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Full-Duplex Massive MIMO Relaying: An Energy Efficiency Perspective

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This paper investigates the multi-pair full-duplex massive MIMO relaying, where multiple source-destination pairs communicate simultaneously with the help of a common full-duplex decode-and-forward relay. It is assumed that the sources and destinations are equipped with single antenna while the relay is equipped with very large antenna arrays. The asymptotic end-to-end signal-to-interference-plus-noise ratio (SINR) is analyzed under the general power scaling scheme, when maximal ratio combining/maximal ratio transmission scheme or zero-forcing reception/zero-forcing transmission scheme is employed at the relay. Theoretical results show that the effect of echo interference due to full-duplex operation can be eliminated by the large antenna arrays of the relay, if the power scaling scheme is selected properly. On the basis of the SINR expressions, the energy efficiency scaling law is derived. Furthermore, we present the power control scheme at the sources and relay to maximize the energy efficiency, subject to the required spectral efficiency and maximum power constraints. We show that the power control problem can be approximated as a geometric program problem and solved efficiently by the convex optimization tools. Numerical results are presented to validate the asymptotic analysis as well as the proposed power control scheme. The results demonstrate that the deployment of full-duplex relay is beneficial to achieve energy efficient transmission in massive MIMO relaying network.

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  1. 1.

    We will reuse the variables \(I_{R,k}^{\mathrm{CE}}, I_{R,k}^{\mathrm{EI}}, I_{D,k}^{\mathrm{CE}}\) in this subsection when no confusion occurs.

  2. 2.

    In this section, the power scaling scheme is said to be optimal for the EE if and only if it results in the optimal SE as \(N\rightarrow \infty \). However, for the finite N case, such scheme is not necessary to be optimal.

  3. 3.

    In simulations, we set \(K=10\) for illustration. Larger K is possible in practice. From the asymptotic analysis in Sect. 3, the MPI and interference caused by channel estimation are increasing functions of K. This means that larger source-destination pairs result in stronger interference. In this case, to keep the interference level fixed as K increases, the number of relay antennas N must be increased accordingly.

  4. 4.

    Similarly, one can also consider the antenna conserved scenario where 2N antennas are used for reception/transmition at the relay for multi-pair HDR. However, this requires 4N RF chain at the relay which is not preferred in practice, since the deployment of an additional RF chain is much more expensive than adding an extra antenna.


  1. 1.

    Marzetta, T. L. (2010). Noncooperative cellular wireless with unlimited numbers of base station antennas. IEEE Transactions on Wireless Communications, 9(11), 3590–3600.

  2. 2.

    Pitarokoilis, A., Mohammed, S. K., & Larsson, E. G. (2012). On the optimality of single-carrier transmission in large-scale antenna systems. IEEE Wireless Communications Letters, 1(4), 276–279.

  3. 3.

    Ngo, H. Q., Larsson, E. G., & Marzetta, T. L. (2013). Energy and spectral efficiency of very large multiuser MIMO systems. IEEE Transactions on Communications, 61(4), 1436–1449.

  4. 4.

    Kim, S. J., Devroye, N., Mitran, P., & Tarokh, V. (2011). Achievable rate regions and performance comparison of half duplex bi-directional relaying protocols. IEEE Transactions on Information Theory, 57(10), 6405–6418.

  5. 5.

    Xia, X., Xu, K., Ma, W., & Xu, Y. (2013). On the design of relay selection strategy for two-way amplify-and-forward mobile relaying. IET Communications, 7(17), 1948–1957.

  6. 6.

    Xu, Y., Xia, X., Xu, K., & Zhang, D. (2013). On the hybrid relaying protocol for time division broadcasting. Transactions on Emerging Telecommunications Technologies.

  7. 7.

    Xia, X., Zhang, D., Xu, K., & Xu, Y. (2013). Interference-limited Two-Way DF Relaying: Symbol Error Rate Analysis and Comparison. IEEE Transactions on Vehicular Technology, 63(7), 3474–3480.

  8. 8.

    Xia, X., Xu, Y., Xu, K., Zhang, D., & Li, N. (2013). Outage performance of AF-based time division broadcasting protocol in the presence of co-channel interference. In Wireless Communications and Networking Conference (WCNC), 2013 IEEE, (pp. 3482–3487): IEEE.

  9. 9.

    Bastami, A. H., & Olfat, A. (2013). BER-constrained incremental relaying with relay selection in cooperative wireless networks. Wireless Personal Communications, 72(1), 121–136.

  10. 10.

    Hongyu, C., Lingyang, S., & Bingli, J. (2014). Multi-pair two-way amplify-and-forward relaying with very large number of relay antennas. IEEE Transactions on Wireless Communications, 13(5), 2636–2645.

  11. 11.

    Suraweera, H. A., Hien Quoc, N., Duong, T. Q., Chau, Y., & Larsson, E. G. (2013). Multi-pair amplify-and-forward relaying with very large antenna arrays. In Communications (ICC), 2013 IEEE international conference on, 2013 pp. 4635–4640.

  12. 12.

    Bharadia, D., McMilin, E., & Katti, S. (2013). Full duplex radios. In Proceedings of the ACM SIGCOMM 2013 conference on SIGCOMM, 2013 (pp. 375–386). ACM.

  13. 13.

    Jong-Ho, L., & Oh-Soon, S. (2013). Full-duplex relay based on distributed beamforming in multiuser MIMO systems. IEEE Transactions on Vehicular Technology, 62(4), 1855–1860.

  14. 14.

    Rui, X., & Chen, Q. (2014). Analysis of full-duplex relaying under fading loop interference channel. Wireless Personal Communications., 77(4), 2919–2926.

  15. 15.

    Suraweera, H. A., Krikidis, I., Gan, Z., Chau, Y., & Smith, P. J. (2014). Low-complexity end-to-end performance optimization in MIMO full-duplex relay systems. IEEE Transactions on Wireless Communications, 13(2), 913–927.

  16. 16.

    Xia, X., Xu, K., Zhang, D., & Xu, Y. (2013). Low-complexity transceiver design and antenna subset selection for sooperative half- and full-duplex relaying systems. In Global Communications Conference (Globemcom), 2014 IEEE, 2013.

  17. 17.

    Liu, G., Ji, H., Yu, F. R., Li, Y., & Xie, R. (2014). Energy-efficient resource allocation in full-duplex relaying networks. In Communications (ICC), 2014 IEEE International conference on, 2014 (pp. 2400–2405): IEEE.

  18. 18.

    Ngo, H. Q., Suraweerat, H. A., Matthaiou, M., & Larsson, E. G. (2014). Multipair massive MIMO full-duplex relaying with MRC/MRT processing. In Communications (ICC), 2014 IEEE International conference on, 2014 (pp. 4807–4813): IEEE.

  19. 19.

    Hassibi, B., & Hochwald, B. M. (2003). How much training is needed in multiple-antenna wireless links? IEEE Transactions on Information Theory, 49(4), 951–963.

  20. 20.

    Xia X., Xie W., Zhang D., & et al. (2015). Multi-pair full-duplex amplify-and-forward relaying with very large antenna arrays. In: Wireless communications and networking conference (WCNC), 2015 IEEE.

  21. 21.

    Evans, J., & Tse, D. N. C. (2000). Large system performance of linear multiuser receivers in multipath fading channels. IEEE Transactions on Information Theory, 46(6), 2059–2078.

  22. 22.

    Liang, Y.-C., & Zhang, R. (2008). Optimal analogue relaying with multi-antennas for physical layer network coding. In Communications, 2008. ICC’08. IEEE International Conference on, 2008 (pp. 3893–3897): IEEE.

  23. 23.

    Boyd, S., Kim, S.-J., Vandenberghe, L., & Hassibi, A. (2007). A tutorial on geometric programming. Optimization and Engineering, 8(1), 67–127.

  24. 24.

    Weeraddana, P. C., Codreanu, M., Latva-aho, M., & Ephremides, A. (2011). Resource allocation for cross-layer utility maximization in wireless networks. IEEE Transactions on Vehicular Technology, 60(6), 2790–2809.

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This work is supported by Major Research Plan of National Natural Science Foundation of China (No. 91438115), National Natural Science Foundation of China (No. 61371123, No. 61301165), Jiangsu Province Natural Science Foundation (BK2011002, BK2012055), China Postdoctoral Science Foundation (2014M552612) and Jiangsu Postdoctoral Science Foundation (No.1401178C).

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Correspondence to Wenfeng Ma.

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Xu, Y., Xia, X., Ma, W. et al. Full-Duplex Massive MIMO Relaying: An Energy Efficiency Perspective. Wireless Pers Commun 84, 1933–1961 (2015).

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  • Multi-pair full-duplex relaying
  • Very large antenna arrays
  • Energy efficiency
  • Power control