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We consider the problem where a network of sensors has to detect the presenceof targets at any of $n$ possible locations in a finite region. All suchlocations may not be occupied by a target. The data from sensors is fused todetermine the set of locations that have targets. We term this the separabilityproblem. In this paper, we address the separability of an asymptotically largenumber of static target locations by using binary proximity sensors. Two modelsfor target locations are considered: (i) when target locations lie on auniformly spaced grid; and, (ii) when target locations are i.i.d. uniformlydistributed in the area. Sensor locations are i.i.d uniformly distributed inthe same finite region, independent of target locations. We derive conditionson the sensing radius and the number of sensors required to achieveseparability. Order-optimal scaling laws, on the number of sensors as afunction of the number of target locations, for two types of separabilityrequirements are derived. The robustness or security aspects of the aboveproblem is also addressed. It is shown that in the presence of adversarialsensors, which toggle their sensed reading and inject binary noise, the scalinglaws for separability remain unaffected.

On the Separability of Targets Using Binary Proximity Sensors