  Simultaneously transmitting and reflecting reconfigurable intelligent surface
(STAR-RIS) is a promising technology to achieve full-space coverage. This paper
investigates the resource allocation problem in a STAR-RIS-assisted
multi-carrier communication network. To maximize the system sum-rate, a joint
optimization problem for orthogonal multiple access (OMA) is first formulated,
which is a mixed-integer non-linear programming problem. To solve this
challenging problem, we first propose a channel assignment scheme utilizing
matching theory and then invoke the alternating optimization-based method to
optimize the resource allocation policy and beamforming vectors iteratively.
Furthermore, the sum-rate maximization problem for non-orthogonal multiple
access (NOMA) is investigated. To efficiently solve it, we first propose a
location-based matching algorithm to determine the sub-channel assignment,
where a transmitted user and a reflected user are grouped on a sub-channel.
Then, a three-step approach is proposed, where the decoding orders,
beamforming-coefficient vectors, and power allocation are optimized by
employing semidefinite programming, convex upper bound approximation, and
geometry programming, respectively. Numerical results unveil that: 1) For OMA,
a general design that includes same-side user-pairing for channel assignment is
preferable, while for NOMA, the proposed transmission-and-reflection scheme can
achieve near-optimal performance. 2) The STAR-RIS-aided NOMA network
significantly outperforms the networks employing conventional RISs and OMA.
