On the Calculation of the Incomplete MGF with Applications to Wireless Communications

TL;DR

This paper introduces a general method for calculating the incomplete moment generating function (IMGF) for any fading distribution, providing exact formulas for the  -  shadowed model and demonstrating its applications in various wireless communication scenarios.

Contribution

It presents a universal approach for IMGF calculation and derives closed-form expressions for the  -  shadowed fading, enabling advanced performance analysis in wireless systems.

Findings

Closed-form IMGF expressions for    shadowed fading.

Application of IMGF in security, outage, capacity, and error rate analyses.

Enhanced analytical tools for wireless communication performance evaluation.

Abstract

The incomplete moment generating function (IMGF) has paramount relevance in communication theory, since it appears in a plethora of scenarios when analyzing the performance of communication systems. We here present a general method for calculating the IMGF of any arbitrary fading distribution. Then, we provide exact closed-form expressions for the IMGF of the very general {\kappa}-{\mu} shadowed fading model, which includes the popular {\kappa}-{\mu}, {\eta}-{\mu}, Rician shadowed and other classical models as particular cases. We illustrate the practical applicability of this result by analyzing several scenarios of interest in wireless communications: (1) Physical layer security in the presence of an eavesdropper, (2) Outage probability analysis with interference and background noise, (3) Channel capacity with side information at the transmitter and the receiver, and (4) Average bit-error rate with adaptive modulation, when the fading on the desired link can be modeled by any of the aforementioned distributions.