Analysis of Area under the ROC Curve of Energy Detection

A simple figure of merit to describe the performance of an energy detector is desirable. The area under the receiver operating characteristic (ROC) curve, denoted (AUC), is such a measure, which varies between 1/2 and 1. If the detector's performance is no better than flipping a coin, then the AUC is 1/2, and it increases to one as the detector performance improves. However, in the wireless literature, the AUC measure has gone unnoticed. In this paper, to address this gap, we comprehensively analyze the AUC of an energy detector with no-diversity reception and with several popular diversity schemes. The channel model is assumed to be Nakagami-m fading. First, the average AUC is derived for the case of no-diversity reception. Second, the average AUC is derived for diversity reception cases including maximal ratio combining (MRC), square-law combining (SLC) and selection combining (SC). Further, for Rayleigh fading channels, the impacts of channel estimation errors and fading correlations are analyzed. High SNR (signal-to-noise ratio) approximations and the detection diversity gain are also derived. The analytical results are verified by numerical computations and by Monte-Carlo simulations.