Cellular Networks with \(\alpha \)-Ginibre Configurated Base Stations

Conference paper
Part of the Mathematics for Industry book series (MFI, volume 1)

Abstract

We consider a cellular network model with base stations configurated according to the \(\alpha \)-Ginibre point process with \(\alpha \in (0,1]\), which is one of the determinantal point processes. In this model, we focus on the asymptotic behavior of the so-called coverage probability (or link success probability) as the threshold value tends to \(0\) and \(\infty \), and discuss the Padé approximation of the coverage probability at \(0\) and the dependence on \(\alpha \in (0,1]\) of the asymptotic constant at \(\infty \) both numerically and theoretically.

Keywords

Cellular network Ginibre point process \(\alpha \)-Ginibre Determinantal point process SINR Coverage probability Padé approximation Stochastic geometry 

References

  1. 1.
    Andrews, J.G., Baccelli, F., Ganti, R.K.: A tractable approach to coverage and rate in cellular networks. IEEE Trans. Commun. 59, 3122–3134 (2011)CrossRefGoogle Scholar
  2. 2.
    Andrews, J.G., Ganti, R.K., Haenggi, M., Jindal, N., Weber, S.: A primer on spatial modeling and analysis in wireless networks. IEEE Commun. Mag. 48, 156–163 (2010)CrossRefGoogle Scholar
  3. 3.
    Baccelli, F., Błaszczyszyn, B.: Stochastic Geometry and Wireless Networks, Vol. I: Theory/Volume II: Applications. Foundations and Trends(R) in Networking 3, 249–449/ 4, 1–312 (2009)Google Scholar
  4. 4.
    Goldman, A.: The palm measure and the Voronoi tessellation for the Ginibre process. Ann. Appl. Probab. 20, 90–128 (2010)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Haenggi, M.: Stochastic Geometry for Wireless Networks. Cambridge University Press, Cambridge (2013)MATHGoogle Scholar
  6. 6.
    Haenggi, M., Andrews, J.G., Baccelli, F., Dousse, O., Franceschetti, M.: Stochastic geometry and random graphs for the analysis and design of wireless networks. IEEE J. Select. Areas Commun. 27, 1029–1046 (2009)CrossRefGoogle Scholar
  7. 7.
    Hough, J.B., Krishnapur, M., Peres, Y., Virág, B.: Zeros of Gaussian Analytic Functions and Determinantal Point Processes. American Mathematical Society, Providence, RI (2009)MATHGoogle Scholar
  8. 8.
    Kostlan, E.: On the spectra of Gaussian matrices. Directions in matrix theory (Auburn, AL, 1990). Linear Algebra Appl. 162(164), 385–388 (1992)Google Scholar
  9. 9.
    Miyoshi, N., Shirai, T.: A cellular network model with Ginibre configurated base stations. To appear in Advances in Applied Probability (2014)Google Scholar
  10. 10.
    Nakata, I., Miyoshi, N.: Spatial stochastic models for analysis of heterogeneous cellular networks with repulsively deployed base stations. To appear in Performance Evaluation (2014)Google Scholar
  11. 11.
    Nagamatsu, H., Miyoshi, N., Shirai, T.: Padé approximation for coverage probability in cellular networks. Proc. 12th Int’l Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt), pp. 699–706, Hammamet, Tunisia, May 2014Google Scholar
  12. 12.
    Shirai, T.: Large deviations for the fermion point process associated with the exponential kernel. J. Stat. Phys. 123, 615–629 (2006)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Shirai, T.: Ginibre-type point processes and their asymptotic behavior. To appear in J. Math. Soc. Japan. http://mathsoc.jp/publication/JMSJ/inpress.html
  14. 14.
    Shirai, T., Takahashi, Y.: Random point fields associated with certain Fredholm determinants I: fermion, poisson and boson processes. J. Funct. Anal. 205, 414–463 (2003)CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Soshnikov, A.: Determinantal random point fields. Russ. Math. Surv. 55, 923–975 (2000)CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Department of Mathematical and Computing SciencesTokyo Institute of TechnologyTokyoJapan
  2. 2.Institute of Mathematics for IndustryKyushu UniversityFukuokaJapan

Personalised recommendations