  In this paper, we consider a non-orthogonal multiple access cognitive radio
network, where a full-duplex multi-antenna relay assists transmission from a
base station (BS) to a cognitive far user, whereas, at the same time, the BS
transmits to a cognitive near user. Our objective is to enlarge the far-near
user rate region by maximizing the rate of the near user under a constraint
that the rate of the far user is above a certain threshold. To this end, a
non-convex joint optimization problem of relay beamforming and the transmit
powers at the BS and cognitive relay is solved as a semi-definite relaxation
problem, in conjunction with an efficiently solvable line-search approach. For
comparisons, we also consider low complexity fixed beamformer design, where the
optimum power allocation between the BS and cognitive relay is solved. Our
results demonstrate that the proposed joint optimization can significantly
reduce the impact of the residual self-interference at the FD relay and
inter-user interference in the near user case.
