Partial area under the receiver operating characteristics curves of diversity-enabled energy detectors in generalised fading channels

A known exponential-type integral representation for the generalised Marcum-Q function Q_v(a, b) is exploited (which is valid for integer order v but for any ratio of a/b) to unify the performance evaluation of the partial area under the receiver operating characteristics curve (partial AUC) metric of average energy detectors with diversity reception in a myriad of fading environments (including the η - μ, κ - μ, α - μ, K, G and K_G generalised 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. The numerical results also show that the partial AUC performance 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. The 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 partial AUC performance of energy detectors.