  We investigate the spectral efficiency of full-duplex small cell wireless
systems, in which a full-duplex capable base station (BS) is designed to
send/receive data to/from multiple halfduplex users on the same system
resources. The major hurdle for designing such systems is due to the
self-interference at the BS and co-channel interference among users. Hence, we
consider a joint beamformer design to maximize the spectral efficiency subject
to certain power constraints. The design problem is first formulated as a
rank-constrained optimization one, and the rank relaxation method is then
applied. However the relaxed problem is still nonconvex, and thus optimal
solutions are hard to find. Herein, we propose two provably convergent
algorithms to obtain suboptimal solutions. Based on the concept of the
difference of convex functions programming, we approximate the design problem
by a determinant maximization program in each iteration of the first algorithm.
The second method is built upon the sequential parametric convex approximation
method, which allows us to transform the relaxed problem into a semidefinite
program in each iteration. Extensive numerical experiments under small cell
setups illustrate that the full-duplex system with the proposed algorithms can
achieve a large gain over the half-duplex one.
