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In this paper, we consider multipair two-way massive multiple-input and multiple-output (MIMO) communication system, in which multiple pairs of source nodes exchange messages with the help of one shared amplify-and-forward relay provisioned with large number of antennas. Unlike the perfect channel state information (CSI) assumption, the practical minimum mean-squared error-based channel estimation is considered. And the asymptotic signal to interference plus noise ratio (SINR) analysis of four power-scaling scenarios is presented to show that, even with the imperfect CSI, the interpair interference can still be eliminated, the small-scale fading as well as the noise at source nodes and the relay can be averaged out in the regime of very large number of antenna. It is unveiled that the impact of the channel estimation error will present in the effective large-scale fading coefficient, which explicates the degradation by the imperfect CSI estimate and consumes the results with perfect CSI as special cases. On the basis of the asymptotic SINR analysis results, the optimal power allocation problem is formulated to derive the energy efficient relaying scheme for the maximum ratio combining-maximum ratio transmission precoding scheme. Finally, numerical results are presented to validate that the energy efficient design can effectively reduce the power consumption while maintaining a reasonable sum rate in the multipair two-way massive MIMO relaying system, even in the presence of CSI error.

On the Energy Efficient Multi-Pair Two-Way Massive MIMO AF Relaying With Imperfect CSI and Optimal Power Allocation