Non-orthogonal multiple access (NOMA) has been proposed as a promising technique for the fifth generation wireless networks. In this study, the authors investigate the performance of a cooperative relaying scheme using NOMA (termed NOMA-AF-CRS), where two sources communicate with their corresponding destinations over the same frequency simultaneously through a shared amplify-and-forward (AF) relay. First, the closed-form approximations are derived for the outage probability. The analytical results are further evaluated in the high signal-to-noise ratio region to characterise the diversity order achieved by the system. Then, the ergodic sum capacity of NOMA-AF-CRS is analysed and an upper bound to the ergodic sum capacity is derived. Finally, simulation results are presented to verify the proposed analysis and demonstrate the advantages of NOMA-AF-CRS over the conventional orthogonal multiple access techniques.