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Analysis of Multi-Antenna Wireless Networks

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

Abstract

This chapter applies the analytical framework presented in Chap.  3 to two types of wireless networks with different propagation characteristics, namely, single-tier multi-antenna small cell networks and mm-wave wireless networks. For multi-antenna small cell networks, compared with Chap.  3, a more comprehensive analysis is performed, including the coverage probability, ASE, and energy efficiency. Closed-form expressions are derived for these metrics, which reveal the impacts of the BS density and antenna size, and also discover a phase transition phenomenon of the ASE-density relation. For mm-wave networks, both the ad hoc and cellular network models are considered, with a special focus on the unique propagation characteristics of mm-wave signals. It is shown that the coverage probabilities of both types of networks increase as a non-decreasing concave function with the antenna array size. Results presented in this chapter demonstrate the tractability and wide applicability of the general framework, as well as specific analytical methodologies for applying it to different network models.

References

  1. 1.
    H.S. Dhillon, R.K. Ganti, F. Baccelli, J.G. Andrews, Modeling and analysis of \(K\)-tier downlink heterogeneous cellular networks. IEEE J. Sel. Areas Commun. 30, 550–560 (2012)CrossRefGoogle Scholar
  2. 2.
    J. Zhang, J. Andrews, Distributed antenna systems with randomness. IEEE Trans. Wirel. Commun. 7, 3636–3646 (2008)CrossRefGoogle Scholar
  3. 3.
    C. Lee, M. Haenggi, Interference and outage in poisson cognitive networks. IEEE Trans. Wirel. Commun. 11, 1392–1401 (2012)CrossRefGoogle Scholar
  4. 4.
    J. Ferenc, Z. Néda, On the size distribution of Poisson Voronoi cells. Phys. A Stat. Mech. Appl. 385(2), 518–526 (2007)CrossRefGoogle Scholar
  5. 5.
    T. Kiang, Random fragmentation in two and three dimensions. Zeitschrift fur Astrophysik 64, 433 (1966)Google Scholar
  6. 6.
    D. Cao, S. Zhou, Z. Niu, Optimal base station density for energy-efficient heterogeneous cellular networks, in Proceedings of IEEE International Conference on Communications (ICC), Ottawa, Canada (2012)Google Scholar
  7. 7.
    M. Kountouris, J.G. Andrews, Downlink SDMA with limited feedback in interference-limited wireless networks. IEEE Trans. Wirel. Commun. 11, 2730–2741 (2012)Google Scholar
  8. 8.
    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)CrossRefGoogle Scholar
  9. 9.
    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)CrossRefGoogle Scholar
  10. 10.
    R.H.Y. Louie, M.R. McKay, I.B. Collings, Open-loop spatial multiplexing and diversity communications in ad hoc networks. IEEE Trans. Inf. Theory 57, 317–344 (2011)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Y. Wu, R.H.Y. Louie, M.R. McKay, I.B. Collings, Generalized framework for the analysis of linear MIMO transmission schemes in decentralized wireless ad hoc networks. IEEE Trans. Wirel. Commun. 11, 2815–2827 (2012)Google Scholar
  12. 12.
    M. Kountouris, J.G. Andrews, Transmission capacity scaling of SDMA in wireless ad hoc networks, in Proceedings of 2009 IEEE Information Theory Workshop, Volos, Greece (2009), pp. 534–538Google Scholar
  13. 13.
    A. Vecchio, A bound for the inverse of a lower triangular Toeplitz matrix. SIAM J. Matrix Anal. Appl. 24(4), 1167–1174 (2003)Google Scholar
  14. 14.
    D. Commenges, M. Monsion, Fast inversion of triangular Toeplitz matrices. IEEE Trans. Autom. Control 29(3), 250–251 (1984)MathSciNetCrossRefGoogle Scholar
  15. 15.
    J. Andrews, H. Claussen, M. Dohler, S. Rangan, M. Reed, Femtocells: past, present, and future. IEEE J. Sel. Areas Commun. 30, 497–508 (2012)CrossRefGoogle Scholar
  16. 16.
    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)CrossRefGoogle Scholar
  17. 17.
    Z. Hasan, H. Boostanimehr, V.K. Bhargava, Green cellular networks: a survey, some research issues and challenges. IEEE Commun. Surv. Tutor. 13, 524–540 (2011)CrossRefGoogle Scholar
  18. 18.
    G. Auer, V. Giannini, C. Desset, I. Godor, P. Skillermark, M. Olsson, M.A. Imran, D. Sabella, M.J. Gonzalez, O. Blume, A. Fehske, How much energy is needed to run a wireless network? IEEE Wirel. Commun. 18, 40–49 (2011)CrossRefGoogle Scholar
  19. 19.
    G. Auer et al., D2.3: energy efficiency analysis of the reference systems, areas of improvements and target breakdown, INFSO-ICT-247733 EARTH (Energy Aware Radio and NeTwork TecHnologies) (2010)Google Scholar
  20. 20.
    M.R. Akdeniz, Y. Liu, M.K. Samimi, S. Sun, S. Rangan, T.S. Rappaport, E. Erkip, Millimeter wave channel modeling and cellular capacity evaluation. IEEE J. Sel. Areas Commun. 32, 1164–1179 (2014)CrossRefGoogle Scholar
  21. 21.
    T.S. Rappaport, R.W. Heath Jr., R.C. Daniels, J.N. Murdock, Millimeter Wave Wireless Communications (Pearson Education, 2014)Google Scholar
  22. 22.
    M. Haenggi, Stochastic Geometry for Wireless Networks (Cambridge University Press, Cambridge, U.K., 2012)Google Scholar
  23. 23.
    X. Yu, J. Zhang, M. Haenggi, K.B. Letaief, Coverage analysis for millimeter wave networks: the impact of directional antenna arrays. IEEE J. Sel. Areas Commun. 35, 1498–1512 (2017)CrossRefGoogle Scholar
  24. 24.
    T. Bai, R.W. Heath Jr., Coverage and rate analysis for millimeter-wave cellular networks. IEEE Trans. Wirel. Commun. 14, 1100–1114 (2015)CrossRefGoogle Scholar
  25. 25.
    X. Zhang, J.G. Andrews, Downlink cellular network analysis with multi-slope path loss models. IEEE Trans. Commun. 63, 1881–1894 (2015)CrossRefGoogle Scholar
  26. 26.
    J.G. Andrews, T. Bai, M.N. Kulkarni, A. Alkhateeb, A.K. Gupta, R.W. Heath Jr., Modeling and analyzing millimeter wave cellular systems. IEEE Trans. Commun. 65, 403–430 (2017)Google Scholar
  27. 27.
    A. Thornburg, T. Bai, R.W. Heath Jr., Performance analysis of outdoor mmWave ad hoc networks. IEEE Trans. Signal Process. 64, 4065–4079 (2016)MathSciNetCrossRefGoogle Scholar
  28. 28.
    X. Yu, J. Zhang, K.B. Letaief, Coverage analysis for dense millimeter wave cellular networks: the impact of array size, in IEEE Wireless Communications and Networking Conference (2016), pp. 1–6Google Scholar
  29. 29.
    G. Lee, Y. Sung, J. Seo, Randomly-directional beamforming in millimeter-wave multiuser MISO downlink. IEEE Trans. Wirel. Commun. 15, 1086–1100 (2016)CrossRefGoogle Scholar
  30. 30.
    G. Lee, Y. Sung, M. Kountouris, On the performance of random beamforming in sparse millimeter wave channels. IEEE J. Sel. Top. Signal Process. 10, 560–575 (2016)CrossRefGoogle Scholar
  31. 31.
    A. Alkhateeb, G. Leus, R.W. Heath Jr., Limited feedback hybrid precoding for multi-user millimeter wave systems. IEEE Trans. Wirel. Commun. 14, 6481–6494 (2015)CrossRefGoogle Scholar
  32. 32.
    J. Brady, N. Behdad, A.M. Sayeed, Beamspace MIMO for millimeter-wave communications: system architecture, modeling, analysis, and measurements. IEEE Trans. Antennas Propag. 61, 3814–3827 (2013)CrossRefGoogle Scholar
  33. 33.
    C.A. Balanis, Antenna Theory: Analysis and Design (Wiley, Hoboken, NJ, USA, 2005)Google Scholar
  34. 34.
    K. Venugopal, M.C. Valenti, R.W. Heath, Jr., Interference in finite-sized highly dense millimeter wave networks, in Proceedings of Information Theory and Application (ITA), San Diego, CA, USA (2015), pp. 175–180Google Scholar
  35. 35.
    M.D. Renzo, Stochastic geometry modeling and analysis of multi-tier millimeter wave cellular networks. IEEE Trans. Wirel. Commun. 14, 5038–5057 (2015)CrossRefGoogle Scholar
  36. 36.
    S.L. Cotton, W.G. Scanlon, B.K. Madahar, Millimeter-wave soldier-to-soldier communications for covert battlefield operations. IEEE Commun. Mag. 47, 72–81 (2009)CrossRefGoogle Scholar
  37. 37.
    J. Qiao, X.S. Shen, J.W. Mark, Q. Shen, Y. He, L. Lei, Enabling device-to-device communications in millimeter-wave 5G cellular networks. IEEE Commun. Mag. 53, 209–215 (2015)CrossRefGoogle Scholar
  38. 38.
    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

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