Critical Density for Coverage and Connectivity in Two-Dimensional Aligned-Orientation Directional Sensor Networks Using Continuum Percolation

Sensing coverage is one of the fundamental design issues in wireless sensor networks, which reflects the surveillance quality provided by them. Moreover, network connectivity enables the gathered data by sensors to reach to the sink node. Given an initially uncovered field, and as more and more directional sensors are continuously added to the sensor network, the size of partial covered areas increases. At some point, the situation abruptly changes from small fragmented covered areas to a single large covered area. We call this abrupt change the sensing-coverage phase transition (SCPT). Likewise, given an originally disconnected sensor network, as more and more sensors are added, the number of connected components changes such that the sensor network suddenly becomes connected at some point. We call this sudden change the network connectivity phase transition (NCPT). The nature of such phase transitions is a central topic in the percolation theory. In this paper, we introduce aligned-orientation directional sensor networks in which nodes are deployed based on Poisson point process and the orientation of all sensor nodes is the same. Then, we propose an approach to compute density of nodes at critical percolation for both of the SCPT and NCPT problems in such networks, for all angles of field-of-view between 0 and π by using continuum percolation. Due to percolation theory, the critical density is infimum density that for densities above it SCPT and NCPT almost surely occur. In addition, we propose a model for percolation in directional sensor networks, which provides a basis for solving the SCPT and NCPT problems together.