Series Representation of Modified Bessel Functions and Its Application in AF Cooperative systems

TL;DR

This paper introduces a new series representation of modified Bessel functions using fractional calculus, enabling simplified analysis of relay-assisted communication systems.

Contribution

It presents a novel series expansion of Bessel functions and applies it to derive analytical expressions for key performance metrics in AF cooperative systems.

Findings

Accurate outage probability expressions

Simplified bit error probability formulas

Closed-form ergodic capacity results

Abstract

Using fractional-calculus mathematics, a novel approach is introduced to rewrite modified Bessel functions in series form using simple elementary functions. Then, a statistical characterization of the total receive-SNR at the destination, corresponding to the source-relay-destination and the source-destination link SNR, is provided for a general relaying scenario, in which the destination exploits a maximum ratio combining (MRC) receiver. Using the novel statistical model for the total receive SNR at the destination, accurate and simple analytical expressions for the outage probability, the bit error probability and the ergodic capacity are obtained.