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In this paper, we consider a multi-user full-duplex (FD) massive multiple-input multiple-output (MIMO) system. The FD base station (BS) is equipped with large-scale antenna arrays, while each FD user is equipped with two antennas (one for transmission and the other one for reception). We assume that the channel state information (CSI) is imperfect, and no instantaneous CSI of loop interference (LI) channel is obtained. On the basis of low-complexity uplink beamforming and downlink precoding techniques, i.e. maximum-ratio combining/maximum-ratio transmission (MRC/MRT) and zero-forcing reception/zero-forcing transmission (ZFR/ZFT), the asymptotic expressions of signal-to-interference-plus-noise ratio (SINR) of uplink and downlink are derived respectively when the number of antennas of the BS tends to infinity. Based on the asymptotic SINR expressions, we first analyse the spectral efficiency (SE) performance assuming that the generalized power scaling scenario is adopted. Through the theoretical derivation, it is shown that the detrimental impact of the LI can be eliminated by the very large number of antennas at the BS if the power scaling scenario is appropriately applied, as well as the interference caused by the imperfect channel estimation, the multi-user interference (MUI) and inter-user interference (IUI). Then, we propose power allocation (PA) scenarios to maximize the energy efficiency (EE) and the sum SE with the constraint of maximum powers at the BS and users. The simulation results verify the accuracy of the asymptotic method, we also validate the effectiveness of the EE and the sum SE maximization PA algorithms. We show that adopting the PA scheme to maximize the sum SE can make the multi-user FD massive MIMO system outperform the half-duplex (HD) counterpart regardless of the level of LI.

On the energy/spectral efficiency of multi-user full-duplex massive MIMO systems with power control