Skip to main content
SpringerLink
Log in

Connectivity of Wireless Multihop Networks in a Shadow Fading Environment

  • Published:
Wireless Networks Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. C. Bettstetter, Mobility modeling in wireless networks: Categorization, smooth movement, and border effects. ACM Mobile Computing and Commun. Rev. 5(3) (2001) 55–67.

    Google Scholar 

  2. C. Bettstetter, On the minimum node degree and connectivity of a wireless multihop network, in: Proc. ACM Intern. Symp. on Mobile Ad Hoc Netw. and Comp. (MobiHoc), Lausanne, Switzerland (June 2002).

  3. C. Bettstetter, On the connectivity of ad hoc networks, The Computer Journal 47(4) (2004) 432–447. Oxford University Press.

    Article  Google Scholar 

  4. C. Bettstetter and C. Hartmann, Connectivity of wireless multihop networks in a shadow fading environment, in: Proc. ACM Intern. Workshop on Modeling, Analysis, and Sim. of Wireless and Mobile Systems (MSWiM), San Diego, USA (Sept. 2003).

  5. B. Bollob’as, Modern Graph Theory (Springer, 1998).

  6. L. Booth, J. Bruck, M. Cook and M. Franceschetti, Ad hoc wireless networks with noisy links, in: Proc. IEEE Intern. Symp. on Information Theory (ISIT), Yokohama, Japan (June 2003), pp. 386.

  7. Y.-C. Cheng and T.G. Robertazzi, Critical connectivity phenomena in multihop radio models, IEEE Trans. Commun. 37(7) (1989) 770–777.

    Article  Google Scholar 

  8. D.J. Daley and D. Vere-Jones, An Introduction to the Theory of Point Processes (Springer, 1988).

  9. M. Desai and D. Manjunath, On the connectivity in finite ad hoc networks, IEEE Comm. Letters 6 (2002) 437–439.

    Article  Google Scholar 

  10. O. Dousse, F. Baccelli and P. Thiran, Impact of interferences on connectivity in ad hoc networks, in: Proc. IEEE Infocom, San Francisco, USA (Apr. 2003).

  11. O. Dousse, P. Thiran and M. Hasler, Connectivity in ad-hoc and hybrid networks, in: Proc. IEEE Infocom, New York, USA (June 2002).

  12. P. Erdös and A. Rènyi, On the evolution of random graphs. Publ. Math. Inst. Hungar. Acad. Sci. 5 (1960) 17–61.

    Google Scholar 

  13. N. Geng and W. Wiesbeck, Planungsmethoden für die Mobilkommunikation (Springer, 1998).

  14. I. Gruber and H. Li, Path expiration times in mobile ad hoc networks, in: Proc. European Personal Mobile Commun. Conf. (EPMCC), Glasgow, Britain (April 2003).

  15. P. Gupta and P.R. Kumar, Critical power for asymptotic connectivity in wireless networks, in: Stochastic Analysis, Control, Optimization and Applications, (Birkhäuser, 1998), pp. 547–566.

  16. R. Jain, A. Puri and R. Sengupta, Geographical routing using partial information for wireless ad hoc networks, IEEE Personal Commun. Mag. 8(1) (2001) 48–57.

    Article  Google Scholar 

  17. M.K. Marina and S.R. Das, On-demand multipath distance vector routing in ad hoc networks, in: Proc. Intern. Conf. for Netw. Procotols (ICNP), Riverside, USA (Nov. 2001).

  18. M.K. Marina and S.R. Das, Routing performance in the presence of unidirectional links in multihop wireless networks, in: Proc. ACM Intern. Symp. on Mobile Ad Hoc Netw. and Comp. (MobiHoc), Lausanne, Switzerland (June 2002).

  19. A.B. McDonald and T. Znati, A path availability model for wireless ad-hoc networks, in: Proc. IEEE Wireless Commun. and Netw. Conf. (WCNC), New Orleans, USA (Sept. 1999).

  20. R. Meester and R. Roy, Continuum Percolation (Cambridge University Press, 1996).

  21. M.D. Penrose, The longest edge of the random minimal spanning tree. Annals of Applied Probability 7(2) (1997) 340–361.

    Article  Google Scholar 

  22. P. Piret, On the connectivity of radio networks, IEEE Trans. Inform. Theory 37(5) (1991) 1490–1492.

    Article  Google Scholar 

  23. R. Ramanathan and R. Rosales-Hain, Topology control of multihop wireless networks using transmit power adjustment, in: Proc. IEEE Infocom, Tel Aviv, Israel (March 2000).

  24. T.S. Rappaport, Wireless Communications: Principles and Practice (Prentice Hall, 1996).

  25. N. Sadagopan, F. Bai, B. Krishnamachari and A. Helmy, PATHS: Analysis of path duration statistics and their impact on reactive MANET routing protocols, in: Proc. ACM Intern. Symp. on Mobile Ad Hoc Netw. and Comp. (MobiHoc), Annapolis, USA (June 2003).

  26. P. Santi and D. M. Blough, The critical transmitting range for connectivity in sparse wireless ad hoc networks, IEEE Trans. Mobile Comput. 2(1) (2003) 25–39.

    Article  Google Scholar 

  27. P. Santi, D.M. Blough and F. Vainstein, A probabilistic analysis for the radio range assignment problem in ad hoc networks, in: Proc. ACM Intern. Symp. on Mobile Ad Hoc Netw. and Comp. (MobiHoc), Long Beach, USA (Oct. 2001).

  28. M. Takai, J. Martin and R. Bagrodia, Effects of wireless physical layer modeling in mobile ad hoc networks, in: Proc. ACM Intern. Symp. on Mobile Ad Hoc Netw. and Comp. (MobiHoc), Long Beach, USA (Oct. 2001).

  29. M. Zorzi and S. Pupolin, Optimum transmission ranges in multihop packet radio networks in the presence of fading, IEEE Trans. Commun. 43(7) (1995) 2201–2205.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. DoCoMo Euro-Labs, Future Networking Lab, Munich, Germany

    Christian Bettstetter

  2. Institute of Communication Networks, Technische Universität München, Munich, Germany

    Christian Hartmann

Authors
  1. Christian Bettstetter
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christian Hartmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christian Bettstetter.

Additional information

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.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bettstetter, C., Hartmann, C. Connectivity of Wireless Multihop Networks in a Shadow Fading Environment. Wireless Netw 11, 571–579 (2005). https://doi.org/10.1007/s11276-005-3513-x

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11276-005-3513-x

Keywords

Search

Navigation