OpenAIRE is about to release its new face with lots of new content and services.
During September, you may notice downtime in services, while some functionalities (e.g. user registration, login, validation, claiming) will be temporarily disabled.
We apologize for the inconvenience, please stay tuned!
For further information please contact helpdesk[at]

fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Ross, Nathan; Schuhmacher, Dominic (2016)
Languages: English
Types: Preprint
Subjects: 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.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [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.
    • [Brown, 2000] Brown, T. X. (2000). Cellular performance bounds via shotgun cellular systems. IEEE Journal on Selected Areas in Communications, 18(11):2443{2455.
    • [Catrein and Mathar, 2008] Catrein, D. and Mathar, R. (2008). Gaussian random elds as a model for spatially correlated log-normal fading. In Telecommunication Networks and Applications Conference, 2008. ATNAC 2008. Australasian, pages 153{157. IEEE.
    • [Chen et al., 2011] Chen, L. H. Y., Goldstein, L., and Shao, Q.-M. (2011). Normal approximation by Stein's method. Probability and its Applications (New York). Springer, Heidelberg.
    • [Chiaraviglio et al., 2016] Chiaraviglio, L., Cuomo, F., Maisto, M., Gigli, A., Lorincz, J., Zhou, Y., Zhao, Z., Qi, C., and Zhang, H. (2016). What is the best spatial distribution to model base station density? A deep dive into two European mobile networks. IEEE Access, 4:1434{1443.
    • [Daley and Vere-Jones, 2008] Daley, D. J. and Vere-Jones, D. (2008). An introduction to the theory of point processes. Vol. II. Probability and its Applications. Springer, New York, second edition.
    • [Gabriel et al., 2014] Gabriel, E., Diggle, P. J., and stan function by Barry Rowlingson (2014). stpp: Space-time point pattern simulation, visualisation and analysis. http: // R package version 1.0-5.
    • [Gelfand et al., 2010] Gelfand, A. E., Diggle, P. J., Fuentes, M., and Guttorp, P., editors (2010). Handbook of spatial statistics. Chapman & Hall/CRC Handbooks of Modern Statistical Methods. CRC Press, Boca Raton, FL.
    • [Gudmundson, 1991] Gudmundson, M. (1991). Correlation model for shadow fading in mobile radio systems. Electronics Letters, 27(23):2145{2146.
    • [Haenggi and Ganti, 2008] Haenggi, M. and Ganti, R. K. (2008). Interference in large wireless networks. Foundations and Trends in Networking, 3(2):127{248.
    • [Heinrich, 2013] Heinrich, L. (2013). Asymptotic Methods in Statistics of Random Point Processes, pages 115{150. Springer Berlin Heidelberg, Berlin, Heidelberg.
    • [Heinrich and Pawlas, 2013] Heinrich, L. and Pawlas, Z. (2013). Absolute regularity and Brillinger-mixing of stationary point processes. Lith. Math. J., 53(3):293{310.
    • [Kallenberg, 1983] Kallenberg, O. (1983). Random Measures. Academic Press, London, 3rd edition.
    • [Kallenberg, 2002] Kallenberg, O. (2002). Foundations of modern probability. Probability and its Applications (New York). Springer-Verlag, New York, second edition.
    • [Keeler et al., 2014] Keeler, H. P., Ross, N., and Xia, A. (2014). When do wireless network signals appear Poisson? Preprint
    • [Keeler et al., 2016] Keeler, H. P., Ross, N., Xia, A., and Blaszczyszyn, B. (2016). Stronger wireless signals appear more Poisson. Preprint 1604.02986.
    • [Miyoshi and Shirai, 2014] Miyoshi, N. and Shirai, T. (2014). A cellular network model with Ginibre con gured base stations. Adv. in Appl. Probab., 46(3):832{845.
    • [M ller and Waagepetersen, 2004] M ller, J. and Waagepetersen, R. P. (2004). Statistical inference and simulation for spatial point processes, volume 100 of Monographs on Statistics and Applied Probability. Chapman & Hall/CRC, Boca Raton, FL.
    • [Nychka et al., 2015] Nychka, D., Furrer, R., and Sain, S. (2015). elds: Tools for spatial data. R package version 8.2-1.
    • [R Core Team, 2016] R Core Team (2016). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.
    • [Schuhmacher, 2005] Schuhmacher, D. (2005). Distance estimates for dependent superpositions of point processes. Stochastic Process. Appl., 115(11):1819{1837.
    • [Schuhmacher et al., 2008] Schuhmacher, D., Vo, B. T., and Vo, B. N. (2008). A consistent metric for performance evaluation of multi-object lters. IEEE Transactions on Signal Processing, 56(8):3447{3457.
    • [Schuhmacher and Xia, 2008] Schuhmacher, D. and Xia, A. (2008). A new metric between distributions of point processes. Adv. in Appl. Probab., 40(3):651{672.
    • [Stoyan et al., 1987] Stoyan, D., Kendall, W.S., and Mecke, J. (1987). Stochastic geometry and its applications. Akademie-Verlag, Berlin.
    • [Szyszkowicz and Yanikomeroglu, 2014] Szyszkowicz, S. S. and Yanikomeroglu, H. (2014). A simple approximation of the aggregate interference from a cluster of many interferers with correlated shadowing. IEEE Transactions on Wireless Communications, 13(8):4415{4423.
    • [Szyszkowicz et al., 2010] Szyszkowicz, S. S., Yanikomeroglu, H., and Thompson, J. S. (2010). On the feasibility of wireless shadowing correlation models. IEEE Transactions on Vehicular Technology, 59(9):4222{4236.
    • [Wendland, 2005] Wendland, H. (2005). Scattered data approximation, volume 17 of Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, Cambridge.
    • [Wickham, 2009] Wickham, H. (2009). ggplot2: elegant graphics for data analysis. Springer New York.
    • [Win et al., 2009] Win, M. Z., Pinto, P. C., and Shepp, L. A. (2009). A mathematical theory of network interference and its applications. Proceedings of the IEEE, 97(2):205{ 230.
  • No related research data.
  • No similar publications.

Share - Bookmark

Funded by projects

Cite this article

Collected from

Cookies make it easier for us to provide you with our services. With the usage of our services you permit us to use cookies.
More information Ok