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In this paper, a novel resource allocation design is investigated for non-orthogonal multiple access (NOMA) enhanced heterogeneous networks (HetNets), where small cell base stations (SBSs) are capable of communicating with multiple small cell users (SCUs) via the NOMA protocol. With the aim of maximizing the sum rate of SCUs while taking the fairness issue into consideration, a joint problem of spectrum allocation and power control is formulated. In particular, the spectrum allocation problem is modeled as a many-to-one matching game with peer effects. We propose a novel algorithm where the SBSs and resource blocks interact to decide their desired allocation. The proposed algorithm is proved to converge to a two-sided exchange-stable matching. Furthermore, we introduce the concept of `exploration' into the matching game for further improving the SCUs' sum rate. The power control of each SBS is …