Square tessellation for stochastic connected k- coverage in planar wireless sensor networks

In this paper, we focus on the problem of connected k-coverage in planar wireless sensor networks (PWSNs), where every point in a field of interest (FoI) is covered by at least
$k$
sensors simultaneously, while all the participating sensors are mutually connected, where k > 1. To this end, we develop a global framework using a square tessellation that considers both deterministic and stochastic sensing models. Initially, we tessellate a planar FoI into adjacent and congruent square tiles. In each tile of this tessellation, we construct a cusp-square area for sensor placement to achieve k-coverage. Based on this cusp-squared square tile configuration, we compute the minimum sensor density that is required for deterministic and stochastic k-coverage in PWSNs. Then, we establish the necessary relationship that should exist between the sensing and communication ranges of the sensors to maintain network connectivity in k-covered PWSNs. Finally, we propose our stochastic k-coverage protocol for sensor scheduling and substantiate our theoretical analysis with simulation results.