of the ASER in the low-SNR regime for different fading environments. Closed-form approximations for the ergodic (average) channel capacities of different types of fading channels with/without diversity reception are also derived.