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Full-Duplex Massive MIMO Relaying: An Energy Efficiency Perspective

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Abstract

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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Notes

  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.

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Acknowledgments

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). https://doi.org/10.1007/s11277-015-2547-3

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Keywords

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