Wireless network signals with moderately correlated shadowing still appear Poisson

Preprint English OPEN
Ross, Nathan ; Schuhmacher, Dominic (2016)
  • Subject: Computer Science - Information Theory | Mathematics - Probability | Computer Science - Networking and Internet Architecture

We consider the point process of signal strengths emitted from transmitters in a wireless network and observed at a fixed position. In our model, transmitters are placed deterministically or randomly according to a hard core or Poisson point process and signals are subjected to power law path loss and random propagation effects that may be correlated between transmitters. We provide bounds on the distance between the point process of signal strengths and a Poisson process with the same mean measure, assuming correlated log-normal shadowing. For "strong shadowing" and moderate correlations, we find that the signal strengths are close to a Poisson process, generalizing a recently shown analogous result for independent shadowing.
  • References (38)
    38 references, page 1 of 4

    [Abramowitz and Stegun, 1972] Abramowitz, M. and Stegun, I. A. (1972). Handbook of mathematical functions. Dover, New York.

    [Baccelli and Blaszczyszyn, 2008] Baccelli, F. and Blaszczyszyn, B. (2008). Stochastic geometry and wireless networks: Volume I, theory. Foundations and Trends in Networking, 3(3{4):249{449.

    [Baccelli et al., 1997] Baccelli, F., Klein, M., Lebourges, M., and Zuyev, S. (1997). Stochastic geometry and architecture of communication networks. Telecommunication Systems, 7(1):209{227.

    [Baddeley and Turner, 2005] Baddeley, A. and Turner, R. (2005). spatstat: An R package for analyzing spatial point patterns. Journal of Statistical Software, 12(1):1{42.

    [Barbour and Brown, 1992] Barbour, A. D. and Brown, T. C. (1992). Stein's method and point process approximation. Stochastic Process. Appl., 43(1):9{31.

    [Barbour et al., 1992] Barbour, A. D., Holst, L., and Janson, S. (1992). Poisson approximation, volume 2 of Oxford Studies in Probability. The Clarendon Press Oxford University Press, New York. Oxford Science Publications.

    [Biscio and Lavancier, 2016] Biscio, C. A. N. and Lavancier, F. (2016). Brillinger mixing of determinantal point processes and statistical applications. Electron. J. Stat., 10(1):582{607.

    [Blaszczyszyn et al., 2013] Blaszczyszyn, B., Karray, M. K., and Keeler, H. P. (2013). Using Poisson processes to model lattice cellular networks. In INFOCOM, 2013 Proceedings IEEE, pages 773{781.

    [Blaszczyszyn et al., 2015] Blaszczyszyn, B., Karray, M. K., and Keeler, H. P. (2015). Wireless networks appear Poissonian due to strong shadowing. IEEE Transactions on Wireless Communications, 14(8):4379{4390.

    [Borchers, 2015] Borchers, H. W. (2015). pracma: Practical Numerical Math Functions. R package version 1.8.3.

  • Metrics
    No metrics available
Share - Bookmark