Performance analysis for uplink massive MIMO systems with a large and random number of UEs



In this paper, we analyze the ergodic achievable rate of an uplink massive multi-user multipleinput multiple-output (MIMO) system with a large and Poisson distributed number of users. In the considered scenario, multiple user equipments (UEs) transmit their information to a base station equipped with a very large number of antennas. New asymptotic expressions for the ergodic achievable rate for large and deterministic number of users are derived for both maximum ratio combining (MRC) detector and zero-forcing (ZF) detector, as well as the ergodic achievable rate for large and random number of users. Simulation results assess the accuracy of these analytical expressions. It is shown that compared with the MRC detector, ZF detector can achieve much higher spectrum efficiency. Also, the results provide a meaningful fact that with different settings the randomness of the number of users will result in different extents of impact on the performance of massive MIMO.



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  1. 1

    Osseiran A, Boccardi F, Braun V, et al. Scenarios for 5G mobile and wireless communications: The vision of the METIS project. IEEE Commun Mag, 2014, 52: 26–35

    Article  Google Scholar 

  2. 2

    Jungnickel V, Manolakis K, Zirwas W, et al. The role of small cells, coordinated multipoint, and massive MIMO in 5G. IEEE Commun Mag, 2014, 52: 44–51

    Article  Google Scholar 

  3. 3

    Telatar E. Capacity of multi-antenna Gaussian channels. Eur Trans Telecomm, 1999, 10: 585–596

    Article  Google Scholar 

  4. 4

    Jing Y, Hassibi B. Distributed space-time coding in wireless relay networks. IEEE Trans Wirel Commun, 2006, 5: 3524–3536

    Article  Google Scholar 

  5. 5

    Zhang Z S, Zhang W, Tellambura C. MIMO-OFDM channel estimation in the presence of frequency offsets. IEEE Trans Wirel Commun, 2008, 7: 2329–2339

    Article  Google Scholar 

  6. 6

    Sibille A, Oestges C, Zanella A. MIMO: from Theory to Implementation. New York: Academic Press, 2010

    Google Scholar 

  7. 7

    Cui Q M, Huang X Q, Luo B, et al. Capacity analysis and optimal power allocation for coordinated transmission in MIMO-OFDM systems. Sci China Inf Sci, 2012, 55: 1372–1387

    MathSciNet  Article  MATH  Google Scholar 

  8. 8

    Wang D M, Wang J Z, You X H, et al. Spectral efficiency of distributed MIMO systems. IEEE J Sel Areas Commun, 2013, 31: 2112–2127

    Article  Google Scholar 

  9. 9

    Wu Y, Zheng M, Fei Z S, et al. Outage probability analysis for superposition coded symmetric relaying. Sci China Inf Sci, 2013, 56: 022307

    MathSciNet  Google Scholar 

  10. 10

    Xing C W, Fei Z S, Li N, et al. Statistically robust resource allocation for distributed multi-carrier cooperative networks. Sci China Inf Sci, 2013, 56: 109–121

    MathSciNet  Article  Google Scholar 

  11. 11

    Fei Z S, Ni J Q, Zhao D, et al. Ergodic secrecy rate of two-user MISO interference channels with statistical CSI. Sci China Inf Sci, 2014, 57: 102302

    Google Scholar 

  12. 12

    Fei Z S, Ding H C, Xing C W, et al. Performance analysis for range expansion in heterogeneous networks. Sci China Inf Sci, 2014, 57: 082305

    Google Scholar 

  13. 13

    Marzetta T L. Noncooperative cellular wireless with unlimited numbers of base station antennas. IEEE Trans Wirel Commun, 2010, 9: 3590–3600

    Article  Google Scholar 

  14. 14

    Rusek F, Persson D, Lau B K, et al. Scaling up MIMO: opportunities and challenges with very large arrays. IEEE Signal Process Mag, 2013, 30: 40–46

    Article  Google Scholar 

  15. 15

    Wang D M, Ji C, Gao X Q, et al. Uplink sum-rate analysis of multi-cell multi-user massive MIMO system. In: Proceedings of IEEE International Conference on Communications, Budapest, 2013. 5404–5408

    Google Scholar 

  16. 16

    Zhang J, Wen C K, Jin S, et al. On capacity of large-scale MIMO multiple access channels with distributed sets of correlated antennas. IEEE J Sel Areas Commun, 2013, 31: 133–148

    Article  Google Scholar 

  17. 17

    Ngo H Q, Larsson E G, Marzetta T L. Energy and spectral efficiency of very large multiuser MIMO systems. IEEE Trans Commun, 2013, 61: 1436–1449

    Article  Google Scholar 

  18. 18

    Artigue C, Loubaton P. On the precoder design of flat fading MIMO systems equipped with MMSE receivers: a large system approach. IEEE Trans Inf Theory, 2011, 57: 4138–4155

    MathSciNet  Article  Google Scholar 

  19. 19

    Pitarokoilis A, Mohammed S K, Larsson E G. On the optimality of single-carrier transmission in large-scale antenna systems. IEEE Wirel Commun Lett, 2012, 1: 276–279

    Article  Google Scholar 

  20. 20

    Huh H, Caire G, Papadopoulos H C, et al. Achieving massive MIMO spectral efficiency with a not-so-large number of antennas. IEEE Trans Wirel Commun, 2012, 11: 3226–3239

    Article  Google Scholar 

  21. 21

    Datta T, Kumar N A, Chockalingam A, et al. A novel Monte Carlo sampling based receiver for large-scale uplink multiuser MIMO systems. IEEE Trans Veh Technol, 2013, 62: 3019–3038

    Article  Google Scholar 

  22. 22

    Hoydis J, Brink S T, Debbah M. Massive MIMO in UL/DL cellular systems: how many antennas do we need? IEEE J Sel Areas Commun, 2013, 31: 160–171

    Article  Google Scholar 

  23. 23

    Yang H, Marzetta T L. Performance of conjugate and zero-forcing beamforming in large-scale antenna systems. IEEE J Sel Areas Commun, 2013, 31: 172–179

    Article  Google Scholar 

  24. 24

    Fernandes F, Ashikhmin A, Marzetta T L. Inter-cell interference in noncooperative TDD large scale antenna systems. IEEE J Sel Areas Commun, 2013, 31: 192–201

    Article  Google Scholar 

  25. 25

    Cao J, Wang D M, Li J M, et al. Uplink sum-rate analysis of massive MIMO system with pilot contamination and CSI delay. Wirel Pers Commun, 2014, 78: 297–312

    Article  Google Scholar 

  26. 26

    Li J M, Wang D M, Zhu P C, et al. Spectral efficiency analysis of single-cell multi-user large-scale distributed antenna system. IET Commun, 2014, 8: 2213–2221

    MathSciNet  Article  Google Scholar 

  27. 27

    Kingman J. Poisson Processes. Oxford: Oxford University Press, 1993

    Google Scholar 

  28. 28

    Goldsmith A. Wireless Communications. Cambridge: Cambridge University Press, 2005

    Google Scholar 

  29. 29

    Tse D, Viswanath P. Fundamentals of Wireless Communication. Cambridge: Cambridge University Press, 2005

    Google Scholar 

  30. 30

    Park E, Lee S R, Lee I. Antenna placement optimization for distributed antenna systems. IEEE Trans Wirel Commun, 2012, 11: 2468–2477

    Article  Google Scholar 

  31. 31

    Choi W, Kim J Y. Forward-link capacity of a DS/CDMA system with mixed multirate sources. IEEE Trans Veh Technol, 2001, 50: 737–749

    Article  Google Scholar 

  32. 32

    Cramér H. Random Variables and Probability Distributions. Cambridge University Press, 1970

    Google Scholar 

  33. 33

    Gradshteyn I S, Ryzhik I M. Table of Integrals, Series, and Products, 7th ed. New York: Academic Press, 2007

    Google Scholar 

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Correspondence to Chengwen Xing.

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Yang, A., Xing, C., Fei, Z. et al. Performance analysis for uplink massive MIMO systems with a large and random number of UEs. Sci. China Inf. Sci. 59, 1–9 (2016).

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  • massive MIMO
  • large numbers of UEs
  • maximum ratio combining detector
  • zero-forcing detector
  • ergodic achievable rates


  • 022312


  • 大规模天线
  • 大数目用户
  • 最大比合并接收机
  • 迫零接收机
  • 遍历可达速率