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We consider a multipair decode-and-forward relay channel, where multiplesources transmit simultaneously their signals to multiple destinations with thehelp of a full-duplex relay station. We assume that the relay station isequipped with massive arrays, while all sources and destinations have a singleantenna. The relay station uses channel estimates obtained from received pilotsand zero-forcing (ZF) or maximum-ratio combining/maximum-ratio transmission(MRC/MRT) to process the signals. To reduce significantly the loop interferenceeffect, we propose two techniques: i) using a massive receive antenna array; orii) using a massive transmit antenna array together with very low transmitpower at the relay station. We derive an exact achievable rate in closed-formfor MRC/MRT processing and an analytical approximation of the achievable ratefor ZF processing. This approximation is very tight, especially for largenumber of relay station antennas. These closed-form expressions enable us todetermine the regions where the full-duplex mode outperforms the half-duplexmode, as well as, to design an optimal power allocation scheme. This optimalpower allocation scheme aims to maximize the energy efficiency for a given sumspectral efficiency and under peak power constraints at the relay station andsources. Numerical results verify the effectiveness of the optimal powerallocation scheme. Furthermore, we show that, by doubling the number oftransmit/receive antennas at the relay station, the transmit power of eachsource and of the relay station can be reduced by 1.5dB if the pilot power isequal to the signal power, and by 3dB if the pilot power is kept fixed, whilemaintaining a given quality-of-service.

Multipair Full-Duplex Relaying with Massive Arrays and Linear Processing