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In the fifth generation (5G) of wireless communication systems, hitherto unprecedented requirements are expected to be satisfied. As one of the promising techniques of addressing these challenges, non-orthogonal multiple access (NOMA) has been actively investigated in recent years. In contrast to the family of conventional orthogonal multiple access (OMA) schemes, the key distinguishing feature of NOMA is to support a higher number of users than the number of orthogonal resource slots with the aid of non-orthogonal resource allocation. This may be realized by the sophisticated inter-user interference cancellation at the cost of an increased receiver complexity. In this paper, we provide a comprehensive survey of the original birth, the most recent development, and the future research directions of NOMA. Specifically, the basic principle of NOMA will be introduced at first, with the comparison between NOMA and …