  In contrast to conventional reconfigurable intelligent surface (RIS),
simultaneous transmitting and reflecting reconfigurable intelligent surface
(STAR-RIS) has been proposed recently to enlarge the serving area from 180o to
360o coverage. This work considers the performance of a STAR-RIS aided
full-duplex (FD) non-orthogonal multiple access (NOMA) communication systems.
The STAR-RIS is implemented at the cell-edge to assist the cell-edge users,
while the cell-center users can communicate directly with a FD base station
(BS). We first introduce new user clustering schemes for the downlink and
uplink transmissions. Then, based on the proposed transmission schemes
closed-form expressions of the ergodic rates in the downlink and uplink modes
are derived taking into account the system impairments caused by the self
interference at the FD-BS and the imperfect successive interference
cancellation (SIC). Moreover, an optimization problem to maximize the total
sum-rate is formulated and solved by optimizing the amplitudes and the
phase-shifts of the STAR-RIS elements and allocating the transmit power
efficiently. The performance of the proposed user clustering schemes and the
optimal STAR-RIS design are investigated through numerical results
