This paper investigates non-orthogonal multiple access (NOMA) system, where the near NOMA user is able to communicate with a base station (BS) directly while the far NOMA user needs to resort to a full-duplex (FD) relay. Wireless power transfer is applied to our system where the FD relay integrated with power splitting architecture can be powered wirelessly by the ambient radio signals simultaneously. Moreover, we assume that self-interference cancellation at the relay and inter-user interference cancellation at the near NOMA user are imperfect. For the purpose of maximizing the energy efficiency of the NOMA system, the power splitting ratio and transmit beamforming vectors are researched for the BS and relay with the guarantee of QoS requirements for two users. The formulated problem appears to be nonlinear fractional programming, which is highly nonconvex and the global optimality is hard to obtain. By introducing Charnes-Cooper's transformation and inner approximation method, we develop an iterative algorithm to gain the near optimal solution. The simulation results show that the proposed joint optimizing algorithm outperforms the existing scheme in terms of energy efficiency as well as the effect of SI cancellation on performance gain. INDEX TERMS Non-orthogonal multiple access (NOMA), full-duplex relay, power splitting, fractional programming, iterative algorithm.

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