A Performance Study of Energy Detection for Dual-Hop Transmission with Fixed Gain Relays: Area under ROC Curve (AUC) Approach

In this paper, energy detector's performance is investigated for the blind (fixed gain) amplify & forward (AF) dual-hop relay networks using the area under the receiver operating characteristic curve (AUC) metric. Different from the well-known receiver operating characteristics (ROC) metric, AUC is a single statistical parameter which can be used to describe and compare performance of different types of energy detectors. In this article, we derive closed-form AUC expressions for the fixed-gain AF relay networks over the Rayleigh fading channels. The analysis is then extended to the maximum ratio combing (MRC) and square-law combing (SLC) diversity detectors for a dual-hop but multi-relay systems. Our analytical framework and the closed-form AUC expression is based on the kth order derivatives of the moment generating function (MGF) of the combiner output signal-to-noise ratio (SNR).