  Simultaneously transmitting/refracting and reflecting reconfigurable
intelligent surface (STAR-RIS) has been introduced to achieve full coverage
area. This paper investigate the performance of STAR-RIS assisted
non-orthogonal multiple access (NOMA) networks over Rician fading channels,
where the incidence signals sent by base station are reflected and transmitted
to the nearby user and distant user, respectively. To evaluate the performance
of STAR-RIS-NOMA networks, we derive new approximate expressions of outage
probability and ergodic rate for a pair of users, in which the imperfect
successive interference cancellation (ipSIC) and perfect SIC (pSIC) schemes are
taken into consideration. Based on the asymptotic expressions, the diversity
orders of the nearby user with ipSIC/pSIC and distant user are achieved
carefully. The high signal-to-noise ratio slopes of ergodic rates for nearby
user with pSIC and distant user are equal to $one$ and $zero$, respectively. In
addition, the system throughput of STAR-RIS-NOMA is discussed in delay-limited
and delay-tolerant modes. Simulation results are provided to verify the
accuracy of the theoretical analyses and demonstrate that: 1) The outage
probability of STAR-RIS-NOMA outperforms that of STAR-RIS assisted orthogonal
multiple access (OMA) and conventional cooperative communication systems; 2)
With the increasing of reflecting elements $K$ and Rician factor $\kappa $, the
STAR-RIS-NOMA networks are capable of attaining the enhanced performance; and
3) The ergodic rates of STAR-RIS-NOMA are superior to that of STAR-RIS-OMA.
