Shannon capacity in poisson wireless network model

  • P. Jacquet
Information Theory


We consider a realistic model of a wireless network where nodes are dispatched in an infinite map with uniform distribution. Signals decay with distance according to attenuation factor α. At any time we assume that the distribution of emitters is λ per square unit area. From an explicit formula of the Laplace transform of a received signal, we derive an explicit formula for the information rate received by an access point at a random position, which is α/2(log 2)−1 per Hertz. We generalize to network maps of any dimension.


  1. 1.
    Gupta, P. and Kumar, P.R., The Capacity of Wireless Networks, IEEE Trans. Inform. Theory, 2000, vol.46, no. 2, pp. 388–404.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Jacquet, P., Elément de théorie analytique de l’information, modélisation et évaluation de performances, INRIA Research Report RR-3505, 1998. A vailable at
  3. 3.
    Baccelli, F. and Błaszczyszyn, B., On a Coverage Process Ranging from the Boolean Model to the Poisson-Voronoi Tessellation with Applications to Wireless Communications, Adv. in Appl. Probab., 2001, vol.33, no. 2, pp. 293–323.zbMATHMathSciNetGoogle Scholar
  4. 4.
    Adjih, C., Baccelli, E., Clausen, T.H., Jacquet, P., and Rodolakis, G., Fish Eye OLSR Scaling Properties, IEEE J. Commun. Netw., 2004, vol.6, no. 4, pp. 343–351.Google Scholar
  5. 5.
    Shannon, C.E., A Mathematical Theory of Communication, Bell Syst. Tech. J., 1948, vol.27, no. 3, pp.379–423; no. 4, pp.623–656.zbMATHMathSciNetGoogle Scholar
  6. 6.
    Mandelbrot, B.B. and Wheeler, J.A., The Fractal Geometry of Nature, Amer. J. Phys., 1983, vol.51, no.3, pp. 286–287.CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.INRIA Paris-RocquencourtParisFrance

Personalised recommendations