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Connectivity of Wireless Multihop Networks in a Shadow Fading Environment

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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.

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Correspondence to Christian Bettstetter.

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Christian Bettstetter is a senior researcher in the Future Networking Lab at DoCoMo Euro-Labs. His current research interests are in the area of self-organized networking, especially, in wireless ad hoc and sensor networks. He published several technical articles in this area and co-authored the Wiley book ‘GSM: Switching, services and protocols.’ From 1998 to 2003, he was with the Institute of Communication Networks at the Technische Universität München (TUM), where he did research and teaching on mobile communication networks, and managed a new international graduate program. Christian received the Dr.-Ing. degree (summa cum laude) and the Dipl.-Ing. degree in electrical engineering and information technology from TUM in 2004 and 1998, respectively. During his graduate studies, he worked for Wacker Siltronic, Portland, OR, USA, and wrote his master thesis on turbo decoding at the University of Notre Dame, IN, USA. He is a member of the IEEE and ACM SIGMOBILE.

Christian Hartmann studied electrical engineering at the University of Karlsruhe (TH), where he received the Dipl.-Ing. degree in 1996. In 1997 he joined the Institute of Communication Networks at the Technische Universität München (TUM), where he earned the Dr.-Ing. degree (summa cum laude) in 2003. He is currently a senior researcher and member of the teaching staff at the same institution. During a research leave in the winter of 2000/2001 Christian was with the Wireless Research Lab of Lucent Bell Labs, Crawford Hill, NJ. His main research interests are in the area of mobile and wireless networks, including capacity and performance evaluation, radio resource management, modeling and simulation. He is a member of the IEEE.

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Bettstetter, C., Hartmann, C. Connectivity of Wireless Multihop Networks in a Shadow Fading Environment. Wireless Netw 11, 571–579 (2005).

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