Further results on area under the ROC curve of energy detectors over generalized fading channels

Abstract

A simple measurement to analyze the signal detector's performance is desirable. Although, receiver operating characteristic (ROC) curve has long been used for characterizing system performance, area under the ROC curve (AUC) measurement provides meaningful insights of the system performance. Signal detector's performance can be characterized simply by average AUC, since average AUC varies from 0.5 to 1. In the worst case scenario, the detector's performance can be no less than 0.5 and the best can be 1. In this paper simple expression of average AUC is developed based on the kth order derivative of the moment generating function (MGF) over the generalized fading channels for no-diversity and several diversity cases. Simplified expressions are derived for maximum ratio combing (MRC), square-law combing (SLC) diversity schemes and a simple CDF based single integral expression is developed for selection combining (SC) technique. Examples are given considering the Nakagami-m and Rice channels. Our approaches are simple and analytical results are even shown using the half integer bandwidth-time product (u) and the half integer Nakagami-m fading index. Different factors affecting energy sensing has been analyzed, which can be readily used for other applications such as cognitive radio.