Fundamentals of Wireless Network Analysis

  • Xianghao Yu
  • Chang Li
  • Jun Zhang
  • Khaled B. Letaief


In this chapter, the fundamentals of wireless network analysis via stochastic geometry are introduced. The Poisson network model is first presented, and key performance metrics in wireless networks are defined. By modeling a wireless network as a Poisson point process, the distribution of the aggregate interference is characterized using the Laplace transform, which is a key analytical step leading to tractable results of the signal-to-interference-plus-noise ratio (SINR) distribution. Sample results are presented for coverage and rate analysis in single-antenna cellular and ad hoc networks.


  1. 1.
    E.N. Gilbert, Random plane networks. J. Soc. Ind. Appl. Math. 9(4), 533–543 (1961)MathSciNetCrossRefGoogle Scholar
  2. 2.
    L. Kleinrock, J. Silvester, Optimum transmission radii for packet radio networks or why six is a magic number, in Conference record: national telecommunications conference, (Birmingham, Alabama), pp. 4.3.1-4.3.5, Dec. 1978Google Scholar
  3. 3.
    L. Kleinrock, J. Silvester, Spatial reuse in multihop packet radio networks. Proc. IEEE 75, 156–167 (1987)Google Scholar
  4. 4.
    H. Takagi, L. Kleinrock, Optimal transmission ranges for randomly distributed packet radio terminals. IEEE Trans. Commun. 32, 246–257 (1984)Google Scholar
  5. 5.
    T.-C. Hou, V. Li, Transmission range control in multihop packet radio networks. IEEE Trans. Commun. 34, 38–44 (1986)Google Scholar
  6. 6.
    F. Baccelli, B. Blaszczyszyn, P. Muhlethaler, Stochastic analysis of spatial and opportunistic ALOHA. IEEE J. Sel. Areas Commun. 27, 1105–1119 (2009)Google Scholar
  7. 7.
    M.Z. Win, P.C. Pinto, L.A. Shepp, A mathematical theory of network interference and its applications. Proc. IEEE 97, 205–230 (2009)Google Scholar
  8. 8.
    R.H.Y. Louie, M.R. McKay, I.B. Collings, Open-loop spatial multiplexing and diversity communications in ad hoc networks. IEEE Trans. Inf. Theor. 57, 317–344 (2011)Google Scholar
  9. 9.
    S.P. Weber, X. Yang, J.G. Andrews, G. de Veciana, Transmission capacity of wireless ad hoc networks with outage constraints. IEEE Trans Inf. Theor. 51, 4091–4102 (2005)Google Scholar
  10. 10.
    A.M. Hunter, J.G. Andrews, S. Weber, Transmission capacity of ad hoc networks with spatial diversity. IEEE Trans. Wirel. Commun. 7, 5058–5071 (2008)Google Scholar
  11. 11.
    M. Kountouris, J.G. Andrews, Transmission capacity scaling of SDMA in wireless ad hoc networks, in Proceedings 2009 IEEE Information Theory Workshop, (Volos, Greece), pp. 534-538, Oct. 2009Google Scholar
  12. 12.
    M. Haenggi, J.G. Andrews, F. Baccelli, O. Dousse, M. Franceschetti, Stochastic geometry and random graphs for the analysis and design of wireless networks. IEEE J. Sel. Areas Commun. 27, 1029–1046 (2009)Google Scholar
  13. 13.
    J.G. Andrews, R.K. Ganti, M. Haenggi, N. Jindal, S. Weber, A primer on spatial modeling and analysis in wireless networks. IEEE Commun. Mag. 48, 156–163 (2010)Google Scholar
  14. 14.
    F. Baccelli, M. Klein, M. Lebourges, S. Zuyev, Stochastic geometry and architecture of communication networks. Telecommun. Syst. 7, 209–227 (1997)Google Scholar
  15. 15.
    F. Baccelli, S. Zuyev, Stochastic geometry models of mobile communication networks, in Frontiers in queueing (CRC Press, 1997), pp. 227-243Google Scholar
  16. 16.
    J.G. Andrews, F. Baccelli, R.K. Ganti, A tractable approach to coverage and rate in cellular networks. IEEE Trans. Commun. 59, 3122–3134 (2011)Google Scholar
  17. 17.
    M. Haenggi, R.K. Ganti, Interference in large wireless networks (vol. 3. Now Publishers Inc., 2009)Google Scholar
  18. 18.
    F. Baccelli, B. Błaszczyszyn, Stochastic geometry and wireless networks: volume I theory (vol. 3. Now Publishers Inc., 2009)Google Scholar
  19. 19.
    F. Baccelli, B. Błaszczyszyn, Stochastic geometry and wireless networks: volume II applications (vol. 4. Now Publishers Inc., 2009)Google Scholar
  20. 20.
    S. Weber, J.G. Andrews, Transmission capacity of wireless networks (vol. 5. Now Publishers Inc., 2012)Google Scholar
  21. 21.
    M. Haenggi, Stochastic geometry for wireless networks (Cambridge University Press, Cambridge, U.K., 2012)CrossRefGoogle Scholar
  22. 22.
    S. Mukherjee, Analytical modeling of heterogeneous cellular networks (Cambridge University Press, 2014)Google Scholar
  23. 23.
    H. ElSawy, E. Hossain, M. Haenggi, Stochastic geometry for modeling, analysis, and design of multi-tier and cognitive cellular wireless networks: a survey. IEEE Commun. Surv. Tuts. 15, 996–1019 (2013)Google Scholar
  24. 24.
    S.N. Chiu, D. Stoyan, W.S. Kendall, J. Mecke, Stochastic geometry and its applications (Wiley, 2013)Google Scholar
  25. 25.
    C. Li, J. Zhang, K.B. Letaief, Throughput and energy efficiency analysis of small cell networks with multi-antenna base stations. IEEE Trans. Wirel. Commun. 13, 2505–2517 (2014)Google Scholar
  26. 26.
    N. Devroye, M. Vu, V. Tarokh, Cognitive radio networks. IEEE Signal Process. Mag. 25, 12–23 (2008)Google Scholar
  27. 27.
    Z. Hasan, H. Boostanimehr, V.K. Bhargava, Green cellular networks: a survey, some research issues and challenges. IEEE Commun. Surv. Tuts. 13, 524–540 (2011)Google Scholar
  28. 28.
    J. Xu, L. Qiu, Energy efficiency optimization for MIMO broadcast channels. IEEE Trans. Wirel. Commun. 12, 690–701 (2013)Google Scholar
  29. 29.
    D. Nguyen, L.-N. Tran, P. Pirinen, M. Latva-aho, Precoding for full duplex multiuser MIMO system: spectral and energy efficiency maximization. IEEE Trans. Signal Process. 61, 4038–4050 (2013)Google Scholar
  30. 30.
    T.D. Novlan, H.S. Dhillon, J.G. Andrews, Analytical modeling of uplink cellular networks. IEEE Trans. Wirel. Commun. 12, 2669–2679 (2013)Google Scholar
  31. 31.
    Y. Wang, M. Haenggi, Z. Tan, The meta distribution of the SIR for cellular networks with power control. IEEE Trans. Commun. 66, 1745–1757 (2018)Google Scholar
  32. 32.
    D. Zwillinger, Table of integrals, series, and products (Elsevier, Amsterdam, Netherlands, 2014)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Xianghao Yu
    • 1
  • Chang Li
    • 1
  • Jun Zhang
    • 2
  • Khaled B. Letaief
    • 1
  1. 1.Department of Electronic and Computer EngineeringHong Kong University of Science and TechnologyHong KongChina
  2. 2.Department of Electronic and Information EngineeringHong Kong Polytechnic UniversityKowloon, Hong KongChina

Personalised recommendations