Achieving Physical Security through k-Barrier Coverage in Three-Dimensional Stealthy Lattice Wireless Sensor Networks

Physical security is essential to safeguarding critical areas. Here, we focus on the physical security problem in three-dimensional (3D) stealthy lattice wireless sensor networks using a 3D sensor belt around a critical space. Specifically, we propose a theoretical framework to investigate the 3D k-barrier coverage problem, where any path crossing this belt intersects with the sensing range of at least k sensors. Precisely, we study this problem from a tiling viewpoint, where the sensing ranges of the sensors are touching (or kissing) each other. We analyze various 3D deterministic sensor deployment methods yielding simple cubic, body centered cubic, face centered cubic, and hexagonal close-packed lattice wireless sensor networks. First, using the concept of the unit cell covered volume ratio, we prove that none of these 3D lattices guarantee k-barrier coverage. Second, to remedy this problem, we consider the great rhombicuboctahedron (GR), a polyhedral space-filler. We introduce the concept of intruder’s abstract paths along a 3D k-barrier covered belt, and compute their number. Also, we propose a polynomial representation for all abstract paths. In addition, we compute the number of sensors deployed over a 3D k-barrier covered belt using GR. Third, we corroborate our analysis with numerical and simulation results.