A Broad Gaussian Class of Power Sums Are Gamma Mixtures

Abstract

The aim of this paper is threefold: 1) we introduce a unified statistical characterization for the instantaneous power of a plethora of Gaussian-based fading models; 2) we propose a general framework for the power sum of either independent and identically distributed (i.i.d.) or independent and non-identically distributed (i.non-i.d.) fading distributions; and 3) we provide a unified performance assessment of wireless communications systems in the presence of small-scale fading channels. To accomplish these three goals, we first show that the instantaneous power of a broad Gaussian class of fading models is governed by a mixture of gamma (MG) distribution. Later, we propose novel, tractable, and efficient solutions for the exact sum statistics of i.i.d. and i.non-i.d. MG variates. Lastly, we show that two key performance indicators—namely, the average bit-error rate and the outage probability—of a maximal-ratio combining (MRC) diversity receiver subject to a wide variety of Gaussian-based fading channels can be expressed, in a unified fashion, as a weighted sum of the performance indicators of a single-branch wireless system subject to independent Nakagami-m fading channels. Extensive numerical simulations reveal the outstanding improvement in computational efficiency and mathematical tractability of our derived expressions when compared with state-of-the-art solutions.