  In-band full-duplex (FD) communications have been optimistically promoted to
improve the spectrum utilization and efficiency. However, the penetration of FD
communications to the cellular networks domain is challenging due to the
imposed uplink/downlink interference. This paper presents a tractable
framework, based on stochastic geometry, to study FD communications in cellular
networks. Particularly, we assess the FD communications effect on the network
performance and quantify the associated gains. The study proves the
vulnerability of the uplink to the downlink interference and shows that the
improved FD rate gains harvested in the downlink (up to $97\%$) comes at the
expense of a significant degradation in the uplink rate (up to $94\%$).
Therefore, we propose a novel fine-grained duplexing scheme, denoted as
$\alpha$-duplex scheme, which allows a partial overlap between the uplink and
the downlink frequency bands. We derive the required conditions to harvest rate
gains from the $\alpha$-duplex scheme and show its superiority to both the FD
and half-duplex (HD) schemes. In particular, we show that the $\alpha$-duplex
scheme provides a simultaneous improvement of $28\%$ for the downlink rate and
$56\%$ for the uplink rate. Finally, we show that the amount of the overlap can
be optimized based on the network design objective.
