Effects of wireless physical layer modeling in mobile ad hoc networks
MobiHoc '01 Proceedings of the 2nd ACM international symposium on Mobile ad hoc networking & computing
On the minimum node degree and connectivity of a wireless multihop network
Proceedings of the 3rd ACM international symposium on Mobile ad hoc networking & computing
Wireless Communications: Principles and Practice
Wireless Communications: Principles and Practice
The number of neighbors needed for connectivity of wireless networks
Wireless Networks
Sharp thresholds For monotone properties in random geometric graphs
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A Theory of Network Localization
IEEE Transactions on Mobile Computing
Path loss exponent estimation for wireless sensor network localization
Computer Networks: The International Journal of Computer and Telecommunications Networking
On the connectivity of wireless multi-hop networks with arbitrary wireless channel models
IEEE Communications Letters
Relative location estimation in wireless sensor networks
IEEE Transactions on Signal Processing
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In this paper, we study the well-known phase transition behavior of connectivity in a wireless multi-hop network, but, in contrast to other studies, in a shadowing environment. We consider that a total of n nodes are randomly, independently and uniformly distributed on a unit square in R2, each node has a uniform transmission power and any two nodes are directly connected if and only if the power received by one node from the other node, as determined by the log-normal shadowing model, is larger than or equal to a given threshold. We extend the results obtained under the unit disk communication model in previous work to the more realistic log-normal shadowing model, and derive an analytical formula for the phase transition width of connectivity for large n. We also demonstrate how our results can be extended to higher dimensional networks and to other channel models.