In this paper, the spectral efficiency of a full-duplex densely distributed multi-input multi-output (MIMO) system with wireless backhaul is considered. In-band full-duplex (IBFD) backhauling, in which the backhual and access transmission take place on the same spectrum, is exploited for wireless backhauling to enable efficient spectrum reuse. However, the severe cross-tier interference and cross link interference (CLI) 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 CSI for two wireless links, and the scheme estimates effective interference CSI between APs based on beamforming training to perfom interference cancellation at access points (APs). Given the estimated CSI, the closed-form expressions of the uplink and downlink achievable rates respectively with maximum ratio transmission (MRT) beamforming and maximum ratio combining (MRC) receivers are derived with Gamma approximation. Numerical results verify the accuracy of the derived closed-form expressions and the effectiveness of two-phase channel estimation scheme for interference cancellation. Besides, compared with half-duplex densely distributed MIMO systems, full-duplex systems with interference cancellation provide better performance.