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Achievable rate analysis for multi-pair two-way massive MIMO full-duplex relay systems

In this paper, we consider a multi-pair two-way amplify-and-forward relay interference channel, where multiple pairs of full-duplex users exchange information through a full-duplex relay with very large number of antennas, while each user only has two antennas. In order to save the transmission power, four typical power scaling schemes are proposed based on the maximum-ratio combining/maximum-ratio transmission (MRC/MRT) at the relay without the degradation of the performance. When the number of the relay antennas tends to infinity, the asymptotic achievable sum rates based on the proposed power scaling schemes are derived. We show that the very large antenna array can significantly reduce the effect of loop interference because of the antenna array gain. Furthermore, the theoretical results indicate that the loop interference can be reduced by cutting down the transmission power. Besides, the inter-pair interference and the inter-user interference in such systems can also be eliminated in the regime of very large number of antennas. Moreover, we analytically compare the upper bounds of the sum rates for the proposed power scaling schemes and describe the impact of the number of user pairs on the upper bounds.