On the Coverage Performance of Boolean-Poisson Cluster Models for Wireless Sensor Networks

Abstract

In this paper, we consider wireless sensor networks (WSNs) with sensor nodes exhibiting clustering in their deployment. We model the coverage region of such WSNs by Boolean Poisson cluster models (BPCM) where sensors nodes' location is according to a Poisson cluster process (PCP) and each sensor has an independent sensing range around it. We consider two variants of PCP, in particular Matérn and Thomas cluster process to form Boolean Matérn and Thomas cluster models. We first derive the capacity functional of these models. Using the derived expressions, we compute the sensing probability of an event and compare it with sensing probability of a WSN modeled by a Boolean Poisson model where sensors are deployed according to a Poisson point process. We also derive the power required for each cluster to collect data from all of its sensors for the three considered WSNs. We show that a BPCM WSN has less power requirement in comparison to the Boolean Poisson WSN, but it suffers from lower coverage, leading to a trade-off between per-cluster power requirement and the sensing performance.A cluster process with desired clustering may provide better coverage while maintaining low power requirements. I. INTRODUCTIONIn WSNs, sensors are deployed over a region such as forest or wetlands, to form a wireless network and exchange mutual data to sense an event. WSN may have a central hub to facilitate the joint detection. There are two essential aspects of WSNs. The first aspect is the coverage aspect i.e. to maximize the region covered by sensors, termed the coverage or sensing region.