3D-kCov-ComFor: An Energy-Efficient Framework for Composite Forwarding in Three-Dimensional Duty-Cycled k-Covered Wireless Sensor Networks

Most existing work on coverage, connectivity, and geographic forwarding considers a two-dimensional (2D) space, where the sensors are deployed in a 2D field. However, there are several cases where the 2D assumption is not valid for the design of those types of wireless sensor networks (WSNs), such as underwater sensor deployment and sensors deployed on the trees of different heights in a forest. In this article, we investigate the problem of k-coverage in three-dimensional (3D) WSNs, where each point in a 3D field is covered by at least k sensors simultaneously. Moreover, it is commonly assumed in most of the work on the problem of geographic forwarding in WSNs that all the sensors are always on (or active) during the network operational lifetime, and, particularly, during data forwarding. However, this type of design is neither practical nor efficient for the sensors whose energy is crucial and limited. Therefore, we consider geographic forwarding in 3D duty-cycled k-covered WSNs, where the sensors can switch between on and off states (i.e., duty-cycled sensors) to save energy. First, we provide a rigorous analysis of the k-coverage problem in 3D WSNs using Helly's Theorem and the Reuleaux tetrahedron model, and compute the sensor spatial density to k-cover a 3D field. Second, based on this analysis, we compute a lower bound and an upper bound on the number of overlapping Reuleaux tetrahedra that are necessary to fill a 3D convex shape, such as the sensing sphere of a sensor. Third, using these results, we present a localized (i.e., based on local information of one-hop neighbors), pseudo-distributed (i.e., not fully distributed) protocol to achieve k-coverage of a 3D field with a reduced number of active sensors, while ensuring connectivity between them. Fourth, we discuss our composite geographic forwarding protocol for 3D duty-cycled k-covered WSNs using a combination of deterministic and opportunistic schemes to forward sensed data towards the sink. We will study the problem of 3D space filling (or space covering) in the context of the above-mentioned problems in 3D WSNs. Fifth, we relax two widely used assumptions, namely sensor homogeneity and sensing range convexity, to generalize our k-coverage protocol in 3D space. Last, we show several simulation results of our framework for joint k-coverage and composite geographic forwarding in 3D duty-cycled WSNs, called 3D-kCov-ComFor. We found a close-to-perfect match between our theoretical and simulation results.