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This paper investigates the power allocation problem of full-duplex cooperative non-orthogonal multiple access (FD-CNOMA) systems, in which the strong users relay data for the weak users via a full duplex relaying mode. For the purpose of fairness, our goal is to maximize the minimum achievable user rate in a NOMA user pair. More specifically, we consider the power optimization problem for two different relaying schemes, i.e., the fixed relaying power scheme and the adaptive relaying power scheme. For the fixed relaying scheme, we demonstrate that the power allocation problem is quasi-concave and a closed-form optimal solution is obtained. Then, based on the derived results of the fixed relaying scheme, the optimal power allocation policy for the adaptive relaying scheme is also obtained by transforming the optimization objective function as a univariate function of the relay transmit power . Simulation …