  This paper investigates the downlink transmission of reconfigurable
intelligent surface (RIS)-aided cooperative non-orthogonal-multiple-access
(C-NOMA), where both half-duplex (HD) and full-duplex (FD) relaying modes are
considered. The system model consists of one base station (BS), two users and
one RIS. The goal is to minimize the total transmit power at both the BS and at
the user-cooperating relay for each relaying mode by jointly optimizing the
power allocation coefficients at the BS, the transmit power coefficient at the
relay user, and the passive beamforming at the RIS, subject to power budget
constraints, the successive interference cancellation constraint and the
minimum required quality-of-service at both cellular users. To address the
high-coupled optimization variables, an efficient algorithm is proposed by
invoking an alternating optimization approach that decomposes the original
problem into a power allocation sub-problem and a passive beamforming
sub-problem, which are solved alternately. For the power allocation
sub-problem, the optimal closed-form expressions for the power allocation
coefficients are derived. Meanwhile, the semi-definite relaxation approach is
exploited to tackle the passive beamforming sub-problem. The simulation results
validate the accuracy of the derived power control closed-form expressions and
demonstrate the gain in the total transmit power brought by integrating the RIS
in C-NOMA networks.
