Unified analysis of diversity average energy detectors over generalized fading channels

In this article, we present a novel moment generating function (MGF) based technique to unify the performance evaluation of an average energy detector for detecting unknown deterministic signals over generalized fading environments (including the η-μ, κ-μ and α-μ generalized fading distributions) with diversity reception. Specifically, we exploit a known exponential-type integral representation for the generalized Marcum g-function QM, b) with finite integration limits and that is valid for any ratio of a/b to greatly simplify the task of finding the statistical expectation over the fading signal-to-noise ratio (SNR) random variables in the computation of the average detection probability. This new approach leads to a very compact and an elegant solution for many practical cases of interest including the independent but non-identically distributed (i.n.d) fading statistics and/or arbitrarily correlated diversity branches in maximal-ratio combining (MRC) and square-law combining (SLC) diversity receivers. Our numerical results also show that the performance of the average energy detector is superior to the classical total energy detector with the increasing number of samples owing to the noise averaging effect. We have also demonstrated the versatility and utility of the proposed analytical framework to investigate the impact of dissimilar mean signal strengths, fading parameters, diversity order and signal combining techniques on the receiver operating characteristics (ROC) of diversity energy detectors in a myriad of fading environments that had heretofore resisted simple solutions.