  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 (AF) 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 dynamic matching algorithm converge to a
pair-wise stable matching after a limited number of iterations. Simulation
results show that the capacity of both proposed algorithms in the NOMA scheme
significantly outperforms the conventional orthogonal multiple access scheme.
The proposed matching algorithms in NOMA scheme also achieve a better
user-fairness performance than the conventional orthogonal multiple access.
