Area under the ROC Curve of Enhanced Energy Detector

The area under the Receiver-Operating-Characteristic (ROC) curve of a detector is a simple and suitable figure-of-merit of its detection capability. However the problem of determining the Area-Under-the-Curve (AUC) of an ROC is a non-trivial exercise and hence it has gone usually unnoticed in literature. In this report we analyze the AUC of the recently proposed enhanced energy detector for spectrum sensing. We derive a simple expression for the AUC which can also be applied to determine the AUC of the conventional energy detector as a special case.