On the divergence-cost function in distributed detection with a secrecy constraint

An energy-constrained wireless sensor network (WSN) is engaged in a binary detection task. An eavesdropper intercepts the messages sent by the nodes towards the central unit, thus trying to infer the state of the nature scrutinized by the system. We show that, under appropriate countermeasures against the eavesdropper, and adopting appropriate energy saving strategies, the system performances are characterized by a divergence-cost function D(beta) belonging to the class of the Ali-Silvey distances, where beta is related to the total energy consumption of the network. We also show that the most economic way of conveying information for detection is characterized by the related divergence per unit cost function D = sup_beta D(beta)/beta. The properties of these performance metrics are investigated and two scenarios of interest are addressed: parallel and multiple access channels.