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We consider a multi-pair massive multiple-input multiple-output relay network, where the relay is equipped with a large number, N, of antennas, but driven by a far smaller number, L, of radio-frequency (RF) chains. We assume that K pairs of users are scheduled for simultaneous transmission, where K satisfies 2K=L. A hybrid signal processing scheme is presented for both uplink and downlink transmissions of the network. Analytical expressions of both spectral efficiency (SE) and energy efficiency (EE) are derived with respect to the RF chain number under imperfect channel estimation. It is revealed that, under the condition N&gt;&#x230A;4L2/&#x03C0;&#x230B;, the transmit power of each user and the relay can be, respectively, scaled down by 1/&#x221A;N and 2K/&#x221A;N if pilot power scales with signal power, or they can be, respectively, scaled down by 1/N and 2K/N if the pilot power is kept fixed, while maintaining an asymptotically unchanged SE. While regarding EE of the network, the optimal EE is shown to be achieved when Pr = 2K Ps, where Pr and Ps, respectively, refer to the transmit power of the relay and each source terminal. We show that the network EE is a quasi-concave function with respect to the number of RF-chains which, therefore, admits a unique globally optimal choice of the RF-chain number. Numerical simulations are conducted to verify our observations.

Spectral and Energy Efficiency of Multi-Pair Massive MIMO Relay Network With Hybrid Processing