A Computational Geometry-based Approach for Planar k-Coverage in Wireless Sensor Networks

The problem of coverage is one of the most crucial issues among the problems in the lifecycle of the development of wireless sensor networks (WSNs). It is still open and stirs as much concern in the research community in this area. The problem of k-coverage in WSNs is even more challenging. In this article, we investigate the k-coverage problem in planar (or two-dimensional) WSNs, where each point in a field of interest (FoI) is covered by at least k sensors simultaneously, where k >= 1. Our contribution is four-fold: First, we determine the optimal planar convex tile that maximizes the usage of the sensors' sensing range. Then, we propose a few sensor placement strategies based on the degree of coverage k using a hexagonal tiling-based approach. In addition, we compute the sensor density (i.e., number of sensors per unit area) for each of the above sensor placement strategies. Second, we propose a generalized one using irregular hexagons, which are denoted by IRH(r/n), where r stands for the radius of the sensors' sensing range and n = 2 is a natural number. Also, we derive the corresponding sensor density. Moreover, we prove that IRH(r/n) are capable of tiling the Euclidean plane using a mathematical induction proof. Third, we compute the relationship between the sensing range r of the sensors and their communication range R for the above sensor placement strategies. Fourth, we corroborate our analysis with simulation results.