  A simultaneously transmitting and reflecting reconfigurable intelligent
surface (STAR-RIS) aided communication system is investigated, where an access
point sends information to two users located on each side of the STAR-RIS.
Different from current works assuming that the phase-shift coefficients for
transmission and reflection can be independently adjusted, which is non-trivial
to realize for purely passive STAR-RISs, a coupled transmission and reflection
phase-shift model is considered. Based on this model, a power consumption
minimization problem is formulated for both non-orthogonal multiple access
(NOMA) and orthogonal multiple access (OMA). In particular, the amplitude and
phase-shift coefficients for transmission and reflection are jointly optimized,
subject to the rate constraints of the users. To solve this non-convex problem,
an efficient element-wise alternating optimization algorithm is developed to
find a high-quality suboptimal solution, whose complexity scales only linearly
with the number of STAR elements. Finally, numerical results are provided for
both NOMA and OMA to validate the effectiveness of the proposed algorithm by
comparing its performance with that of STAR-RISs using the independent
phase-shift model and conventional reflecting/transmitting-only RISs.
