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In this paper, we consider a non-orthogonal multiple access cognitive radio network, where a full-duplex (FD) multi-antenna relay assists transmission from an access point (AP) to a cognitive far user, while at the same time, the AP transmits to a cognitive near user. Our objective is to maximize 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 AP and FD relay is solved as a semi-definite relaxation problem, in conjunction with an efficiently solvable line-search approach. We also consider a low complexity fixed beamformer design, where the optimum power allocation between the AP and FD relay is solved. Several fixed beamforming designs based on the zero-forcing criterion are proposed for which exact and asymptotic outage probability expressions …