Non-orthogonal multiple access (NOMA) is one promising technology, which provides high system capacity, low latency, and massive connectivity, to address several challenges in the fifth-generation wireless systems. In this paper, we first reveal that the NOMA techniques have evolved from single-carrier NOMA (SC-NOMA) into multi-carrier NOMA (MC-NOMA). Then, we comprehensively investigated on the basic principles, enabling schemes and evaluations of the two most promising MC-NOMA techniques, namely sparse code multiple access (SCMA) and pattern division multiple access (PDMA). Meanwhile, we consider that the research challenges of SCMA and PDMA might be addressed with the stimulation of the advanced and matured progress in SC-NOMA. Finally, yet importantly, we investigate the emerging applications, and point out the future research trends of the MC-NOMA techniques, which could be straightforwardly inspired by the various deployments of SC-NOMA.
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