  This paper investigates the performance of reconfigurable intelligent surface
assisted two-way non-orthogonal multiple access (RIS-TW-NOMA) networks, where a
pair of users exchange their information through a RIS. The influence of
imperfect successive interference cancellation on RIS-TW-NOMA is taken into
account. To evaluate the potential performance of RIS-TW-NOMA, we derive the
exact and asymptotic expressions of outage probability and ergodic rate for a
pair of users. Based on the analytical results, the diversity orders and high
signal-to-noise ratio (SNR) slopes are obtained in the high SNR regime, which
are closely related to the number of RIS elements. Additionally, we analyze the
system throughput and energy efficiency of RIS-TW-NOMA networks in both
delay-limited and delay-tolerant transmission modes. Numerical results indicate
that: 1) The outage behaviors and ergodic rate of RIS-TW-NOMA are superior to
that of RIS-TW-OMA and two-way relay OMA (TWR-OMA); 2) As the number of RIS
elements increases, the RIS-TW-NOMA networks are capable of achieving the
enhanced outage performance; and 3) By comparing with RIS-TW-OMA and TWR-OMA
networks, the energy efficiency and system throughput of RIS-TW-NOMA has
obvious advantages.
