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In this paper, we study the resource allocation problem for a single-cell non-orthogonal multiple access (NOMA) relay network where an OFDM amplify-and-forward relay allocates the spectrum and power resources to the source-destination (SD) pairs. We aim to optimize the resource allocation to maximize the average sum-rate. The optimal approach requires an exhaustive search, leading to an NP-hard problem. To solve this problem, we propose two efficient many-to-many two-sided SD pair-subchannel matching algorithms, in which the SD pairs and sub-channels are considered as two sets of players chasing their own interests. The proposed algorithms can provide a sub-optimal solution to this resource allocation problem in affordable time. Both the static matching algorithm and the dynamic matching algorithm converge to a pair-wise stable matching after a limited number of iterations. Simulation results show …