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


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.


Massive MIMO Capacity Asymptotically orthogonal Taylor expansion Higher-order statistics 



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).


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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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