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In this paper, we investigate a full duplex (FD) multi-user non-orthogonal multiple access (NoMA) communication system based on the optimization of received signal-to-interference-plus-noise ratio (SINR) per unit power. Since the communication system operates in the FD mode, co-channel interference (CCI) and self-interference (SI) dominate the system’s performance. Accordingly, to combat the CCI, we adopt a game-theoretic approach and propose users’ clustering algorithms and to suppress the SI, we formulate an optimization problem to maximize the power-normalized SINR (PN-SINR). While the user clustering optimization problem is constrained by: 1) the successive interference cancellation (SIC) constraint and 2) two binary constraints for the allocations of uplink (UL) and downlink (DL) users, the PN-SINR problem is constrained by: 1) total transmit power budget at the base station and UL users; 2) the …