To meet the unprecedented demand for larger capacity in the fifth generation (5G) networks, non-orthogonal multiple access (NOMA) is proposed owing to its massive connectivity and high user fairness. In this paper, NOMA is recognized in a cooperative relaying network to analyze the network performance under Nakagami-m fading channels. Particularly, imperfect channel state information (ICSI) is invoked to model the practical network environment. The outage probability problem is developed, and exact closed-form expression for the outage probability at each user is also derived. Then the two bounds, i.e., the upper and lower bounds, of the outage probability are given to show the network performance limits. To elaborate further, the outage performance in the high signal-to-interference-plus-noise ratio (SINR) regime is investigated to track the existence of error floor (EF). Simulation results reveal that: i) NOMA can help to achieve better outage performance than orthogonal multiple access (OMA); and ii) EF is exist due to the consideration of the channel estimation error.