On the marginal area under the receiver operating characteristics of diversity energy detectors in generalized fading channels

Abstract

In this article, we exploit an exponential-type integral representation for the generalized Marcum-Q function Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sub> (a,b) (which is valid for any ratio a/b) to unify the performance evaluation of the marginal area under the receiver operating characteristics curve (AUC) metric of average energy detectors with diversity reception in a myriad of fading environments (including the η-μ, κ-μ and α-μ generalized fading distributions). This new metric facilitates the comparison of two different energy detectors within a specified detection threshold range and can also be used to compute the total AUC as a special case. Our numerical results also show that the marginal AUC performance of an average energy detector is superior to that of the classical total energy detector with the increasing sample size due to the noise averaging effect. Our new analytical framework also facilitates the investigation of the effects of dissimilar fading parameters and/or signal strengths, diversity order and diversity combining techniques on the marginal AUC performance of energy detectors.