An Analytical Framework for Multi-Antenna Wireless Networks

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


This chapter presents a general analytical framework for large-scale multi-antenna wireless networks. We first introduce a general wireless network model, along with a brief survey of multi-antenna transmission techniques. Using tools from stochastic geometry, a unified framework is then presented for the tractable analysis of the multi-antenna wireless network model. To illustrate the effectiveness of this analytical framework, tractable expressions for the coverage analysis in both ad hoc and cellular networks are derived. It is shown that the presented framework makes the analysis of multi-antenna networks almost as tractable as single-antenna ones. Furthermore, it helps analytically gain key network design insights, such as revealing the impacts of the antenna size and network density.


  1. 1.
    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
  2. 2.
    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
  3. 3.
    C. Li, J. Zhang, J.G. Andrews, K.B. Letaief, Success probability and area spectral efficiency in multiuser MIMO HetNets. IEEE Trans. Commun. 64, 1544–1556 (2016)CrossRefGoogle Scholar
  4. 4.
    H.S. Jo, Y.J. Sang, P. Xia, J.G. Andrews, Heterogeneous cellular networks with flexible cell association: a comprehensive downlink SINR analysis. IEEE Trans. Wireless Commun. 11, 3484–3495 (2012)CrossRefGoogle Scholar
  5. 5.
    F. Rusek, D. Persson, B.K. Lau, E.G. Larsson, T.L. Marzetta, O. Edfors, F. Tufvesson, Scaling up MIMO: opportunities and challenges with very large arrays. IEEE Signal Process. Mag. 30, 40–60 (2013)CrossRefGoogle Scholar
  6. 6.
    G.L. Stuber, J.R. Barry, S.W. McLaughlin, Y. Li, M.A. Ingram, T.G. Pratt, Broadband MIMO-OFDM wireless communications. Proc. IEEE 92, 271–294 (2004)CrossRefGoogle Scholar
  7. 7.
    A. Paulraj, R. Nabar, D. Gore, Introduction to space-time wireless communications (Cambridge University Press, 2003)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. Theory 57, 317–344 (2011)MathSciNetCrossRefGoogle Scholar
  9. 9.
    D. Gesbert, M. Kountouris, R.W. Heath Jr., C. Chae, T. Salzer, Shifting the mimo paradigm. IEEE Signal Process. Mag. 24, 36–46 (2007)CrossRefGoogle Scholar
  10. 10.
    M. Costa, Writing on dirty paper (corresp.). IEEE Trans. Inf. Theor. 29, 439–441 (1983)CrossRefGoogle Scholar
  11. 11.
    H. Harashima, H. Miyakawa, Matched-transmission technique for channels with intersymbol interference. IEEE Trans. Commun. 20, 774–780 (1972)CrossRefGoogle Scholar
  12. 12.
    Q.H. Spencer, A.L. Swindlehurst, M. Haardt, Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels. IEEE Trans. Signal Process. 52, 461–471 (2004)MathSciNetCrossRefGoogle Scholar
  13. 13.
    X. Yu, C. Li, J. Zhang, M. Haenggi, K.B. Letaief, A unified framework for the tractable analysis of multi-antenna wireless networks. IEEE Trans. Wirel. Commun. 17, 7965–7980 (2018)CrossRefGoogle Scholar
  14. 14.
    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
  15. 15.
    C. Li, J. Zhang, M. Haenggi, K.B. Letaief, User-centric intercell interference nulling for downlink small cell networks. IEEE Trans. Commun. 63, 1419–1431 (2015)CrossRefGoogle Scholar
  16. 16.
    N. Jindal, J.G. Andrews, S. Weber, Multi-antenna communication in ad hoc networks: achieving MIMO gains with SIMO transmission. IEEE Trans. Commun. 59, 529–540 (2011)CrossRefGoogle Scholar
  17. 17.
    X. Yu, C. Li, J. Zhang, K.B. Letaief, A tractable framework for performance analysis of dense multi-antenna networks, in Proceedings of IEEE International Conference on Communications (ICC), (Paris, France), pp. 1–6, 2017Google Scholar
  18. 18.
    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
  19. 19.
    H. Huang, C.B. Papadias, S. Venkatesan, MIMO communication for cellular networks. (Springer Science & Business Media, 2011)Google Scholar
  20. 20.
    X. Zhang, X. Zhou, M.R. McKay, Enhancing secrecy with multi-antenna transmission in wireless ad hoc networks. IEEE Trans. Inf. Forensics Secur. 8, 1802–1814 (2013)CrossRefGoogle Scholar
  21. 21.
    R.W. Heath Jr., T. Wu, Y.H. Kwon, A.C.K. Soong, Multiuser MIMO in distributed antenna systems with out-of-cell interference. IEEE Trans. Signal Process. 59, 4885–4899 (2011)MathSciNetCrossRefGoogle Scholar
  22. 22.
    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
  23. 23.
    D. Zwillinger, Table of integrals, series, and products (Elsevier, Amsterdam, Netherlands, 2014)Google Scholar
  24. 24.
    M. Haenggi, Stochastic geometry for wireless networks (Cambridge University Press, Cambridge, U.K., 2012)Google Scholar
  25. 25.
    V. Chandrasekhar, M. Kountouris, J.G. Andrews, Coverage in multi-antenna two-tier networks. IEEE Trans. Wirel. Commun. 8, 5314–5327 (2009)CrossRefGoogle Scholar
  26. 26.
    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
  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.
    A.K. Gupta, H.S. Dhillon, S. Vishwanath, J.G. Andrews, Downlink multi-antenna heterogeneous cellular network with load balancing. IEEE Trans. Commun. 62, 4052–4067 (2014)CrossRefGoogle Scholar
  29. 29.
    S. Roman, The formula of Faà di Bruno. The Am. Math. Mon. 87(10), 805–809 (1980)CrossRefGoogle Scholar
  30. 30.
    S. Weber, J.G. Andrews, N. Jindal, The effect of fading, channel inversion, and threshold scheduling on Ad Hoc networks. IEEE Trans. Inf. Theor. 53, 4127–4149 (2007)MathSciNetCrossRefGoogle Scholar
  31. 31.
    G.-C. Rota, The number of partitions of a set. The Am. Math. Mon. 71(5), 498–504 (1964)MathSciNetCrossRefGoogle Scholar
  32. 32.
    A. Shojaeifard, K.A. Hamdi, E. Alsusa, D.K.C. So, J. Tang, A unified model for the design and analysis of spatially-correlated load-aware HetNets. IEEE Trans. Commun. 62, 1–16 (2014)CrossRefGoogle Scholar
  33. 33.
    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
  34. 34.
    C. Saha, M. Afshang, H.S. Dhillon, 3GPP-Inspired HetNet model using poisson cluster process: Sum-product functionals and downlink coverage. IEEE Trans. Commun. 66, 2219–2234 (2018)CrossRefGoogle Scholar
  35. 35.
    X. Zhang, J.G. Andrews, Downlink cellular network analysis with multi-slope path loss models. IEEE Trans. Commun. 63, 1881–1894 (2015)CrossRefGoogle Scholar
  36. 36.
    R.K. Ganti, M. Haenggi, Asymptotics and approximation of the SIR distribution in general cellular networks. IEEE Trans. Wirel. Commun. 15, 2130–2143 (2016)CrossRefGoogle Scholar
  37. 37.
    K. Huang, J.G. Andrews, D. Guo, R.W. Heath Jr., R.A. Berry, Spatial interference cancellation for multiantenna mobile ad hoc networks. IEEE Trans. Inf. Theor. 58, 1660–1676 (2012)MathSciNetCrossRefGoogle Scholar
  38. 38.
    A. Shojaeifard, K.A. Hamdi, E. Alsusa, D.K.C. So, J. Tang, K.K. Wong, Design, modeling, and performance analysis of multi-antenna heterogeneous cellular networks. IEEE Trans. Commun. 64, 3104–3118 (2016)CrossRefGoogle Scholar
  39. 39.
    Y. Wu, Y. Cui, B. Clerckx, Analysis and optimization of inter-tier interference coordination in downlink multi-antenna HetNets with offloading. IEEE Trans. Wirel. Commun. 14, 6550–6564 (2015)CrossRefGoogle Scholar
  40. 40.
    P. Henrici, Applied and computational complex analysis (Wiley, New York, NY, USA, 1988)Google Scholar
  41. 41.
    F. Baccelli, B. Błaszczyszyn, Stochastic geometry and wireless networks: volume I theory (vol. 3. Now Publishers Inc., 2009)Google Scholar
  42. 42.
    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)CrossRefGoogle Scholar
  43. 43.
    D. Commenges, M. Monsion, Fast inversion of triangular Toeplitz matrices. IEEE Trans. Autom. Control 29(3), 250–251 (1984)MathSciNetCrossRefGoogle Scholar
  44. 44.
    D. Kressner, R. Luce, Fast computation of the matrix exponential for a Toeplitz matrix, arXiv preprintarXiv:1607.01733 (2016)
  45. 45.
    M. Abramowitz, I.A. Stegun, Handbook of mathematical functions: with formulas, graphs, and mathematical tables (vol. 55. Courier Corporation, 1965)Google Scholar
  46. 46.
    J. Segura, Bounds for ratios of modified Bessel functions and associated Turán-type inequalities. J. Math. Anal. Appl. 374(2), 516–528 (2011)MathSciNetCrossRefGoogle 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