Unified analysis of energy detectors with diversity reception in generalised fading channels

In this paper, the authors present a novel moment generating function-based technique to unify the performance evaluation of an average energy detector for detecting unknown deterministic signals over generalised fading environments (including the η-μ, κ-μ, α-μ, K, G and K_G generalised fading distributions) with diversity reception. Specifically, the authors exploit a known exponential-type integral representation for the generalised Marcum Q-function Q_v(a, b) that is valid for any ratio of a/b but for positive integer order v to greatly simplify the task of finding the statistical expectations over the fading signal-to-noise ratio random variables in the computation of the average detection probability metric. 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 fading statistics and/or arbitrarily correlated diversity branches in maximal-ratio combining, square-law combining and square-law selection diversity receivers. The authors´ numerical results also show that the performance of 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, time-bandwidth product, diversity order and signal combining techniques on the receiver operating characteristics of diversity energy detectors in a myriad of fading environments that had heretofore resisted simple solutions.