Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Antenna selection for two-way full duplex massive MIMO networks with amplify-and-forward relay



In this paper, the antenna selection problem is investigated for the relaying system with the base station having massive multiple antennas, where the relay station works in the full duplex mode and the two-way protocol. The antenna selection scheme is optimized by maximizing the minimum of the two signal to noise ratios (SNRs) with each corresponding to the uplink and the downlink traffics. With the optimized antenna selection scheme, the approximate probability density function (PDF) of the received SNR for each receiver is derived. In what follows, both the overall outage probability and the bit error rate are obtained in the analytical expression for the whole massive multi-input multi-output (MIMO) system. Moreover, the asymptotic overall outage probability is derived in an analytical expression with respect to the growing number of the antennas on the massive MIMO base station. Numerical simulations verify the derived analytical results.


本文研究了基站端采用大规模天线系统的双向全双工中继系统天线选择问题。所提天线选择方案基于最大化最小上下行链路的信噪比。针对所提方案, 本文推导了上下行接收信噪比的近似概率密度函数, 进而得到了系统的中断概率以及误码率在大规模天线近似时的闭合表达式, 并且给出了系统中断概率和基站天线数之间的关系。仿真结果验证了本文所提方案的有效性以及推导的正确性。

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


  1. 1

    Huang Y M, Yang L X, Bengtsson M, et al. A limited feedback joint precoding for amplify-and-forward relaying. IEEE Trans Signal Process, 2010, 58: 1347–1357

  2. 2

    Lin M, An K, Ouyang J, et al. Effect of beamforming on multi-antenna two hop asymmetric fading channels with fixed gain relays. Prog Electromagn Res, 2013, 133: 367–390

  3. 3

    Xu W, Dong X D, Huang Y M. Asymptotic achievable rate analysis for selection strategies in amplify-and-forward MIMO two-hop networks with feedback. IEEE Trans Veh Technol, 2010, 59: 3662–3668

  4. 4

    Zhao R, Yang L X, Huang Y M. Performance analysis of network coding for multicast relay system over Nakagami-m fading channels. Sci China Inf Sci, 2011, 54: 2338–2348

  5. 5

    Huang Y M, He S W, Jin S, et al. Decentralized energy-efficient coordinated beamforming for multicell systems. IEEE Trans Veh Technol, 2014, 63: 4302–4314

  6. 6

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

  7. 7

    Ni Y, Zhang W C, Chen M. Antenna subset selection in MU large-scale MIMO systems. In: Proceedings of IEEE Wireless Communications and Networking Conference (WCNC’2013), Shanghai, 2013. 1–4

  8. 8

    Ahlswede R, Cai N, Li S Y, et al. Network information flow. IEEE Trans Inf Theory, 2000, 46: 1204–1216

  9. 9

    Dai M J, Wang P, Zhang S L, et al. Survey on cooperative strategies for wireless relay channels. Trans Emerg Telecommun Technol, 2014, 25: 926–942

  10. 10

    Popovski P, Yomo H. Physical network coding in two-way wireless relay channels. In: Proceedings of IEEE International Conference on Communications (ICC’2007), Glasgow, 2007. 707–712

  11. 11

    Koike-Akino T, Popovski P, Tarokh V. Optimized constellations for two-way wireless relaying with physical network coding. IEEE J Sel Areas Commun, 2009, 27: 773–787

  12. 12

    Ji B F, Song K, Huang Y M, et al. A cooperative relay selection for two-way cooperative relay networks in Nakagami channels. Wirel Pers Commun, 2013, 71: 2045–2065

  13. 13

    Khina A, Kochman Y, Erez U. Physical-layer MIMO relaying. In: Proceedings of IEEE International Symposium on Information Theory (ISIT’2011), Saint-Petersburg, 2011. 2437–2441

  14. 14

    Zhou X Y, Bai B, Chen W. A low complexity energy efficiency maximization method for multiuser amplify-and-forward MIMO relay systems with a holistic power model. IEEE Commun Lett, 2014, 18: 1371–1374

  15. 15

    Dai M J, Wang H, Lin X H, et al. Opportunistic relaying with analogue and digital network coding for two-way parallel relay network. IET Commun, 2014, 8: 2200–2206

  16. 16

    Kim J, Kim D. BER analysis of dual-hop amplify-and-forward MIMO relaying with best antenna selection in Rayleigh fading channels. IEICE Trans Commun, 2008, 91: 2772–2775

  17. 17

    Peters S, Heath R. Nonregenerative MIMO relaying with optimal transmit antenna selection. IEEE Signal Process Lett, 2008, 15: 421–424

  18. 18

    Cao L, Zhang X, Wang Y W, et al. Transmit antenna selection strategy in amplify-and-forward MIMO relaying. In: Proceedings of IEEE Wireless Communications and Networking Conference (WCNC’2009), Budapest, 2009. 1–4

  19. 19

    Yang K, Yang N, Xing C W, et al. Relay antenna selection in MIMO two-way relay networks over Nakagami-m fading channels. IEEE Trans Veh Technol, 2013, 63: 2349–2362

  20. 20

    Dai M J, Sung C W, Wang Y. Distributed on-off power control for amplify-and-forward relays with orthogonal spacetime block code. IEEE Trans Wirel Commun, 2011, 10: 1895–1903

  21. 21

    Zheng G, Krikidis I, Ottersten B. Full-duplex cooperative cognitive radio with transmit imperfections. IEEE Trans Wirel Commun, 2013, 12: 2498–2511

  22. 22

    Zhou M X, Cui H Y, Song L Y, et al. Transmit-receive antenna pair selection in full duplex systems. IEEE Wirel Commun Lett, 2014, 3: 34–37

  23. 23

    Cheng X L, Yu B, Cheng X, et al. Two-way full-duplex amplify-and-forward relaying. In: Proceedings of IEEE Military Communications Conference (MILCOM’2013), San Diego, 2013. 1–6

  24. 24

    Yu B, Yang L Q, Cheng X, et al. Transmit power optimization for full duplex decode-and-forward relaying. In: Proceedings of IEEE Global Communications Conference (GLOBECOM’2013), Atlanta, 2013. 3347–3352

  25. 25

    Yu B, Yang L Q, Cheng X, et al. Relay location optimization for full-duplex decode-and-forward relaying. In: Proceedings of IEEE Military Communications Conference (MILCOM’2013), San Diego, 2013. 13–18

  26. 26

    Dai M J, Wan S C. Achieving high diversity and multiplexing gains in the asynchronous parallel relay network. Trans Emerg Telecommun Technol, 2013, 24: 232–243

  27. 27

    Suraweera H A, Krikidis I, Zheng G, et al. Low-complexity end-to-end performance optimization in MIMO full-duplex relay systems. IEEE Trans Wirel Commun, 2014, 13: 913–927

  28. 28

    Zheng G. Joint beamforming optimization and power control for full-duplex MIMO two-way relay channel. IEEE Trans Signal Process, 2015, 63: 555–566

  29. 29

    Xia X C, Xu K, Zhang D M, et al. Low-complexity transceiver design and antenna subset selection for cooperative halfand full-duplex relaying systems. In: Proceedings of IEEE Global Communications Conference (GLOBECOM’2014), Austin, 2014, 3314–3319

  30. 30

    Song K, Ji B F, Huang Y M, et al. Performance analysis of antenna selection in two-way relay networks. IEEE Trans Signal Process, 2015, 63: 2520–2532

  31. 31

    Gradshte˘ın I, Ryzhik I, Jeffrey A, et al, Table of Integrals, Series, and Products. New York: Academic, 2007. 334–371

  32. 32

    Guo H, Ge J. Performance analysis of two-way opportunistic relaying over Nakagami-m fading channels. Electron Lett, 2011, 47: 150–152

  33. 33

    Simon M K, Alouini M S. Digital Communication over Fading Channels. New York: Wiley, 2005. 193–218

Download references


This work was supported by National High-Tech R&D Program of China (863) (Grant No. 2014AA01A704), National Basic Research Program of China (973) (Grant No. 2013CB336600), National Natural Science Foundation of China (Grants Nos. 61372101, 61422105, 61271018, 61201172, 61221002), Research Project of Jiangsu Province of China (Grant Nos. BK20130019, BE2015156), National Key Project of Underwater Acoustic Communications (Grant No. 8904004739).

Author information

Correspondence to Luxi Yang.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Song, K., Li, C., Huang, Y. et al. Antenna selection for two-way full duplex massive MIMO networks with amplify-and-forward relay. Sci. China Inf. Sci. 60, 022308 (2017).

Download citation


  • amplify-and-forward
  • bit error rate
  • full duplex
  • massive MIMO
  • outage probability
  • performance analysis


  • 放大转发
  • 误码率
  • 全双工
  • 大规模MIMO
  • 中断概率
  • 性能分析