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In this paper, we consider wireless sensor networks (WSNs) with sensor nodesexhibiting clustering in their deployment. We model the coverage region of suchWSNs by Boolean Poisson cluster models (BPCM) where sensors nodes' location isaccording to a Poisson cluster process (PCP) and each sensor has an independentsensing range around it. We consider two variants of PCP, in particular \maternand Thomas cluster process to form Boolean \matern and Thomas cluster models.We first derive the capacity functional of these models. Using the derivedexpressions, we compute the sensing probability of an event and compare it withsensing probability of a WSN modeled by a Boolean Poisson model where sensorsare deployed according to a Poisson point process. We also derive the powerrequired for each cluster to collect data from all of its sensors for the threeconsidered WSNs. We show that a BPCM WSN has less power requirement incomparison to the Boolean Poisson WSN, but it suffers from lower coverage,leading to a trade-off between per-cluster power requirement and the sensingperformance. A cluster process with desired clustering may provide bettercoverage while maintaining low power requirements.

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