Connected k-coverage in two-dimensional wireless sensor networks using hexagonal slicing and area stretching

Abstract

The problem of coverage in two-dimensional (2D) wireless sensor networks is challenging and is still open. Precisely, determining the minimum sensor density (i.e, minimum number of sensors per unit area) that is required to cover a 2D field of interest (FoI), where every point in the field is covered by at least one sensor, is still under investigation. The problem of 2D k-coverage, which requires that every point in a 2D FoI be covered by at least k sensors, where k≥1, is more challenging. In this paper, we attempt to address the 2D connected k-coverage problem, where a 2D FoI is k-covered, while the underlying set of sensors k-covering the field forms a connected network. We propose to solve this problem using an approach based on slicing 2D FoI into convex regular hexagons. Our goal is to achieve k-coverage of a 2D FoI with a minimum number of sensors in order to maximize the network lifetime. First, we compute the minimum sensor density for 2D k-coverage using the regular convex hexagon, which is a 2D paver (i.e., covers a 2D field without gaps or overlaps). Indeed, we found that the regular convex hexagon best assimilates the sensors’ sensing disk with respect to our proposed metric, sensing range usage rate. Second, we derive the ratio of the communication range to the sensing range of the sensors to ensure connected k-coverage. Third, we propose an energy-efficient connected k-coverage protocol based on hexagonal slicing and area stretching. To this end, we formulate a multi-objective optimization problem, which computes an optimum solution to the 2D k-coverage problem that meets two requirements: Maximizing the size of the k-covered area, Ck, so as to minimize the sensor density to k-cover a 2D FoI (Requirement 1) and maximizing the area of the sensor locality, Lk, i.e., the region where at least k sensors are located to k-cover Ck, so as to minimize the interference between sensors (Requirement 2). Fourth, we show various simulation results to substantiate our theoretical analysis. We found a close-to-perfect match between our theoretical and simulation results.