Moment Generating Functions of Generalized Wireless Fading Channels and Applications in Wireless Communication Theory

TL;DR

This paper derives new, accurate, and simplified moment generating function expressions for various generalized wireless fading models, enabling easier analysis of communication system performance without complex special functions.

Contribution

The paper introduces novel approximate MGF expressions for multiple generalized fading distributions that are both accurate and computationally simpler than previous methods.

Findings

New MGF expressions are highly accurate.

Expressions avoid complex special functions like Meijer-G and Fox H.

Application demonstrated through average bit error rate calculations.

Abstract

In this paper, new exact and approximate moment generating functions (MGF) expression for generalized fading models are derived. Specifically, we consider the ${\eta}-{\lambda}-{\mu}$, ${\alpha}-{\mu}$, ${\alpha}-{\eta}-{\mu}$, ${\alpha}-{\lambda}-{\mu}$, ${\alpha}-{\kappa}-{\mu}$, and ${\alpha}-{\lambda}-{\eta}-{\mu}$ generalized fading distributions to derive approximate MGF expressions. The new expressions are very accurate and, in contrast to earlier results in the literature, avoid any complicated special functions, e.g. the Meijer-$G$ and Fox $H$-functions. As such, the new MGF expressions allow easier and more efficient analytical manipulations, which also apply for their special cases such as the Rayleigh, Rice, and Nakagami-m fading. As an illustrative application, the average bit error rates for each of the fading models are evaluated using the new derived MGF expressions. The accuracy of the analytical results by using the numerically computed results as a basis of comparison as well as published results from the literature.