Non-orthogonal multiple access (NOMA), an emerging technology to improve system capacity and spectrum efficiency, has attracted significant attention. In this study, the authors propose a NOMA-based downlink cooperative cellular system, where the base station communicates with two paired mobile users simultaneously through the help of a half-duplex amplify-and-forward relay. The outage performance of the system is investigated and closed-form expressions for their respective exact and asymptotic outage scheme are derived. Furthermore, they study the ergodic sum rate of the two paired users and the upper bound of the ergodic sum rate is obtained. By comparing the NOMA with conventional multiple access (MA) via numerical simulations, they have shown that NOMA can obtain the same diversity order with conventional MA, and achieve nearly the same sum rate with conventional MA. Furthermore, NOMA can offer better spectral efficiency and user fairness since more users are served at the same time, frequency, and spreading code.