  A two-way relay non-orthogonal multiple access (TWR-NOMA) system is
investigated, 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 account. In order to characterize
the performance of TWR-NOMA systems, we first derive closed-form expressions
for both exact and asymptotic outage probabilities of NOMA users' signals with
ipSIC/pSIC. Based on the derived results, the diversity order and throughput of
the system are examined. Then we study the ergodic rates of users' signals by
providing the asymptotic analysis in high SNR regimes. Lastly, numerical
simulations are provided to verify the analytical results and show that: 1)
TWR-NOMA is superior to TWR-OMA in terms of outage probability in low SNR
regimes; 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; and 3) In delay-limited transmission mode, TWR-NOMA
with ipSIC and pSIC have almost the same energy efficiency. However, in
delay-tolerant transmission mode, TWR-NOMA with pSIC is capable of achieving
larger energy efficiency compared to TWR-NOMA with ipSIC.
