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

Abstract

(c) 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. DOI: 10.1109/TCOMM.2016.2626440The 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 κ-μ shadowed fading model, which includes the popular κ-μ, η-μ, 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.Universidad de Málaga. Campus de Execelencia Internacional. Andalucía Tech