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Non-orthogonal multiple access (NOMA) scheme is seen as a strong candidate for future wireless networks thanks to its spectral efficiency. Thus, NOMA has attracted a great recent attention and the power allocation (PA) in NOMA has been analyzed in terms of various perspectives. However, all these studies analyze only the Shannon limit and the detection at the users have not been considered in detail. In this paper, we propose a true PA constraint for a detectable NOMA signal design in multi-user NOMA schemes with arbitrary M-QAM signalling. With the proposed PA constraint, the successful detection at the receivers are guaranteed. We evaluate the proposed PA with computer simulations. We also compare with other PA strategies in the literature and present that if the provided PA constraint is not satisfied, none of the users can detect it symbols and all users have the worst bit error rate (BER) performance (i …