Partial area under the receiver operating characteristics curve of energy detectors in fading channels

Abstract

This article exploits an exponential-type finite-range integral representation of the generalized Marcum Q-function Qv(a,b) (that is valid for positive integer order v but for any ratio of a/b) to unify the analysis of the partial area under the receiver operating characteristics curve (partial AUC) measure for a class of modified energy detectors with diversity reception in a myriad of fading environments (including the η-μ, κ-μ, α-μ, K, G, and KG generalized fading distributions). This metric facilitates the task of comparing the performance of different diversity-enabled energy detectors within a specified detection threshold range and also encapsulates the total AUC measure as a special case. Numerical results reveal that the partial AUC measure of an average energy detector is superior to that of the classical total energy detector with the increasing sample size owing to the noise averaging effect. In particular, we demonstrate that our proposed analytical framework facilitates the investigation of the effects of dissimilar fading parameters, shadowing, branch correlation, diversity order and different diversity combining techniques on the partial AUC metric of energy detectors.