Simplified Performance Analysis Of Energy Detectors Over Myriad Fading Channels:Area Under The Roc Curve Approach

Abstract

This article investigates the energy detector's performance inmyriad fading environments by exploiting a canonical series representation of the generalized Marcum Q-function (along with higher-order derivatives of the moment generating function (MGF) of end-to-end signal-to-noise ratio (SNR) in closedform) or by a single integral formula involving the cumulative distribution function (CDF) of the end-toend SNR. The detection performance is characterized by the area under the receiver operating characteristic (ROC) curve (AUC), which is a simple statistical performance measuring metric that varies between 0.5 and 1. The proposed frameworks are capable of handling the half-odd positive integer values of the time-bandwidth products (u) and the fading severity indices (m) of the Nakagami-m distribution. The methods simplify the cases where many were either intractable or required complicated mathematical steps with the classical probability density function (PDF)/contour integral approaches. Several receiver diversity combining schemes are examined to demonstrate the versatility of the frameworks over independent but not necessarily identically distributed fading channels. Composite effects (multipath fading + shadowing)are also considered for the analysis. Our proposed frameworks with AUC performance metric inthe myriad fading environments provide new ways of characterizing and evaluating energy detector’s performance .