Analysis of Area under ROC curve of energy detection

Abstract—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