  This paper investigates a two-way relay nonorthogonal multiple access
(TWR-NOMA) system, where two groups of NOMA users exchange messages with the
aid of one half-duplex (HD) decode-and-forward (DF) relay. Since the
signal-plus-interference-to-noise ratios (SINRs) of NOMA signals mainly depend
on effective successive interference cancellation (SIC) schemes, imperfect SIC
(ipSIC) and perfect SIC (pSIC) are taken into consideration. To characterize
the performance of TWR-NOMA systems, we derive closed-form expressions for both
exact and asymptotic outage probabilities of NOMA users' signals with
ipSIC/pSIC. Based on the results derived, the diversity order and throughput of
the system are examined. Numerical simulations demonstrate that: 1) TWR-NOMA is
superior to TWR-OMA in terms of outage probability in low SNR regimes; and 2)
Due to the impact of interference signal (IS) at the relay, error floors and
throughput ceilings exist in outage probabilities and ergodic rates for
TWR-NOMA, respectively.
