In this paper, we propose and investigate the performance of a downlink non-orthogonal multiple access multi-user system with the assistance of an aerial relay station (ARS). The ARS is equipped with multiple antennas, mounted on an unmanned aerial vehicle (UAV), and serves as a relay for cooperative communication between a terrestrial base station (BS) and users. The system performance is evaluated via the outage probability of each user in the urban environment where the ARS and BS are configured with a different number of antennas. More interestingly, the optimization of the ARS trajectory to maximize the data rate of the considered system is also proposed by using the successive convex approximation technique. The results show that the best system performance can be obtained by adjusting the altitude and designing the optimum trajectory of the ARS. Monte-Carlo simulation results are provided to demonstrate the performance of the proposed system and the accuracy of the developed analytical frameworks.