Achieving significant performance gains both in terms of system throughput and massive connectivity, non-orthogonal multiple access (NOMA) has been considered as a very promising candidate for future wireless communications technologies. It has already received serious consideration for implementation in the fifth generation (5G) and beyond wireless communication systems. This is mainly due to NOMA allowing more than one user to utilise one transmission resource simultaneously at the transmitter side and successive interference cancellation (SIC) at the receiver side. However, in order to take advantage of the benefits, NOMA provides in an optimal manner, power allocation needs to be considered to maximise the system throughput. This problem is non-deterministic polynomial-time (NP)-hard which is mainly why the use of deep learning techniques for power allocation is required. In this paper, a state-of-the-art review on cutting-edge solutions to the power allocation optimisation problem using deep learning is provided. It is shown that the use of deep learning techniques to obtain effective solutions to the power allocation problem in NOMA is paramount for the future of NOMA-based wireless communication systems. Furthermore, several possible research directions based on the use of deep learning in NOMA systems are presented.
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