Distributed Inference in the Presence of Byzantine Sensors

A wireless sensor network designed for distributed detection undergoes a Byzantine attack in which a fraction of sensors cooperatively transmit fictitious signals to impair the detection capability of the fusion center. The optimal attacking distributions are derived and the fundamental tradeoff between detection power (best asymptotic exponent of the miss detection error probability) and the attacking power (fraction of compromised sensors) is characterized. Also considered is a hierarchical network made of m-sensors clusters. For large m the optimal miss detection error exponent is found to be a binary divergence, and the asymptotic performance is shown to scale with the number n of clusters but, remarkably, not with the cluster size m. The optimal test, in this case, reduces to a kind of infected-cluster counting.