Detection of signals of unknown duration by multiple energy detectors

Abstract

An extension of the classical energy detector is proposed to deal with the case of unknown signal duration. Multiple energy detectors are applied to partitions of the original observation interval; presence of signal is decided if at least one of the detectors is in favor of it. We have derived the corresponding probabilities of false alarm and detection for a particular strategy of successive segmentations of the original interval, thus obtaining a layered structure of energy detectors. One key problem is that individual decisions obtained from the multiple energy detectors are statistically dependent, thus complicating the derivation of the overall probabilities of detection and false alarm. ROC curves have been computed, showing significant improvements in detectability when there is a large mismatch between the duration of the observation interval and the actual duration of the signal. This can be especially interesting in the framework of novelty detection where specific parameters of the signal, like duration, are totally unknown.