This paper studies the wireless systems by implementing the full-duplex (FD) unmanned aerial vehicle (UAV) relay to allow two nearby base stations joint communicate to distant users. The nonorthogonal multiple access (NOMA) assisted networks and design of multiple-antenna users are considered in order to improve the users' performance. To overcome obstacles in transmission environment, such a model of the uplink (UL) and the downlink (DL) relying on UAV relay is suitable to forward signals to far users. Moreover, practical scenario of imperfect successive interference cancellation (SIC) at each receiver is considered as main reason of degraded performance. To evaluate specific performance metric, we derive the closed-form expressions of outage probability. In addition, the throughput in delay-limited transmission mode of UAV relay assisted UL/DL NOMA system is also considered thoroughly. The derivations and results showed that the higher number of antennas at users could effectively improve the system throughput and reduce the outage probability. The numerical simulation results further indicate the effectiveness of the proposed system and the correctness of theoretical analysis. INDEX TERMS Non-orthogonal Multiple Access, Unmanned Aerial Vehicle, outage probability, throughput, full-duplex, imperfect SIC.