This paper investigates the performance of a non-orthogonal multiple access (NOMA) based two-way relaying system where the users want to exchange independent messages with the help of a decode-and-forward relay. We consider transmission over three phases where the first and second phases are allocated to the transmissions of the users and after detection the relay applies superposition coding and transmits the network encoded symbol to the users in the third phase. Exact analytical expressions are derived to characterize the achievable average rate of the system over independent Rayleigh fading channels. Computer simulations are also presented to confirm the theoretical analysis. Analytical and simulation results show that the proposed three-phase two-way relaying scheme with NOMA outperforms the two-phase and four-phase NOMA-based two-way relaying scenarios in terms of achievable average rate.
