  This paper studies the degrees of freedom of full-duplex multicell networks
that share the spectrum among multiple cells in a non-orthogonal setting. In
the considered network, we assume that {\em full-duplex} base stations with
multiple transmit and receive antennas communicate with multiple single-antenna
mobile users. By spectrum sharing among multiple cells and (simultaneously)
enabling full-duplex radio, the network can utilize the spectrum more flexibly,
but, at the same time, the network is subject to multiple sources of
interference compared to a network with separately dedicated bands for distinct
cells and uplink--downlink traffic. Consequently, to take advantage of the
additional freedom in utilizing the spectrum, interference management is a
crucial ingredient. In this work, we propose a novel strategy based on
interference alignment which takes into account inter-cell interference and
intra-cell interference caused by spectrum sharing and full-duplex to establish
a general achievability result on the sum degrees of freedom of the considered
network. Paired with an upper bound on the sum degrees of freedom, which is
tight under certain conditions, we demonstrate how spectrum sharing and
full-duplex can significantly improve the throughput over conventional cellular
networks, especially for a network with large number of users and/or cells.
