Investigating physical security in stealthy lattice wireless sensor networks using k-barrier coverage

Abstract

Any unauthorized access to a critical space is a physical breach in our society that can be viewed as a physical security problem. It is essential to build a barrier that prevents any intruder's attempt to cross it and access a critical area. In this paper, we address the problem of physical security in stealthy lattice wireless sensor networks using a belt of sensors around a critical area. Precisely, we propose a theoretical framework to analyze the k-barrier coverage problem, where any path that crosses this belt intersects with the sensing range of at least k sensors, k ≥ 1. Precisely, we analyze the k-barrier coverage problem from a tiling perspective, where the sensors’ sensing disks are tangential to each other. We study two deterministic sensor deployment strategies, which yield square lattice and hexagonal lattice wireless sensor networks, respectively. First, we introduce the concept of intruder's abstract paths along a k-barrier covered sensor belt region, and compute their number. Second, we propose a polynomial representation of all abstract paths. Third, we compute the number of sensors deployed over a k-barrier covered sensor belt region for both lattices. Fourth, we define the concept of weakly k-barrier covered path crossing a k-barrier covered sensor belt region, and compute its length for both lattices. Also, we define the observability of intruder's abstract path, and compute its value for both lattices. Fifth, we generalize our results for random intruder's moves across a k-barrier covered sensor belt region. Sixth, we corroborate our analysis with simulation results.