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Wireless Personal Communications

, Volume 97, Issue 3, pp 4551–4561 | Cite as

Analytical Approximation for Capacity in Massive MIMO Systems

  • Kai LiuEmail author
  • Cheng Tao
  • Liu Liu
  • Yinsheng Liu
  • Yongzhi Li
  • Yanping Lu
Article

Abstract

In most existing research on massive multiple-input multiple-output (MIMO) systems, theoretical analysis relies on the assumption that the number of antennas at the base station is infinite. Under this assumption, channel vectors for different users will be asymptotically orthogonal; therefore, the calculation of channel capacity can be greatly simplified. However, in practical systems, the number of antennas is always finite, and the channel vectors for different users cannot be completely orthogonal. In this paper, we propose an analytical approximation for the channel capacity of massive MIMO systems, with a finite number of antennas. Numerical results show that the derived closed-form expression is more accurate than the one assuming that the channel vectors are asymptotically orthogonal.

Keywords

Massive MIMO Capacity Asymptotically orthogonal Taylor expansion Higher-order statistics 

Notes

Acknowledgements

Funding was provided by National High-tech R&D Program of China (863 Program) (Grant No. 2014AA01A706), National Natural Science Foundation of China (Grant No. 61471027), Fundamental Research Funds for the Central Universities (Grant No. 2017JBM306), Southeast University National Mobile Communications Research Laboratory Research Fund (Grant No. 2014D05), Beijing Municipal Natural Science Foundation (Grant No. 4152043).

References

  1. 1.
    Mietzner, J., Schober, R., Lampe, L., et al. (2009). Multiple-antenna techniques for wireless communications—A comprehensive literature survey. IEEE Communications Surveys & Tutorials, 11(2), 87–105.CrossRefGoogle Scholar
  2. 2.
    Marzetta, T. L. (2010). Noncooperative cellular wireless with unlimited numbers of base station antennas. IEEE Transactions on Wireless Communications, 9(11), 3590–3600.CrossRefGoogle Scholar
  3. 3.
    Goldsmith, A., Jafar, S. A., Jindal, N., et al. (2003). Capacity limits of MIMO channels. IEEE Journal on Selected Areas in Communications, 21(5), 684–702.CrossRefGoogle Scholar
  4. 4.
    Gesbert, D., Bolcskei, H., Gore, D. A., et al. (2002). Outdoor MIMO wireless channels: Models and performance prediction. IEEE Transactions on Communications, 50(12), 1926–1934.CrossRefGoogle Scholar
  5. 5.
    Gesbert, D., Shafi, M., Shiu, D., et al. (2003). From theory to practice: An overview of MIMO space-time coded wireless systems. IEEE Journal on Selected Areas in Communications, 21(3), 281–302.CrossRefGoogle Scholar
  6. 6.
    Lu, L., Li, G. Y., Swindlehurst, A. L., et al. (2014). An overview of massive MIMO: Benefits and challenges. IEEE Journal of Selected Topics in Signal Processing, 8(5), 742–758.CrossRefGoogle Scholar
  7. 7.
    Raghavan, V., & Sayeed, A. M. (2011). Sublinear capacity scaling laws for sparse MIMO channels. IEEE Transactions on Information Theory, 57(1), 345–364.MathSciNetCrossRefGoogle Scholar
  8. 8.
    Goldsmith, A. (2005). Wireless communications. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  9. 9.
    Hampton, J. R. (2013). Introduction to MIMO communications. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  10. 10.
    Rusek, F., Persson, D., Lau, B. K., et al. (2013). Scaling up MIMO: Opportunities and challenges with very large arrays. IEEE Signal Processing Magazine, 30(1), 40–60.CrossRefGoogle Scholar
  11. 11.
    Liu, Y., Tan, Z., Hu, H., et al. (2014). Channel estimation for OFDM. IEEE Communications Surveys & Tutorials, 16(4), 1891–1908.CrossRefGoogle Scholar
  12. 12.
    Withers, C. S., & Nadarajah, S. (2010). Expansions for functions of determinants of power series. Canadian Applied Mathematics Quarterly, 18(1), 107–113.Google Scholar
  13. 13.
    Mendel, J. M. (1991). Tutorial on higher-order statistics (spectra) in signal processing and system theory: Theoretical results and some applications. Proceedings of the IEEE, 79(3), 278–305.CrossRefGoogle Scholar
  14. 14.
    Liu, Y., Li, G. Y., Tan, Z., et al. (2015). Noise power estimation in SC-FDMA systems. IEEE Wireless Communications Letters, 4(2), 217–220.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Institute of Broadband Wireless Mobile CommunicationsBeijing Jiaotong UniversityBeijingChina
  2. 2.School of Computer Science and Information Technology and State Key Laboratory of Rail Traffic Control and SafetyBeijing Jiaotong UniversityBeijingChina

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