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Non-orthogonal multiple access (NOMA) technique is an expert on channel differences exploiting.In this paper,a dual-hop NOMA-based cooperative relaying network where a best relay is selected as an active node to accomplish the communication between a source and a destination is discussed.We assume that both decode-and-forward (DF) and amplify-and-forward (AF) protocols are applied to the selected relay.The metrics that ergodic sum-rate and outage probability are investigated,and the closed-form expressions of the latter for DF and AF protocols are derived.Numerical and simulation results are conducted to verify the validity of the theoretical analysis,in which we can see that the NOMA based DF relaying is better than the NOMA based AF relaying and other existing NOMA-based cooperative communication schemes.