A unified framework for the performance analyses of diversity energy detectors over fading channels

Abstract

This paper revisits the problem of energy detection of an unknown deterministic signal over a myriad of fading environments. Specifically, a new analytical approach based on six alternative series representations of the generalised Marcum Q-function of real order in conjunction with moments or derivatives of the Moment Generating Function of Signal-to-Noise Ratio SNR is proposed to analyse the performance of Maximal-Ratio Combining MRC and Square-Law Combining SLC energy detectors with independent but non-identically distributed i.n.d fading statistics. Our analytical framework is sufficiently general, and capable of handling half-odd integer values for the time-bandwidth product and non-integer fading severity indices for the Nakagami-m fading environment, as well as i.n.d Rice and mixed fading scenarios. Many of these cases were either intractable with the classical probability density function/contour integral approaches, or had resisted a simple/computationally efficient solution. Selected numerical results are also provided for the Receiver Operating Characteristic ROC of MRC and SLC diversity-based energy detectors over Rice and Nakagami-m channels.