In this paper, we study the performance improvement methods for a cell-edge user of two-user non-orthogonal multiple access (NOMA) systems in downlink scenarios. To this end, we propose two cooperative relaying schemes, namely ON/OFF-full-duplex relaying (ON/OFF-FDR) and ON/OFF-half-duplex relaying (ON/OFF-HDR) schemes. More specifically, in order to improve the performance of the cell-edge user, we consider a cell-center user as a relay, where either FDR or HDR can be employed to assist the direct NOMA transmission from a base station (BS) to the cell-edge user. An ON/OFF mechanism is proposed to decide whether the cooperative relaying transmission is necessary or not. The ON/OFF relaying decision is made based on the quality of the direct and relaying links from the BS to the cell-edge user. The performance of the two proposed schemes is investigated in terms of outage probability and sum throughput. Numerical results reveal that the proposed schemes not only provide essential outage performance improvements for the cell-edge user, but also are able to improve the sum throughput of the two-user NOMA systems. The advantages and drawbacks of each proposed scheme are highlighted and insightful discussions are provided.