In this paper, the spectral efficiency of a full-duplex (FD) densely distributed multi-input multi-output (MIMO) system with wireless backhaul is considered. In-band full-duplex (IBFD) backhauling, in which the backhaul and access transmissions take place on the same spectrum, is exploited for wireless backhauling to enable an efficient spectrum reuse. However, the severe cross-tier interference and cross-link interference reduce the gains of IBFD backhauling. To evaluate the achievable spectral efficiency with imperfect channel state information (CSI), we propose a two-phase channel estimation scheme to estimate the CSI for two wireless links, and the scheme estimates an effective interference CSI between access points (APs) based on beamforming training to perform interference cancelation at APs. Given the estimated CSI, the closed-form expressions of the uplink and downlink achievable rates with maximum ratio transmission beamforming and maximum ratio combining receivers, respectively, are derived with Gamma approximation. Numerical results verify the accuracy of the derived closed-form expressions and the effectiveness of the two-phase channel estimation scheme for interference cancelation. Moreover, compared with half-duplex densely distributed MIMO systems, FD systems with interference cancelation have a better performance.
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