Wireless Networks

, Volume 11, Issue 5, pp 571–579 | Cite as

Connectivity of Wireless Multihop Networks in a Shadow Fading Environment

  • Christian Bettstetter
  • Christian Hartmann


This article analyzes the connectivity of multihop radio networks in a log-normal shadow fading environment. Assuming the nodes have equal transmission capabilities and are randomly distributed according to a homogeneous Poisson process, we give a tight lower bound for the minimum node density that is necessary to obtain an almost surely connected subnetwork on a bounded area of given size. We derive an explicit expression for this bound, compute it in a variety of scenarios, and verify its tightness by simulation. The numerical results can be used for the practical design and simulation of wireless sensor and ad hoc networks. In addition, they give insight into how fading affects the topology of multihop networks. It is explained why a high fading variance helps the network to become connected.


wireless multihop networks wireless sensor networks ad hoc networking connectivity node isolation 


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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.DoCoMo Euro-Labs, Future Networking LabMunichGermany
  2. 2.Institute of Communication NetworksTechnische Universität MünchenMunichGermany

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