Skip to main content
SpringerLink
Log in

Energy- and spectral-efficiency of zero-forcing beamforming in massive MIMO systems with imperfect reciprocity calibration: bound and optimization

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

In a time-division duplex (TDD) system with massive multiple input multiple output (MIMO), channel reciprocity calibration (RC) is generally required in order to cope with the reciprocity mismatch between the uplink and downlink channel state information. Currently, evaluating the achievable spectral efficiency (SE) and energy efficiency (EE) of TDD massive MIMO systems with imperfect RC (IRC) mainly relies on exhausting Monte Carlo simulations and it is infeasible to precisely and concisely quantify the achievable SE and EE with IRC. In this study, a novel method is presented for tightly bounding the achievable SE of massive MIMO systems with zero-forcing beamforming under IRC. On the basis of the analytical results, we demonstrate key insights for practical system design with IRC in three aspects: the scaling rule for interference power, saturation region of the SE, and the bound on the SE loss. Finally, the trade-off between spectral and energy efficiencies in the presence of IRC is determined with algorithms developed to optimize SE (EE) under a constrained EE (SE) value. The loss of optimal total SE and EE due to IRC is also quantified, which shows that the loss of optimal EE is more sensitive to IRC in a typical range of transmit power values.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Wang D M, Zhang Y, Wei H, et al. An overview of transmission theory and techniques of large-scale antenna systems for 5G wireless communications. Sci China Inf Sci, 2016, 59: 081301

    Article  Google Scholar 

  2. Papazafeiropoulos A K, Ngo H Q, Ratnarajah T. Performance of massive MIMO uplink with zero-forcing receivers under delayed channels. IEEE Trans Veh Technol, 2017, 66: 3158–3169

    Article  Google Scholar 

  3. Cao J, Wang D M, Li J M, et al. Uplink spectral efficiency analysis of multi-cell multi-user massive MIMO over correlated Ricean channel. Sci China Inf Sci, 2018, 61: 082305

    Article  MathSciNet  Google Scholar 

  4. Zhang Z S, Wang X, Zhang C Y, et al. Massive MIMO technology and challenges (in Chinese). Sci Sin Inform, 2015, 45: 1095–1110

    Article  Google Scholar 

  5. Zhang Q, Jin S, Wong K K, et al. Power scaling of uplink massive MIMO systems with arbitrary-rank channel means. IEEE J Sel Top Signal Process, 2014, 8: 966–981

    Article  Google Scholar 

  6. Dai J X, Wang J, Cheng C H, et al. Linear precoding based on a non-ideal Nakagami-m channel in a massive MIMO system. Sci China Inf Sci, 2017, 60: 069301

    Article  Google Scholar 

  7. 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 

  8. Xu S, Zhang H, Tian J, et al. Pilot reuse and power control of D2D underlaying massive MIMO systems for energy efficiency optimization. Sci China Inf Sci, 2017, 60: 100303

    Article  Google Scholar 

  9. Wei H, Wang D M, Wang J Z, et al. Impact of RF mismatches on the performance of massive MIMO systems with ZF precoding. Sci China Inf Sci, 2016, 59: 022302

    Google Scholar 

  10. Zhang W C, Ren H, Pan C H, et al. Large-scale antenna systems with UL/DL hardware mismatch: achievable rates analysis and calibration. IEEE Trans Commun, 2015, 63: 1216–1229

    Article  Google Scholar 

  11. Shepard C, Yu H, Anand N, et al. Argos: practical many-antenna base stations. In: Proceedings of ACM Conference MOBICOM, Turkey, 2012. 53–64

    Google Scholar 

  12. Rogalin R, Bursalioglu O Y, Papadopoulos H, et al. Scalable synchronization and reciprocity calibration for distributed multiuser MIMO. IEEE Trans Wirel Commun, 2014, 13: 1815–1831

    Article  Google Scholar 

  13. Vieira J, Rusek F, Tufvesson F. Reciprocity calibration methods for massive MIMO based on antenna coupling. In: Proceedings of IEEE GLOBECOM, Austin, 2014. 3708–3712

    Google Scholar 

  14. Liu D L, Ma W Z, Shao S H, et al. Performance analysis of TDD reciprocity calibration for massive MU-MIMO systems with ZF beamforming. IEEE Commun Lett, 2016, 20: 113–116

    Article  Google Scholar 

  15. Luo X. Multiuser massive MIMO performance with calibration errors. IEEE Trans Wirel Commun, 2016, 15: 4521–4534

    Google Scholar 

  16. Mi D, Dianati M, Zhang L, et al. Massive MIMO performance with imperfect channel reciprocity and channel estimation error. IEEE Trans Commun, 2017, 65: 3734–3749

    Article  Google Scholar 

  17. Ma W Z, Liu D L, Liu Y, et al. On the capacity of ZF beamforming in massive MIMO systems with imperfect reciprocity calibration. In: Proceedings of IEEE GLOBECOM, Singapore, 2017. 3708–3712

    Google Scholar 

  18. Minasian A, Adve R S, Shahbazpanahi S. The impact of hardware calibration errors on the performance of massive MIMO systems. In: Proceedings of IEEE GLOBECOM, Washington, 2016. 1–6

    Google Scholar 

  19. Bjornson E, Sanguinetti L, Hoydis J, et al. Optimal design of energy-efficient multi-user MIMO systems: Is massive MIMO the answer? IEEE Trans Wirel Commun, 2015, 14: 3059–3075

    Article  Google Scholar 

  20. Liu D L, Zhao B, Wu F, et al. Semi-blind SI cancellation for in-band full-duplex wireless communications. IEEE Commun Lett, 2018, 22: 1078–1081

    Article  Google Scholar 

  21. Suzuki H, Tran T V A, Collings I B, et al. Transmitter noise effect on the performance of a MIMO-OFDM hardware implementation achieving improved coverage. IEEE J Sel Areas Commun, 2008, 26: 867–876

    Article  Google Scholar 

  22. 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 

  23. Jin S, Wang J, Sun Q, et al. Cell coverage optimization for the multicell massive MIMO uplink. IEEE Trans Veh Technol, 2015, 64: 5713–5727

    Article  Google Scholar 

  24. Wei H X, Li Y Z, Xiao L M, et al. Queue-aware energy-efficient scheduling and power allocation with feedback reduction in small-cell networks. Sci China Inf Sci, 2018, 61: 048301

    Article  Google Scholar 

  25. Choi J, Oh H, Jeon H C. Propagation prediction for LTE small cells with antenna beam tilt. In: Proceedings of VTC-Fall, Vancouver, 2014. 1–5

    Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61531009, 61471108, 61771107, 61701075), the National Major Projects (Grant No. 2016ZX03001009), the Fund from the China Scholarship Council (Grant No. 201706070084), and the Fundamental Research Funds for the Central Universities.

Author information

Authors and Affiliations

  1. National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Donglin Liu, Fei Wu, Xin Quan, Wanzhi Ma, Ying Liu & Shihai Shao

Authors
  1. Donglin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fei Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xin Quan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wanzhi Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ying Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Shihai Shao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shihai Shao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, D., Wu, F., Quan, X. et al. Energy- and spectral-efficiency of zero-forcing beamforming in massive MIMO systems with imperfect reciprocity calibration: bound and optimization. Sci. China Inf. Sci. 61, 122302 (2018). https://doi.org/10.1007/s11432-018-9591-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11432-018-9591-8

Keywords

Search

Navigation