  In this paper, we consider a system of small cells assuming full duplex (FD)
capable base stations (BSs) and half duplex (HD) user equipment (UEs). We
investigate a mixed duplexing cellular system composed of FD and HD cells, when
BSs are using directional transmissions. A stochastic geometry based model of
the proposed system is used to derive the coverage and area spectral efficiency
(ASE) of both BSs and UEs. The effect of FD cells on the performance of the
mixed system is presented under different degree of directionality at the BSs.
We show that enabling directional transmissions at the BSs yields significant
ASE and coverage gain in both downlink and uplink directions. With directional
transmissions, the ASE increases rapidly with the number of FD cells while the
drop in the coverage rate due to FD operations reduces significantly.
