Simultaneously Transmitting and Reflecting (STAR)-RISs: A Coupled Phase-Shift Model

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.