The Condition for Probabilistic Connectivity in Wireless Sensor Networks

Wireless sensor networks (WSN) have attracted a lot attention recently. How to maintain the properties of both the full coverage and the connectivity is a hot research topic. The current research results proved that a WSN is connected when the target area is fully covered and Rc (sensor's transmission radius) is larger than twice of Rs (sensor's sensing radius). In this paper, we propose a new concept of one-hop-neighbor Eohn. With Eohn, we conclude that a WSN is probabilistically connected when the target area is fully covered by random deployment and Rc≤㎱Rs(1<α<2). The paper further studies the relationship among deployment density, the ratio of Rc to Rs, and Eohn. The analytical results provide basic requirement for topology control in WSNs, and can also be used in routing algorithms to adjust transmission radius dynamically.