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Sensing coverage, which is one of vital issues in the design of wireless sensor networks (WSNs), can usually interact with other performance metrics such as network connectivity and energy consumption. Whatever the metrics, the fundamental problem is to know at least how many sensor nodes are needed to maintain both sensing coverage and network connectivity. In this paper, we propose a Percolation Model on Novel Gilbert Graph (PM-NGG) to obtain the critical density at which the network can become fully covered and connected considering the similarity between the occurrence of percolation and the formation of a covered and connected network. The PM-NGG is based on directional sensor network where sensors are assigned a determined sensing direction with angular intervals varying from 0 to 2π. Furthermore, we define the sensing and communication model in directional sensor network in presence of channel randomness including deterministic path attenuation, shadow fading, and multipath fading. Besides, we discuss the coverage and connectivity together as a whole under the proposed model. It is worth mentioning that the theoretical analysis and simulation results of the relationship between critical density and transmitting power give insights into the design of directional sensor network in practice.

On Critical Density for Coverage and Connectivity in Directional Sensor Network over Stochastic Channels Using Continuum Percolation