Randomized detection and detection capacity of multidetector networks

In this paper, we study the following detection problem. There are n detectors randomly placed in the unit square S = [ − 2 , 12 2 assigned to detect the presence of a source located at the origin. Time is divided into slots of unit length and Di(t) ∈ {0, 1} represents the (random) decision of the ith detector in time slot t. The location of the source is unknown to the detectors and the goal is to design schemes that use the decisions {Di(t)}i,t and detect the presence of the source in as short time as possible. We first determine the minimum achievable detection time Tcap and show the existence of randomized detection schemes that have detection times arbitrarily close to Tcap for almost all configuration of detectors, provided the number of detectors n is sufficiently large. We call such schemes as capacity achieving and completely characterize all capacity achieving detection schemes.