Sleep Scheduling Protocol for $k$-Coverage of Three-Dimensional Heterogeneous WSNs

An important problem in a 3-D wireless sensor network with dense and random deployment of sensors is the minimization of the number of sensors required to cover a field of interest (FoI). Some monitoring applications may require the FoI to be k-covered, i.e., k ≥ 1, while redundant sensors must be scheduled to sleep to minimize energy consumption. In this paper, we address the problem of determining the probability of a sensor being redundant for the k-coverage of the FoI. We assume that the network is heterogeneous, in which all the sensors may not have the same sensing and/or communication radii. We use a probabilistic approach to estimate the volume of the sensing sphere of an arbitrary sensor that is redundantly covered by its neighbors. We prove a result to determine if a sensor is redundant for k-coverage, which is only based on information about the number of neighbors and their type. We propose a distributed protocol to schedule the redundant sensors to sleep, which requires no geographical information. Results demonstrate that the scheduling protocol reduces the number of active sensors and, thereby, prolongs the network lifetime.