A unified framework for STAR-RIS coefficients optimization

Simultaneously transmitting and reflecting (STAR) reconfigurable intelligent surface (RIS), which serves users located on both sides of the surface, has recently emerged as a promising enhancement to the traditional reflective only RIS. Due to the lack of a unified comparison of communication systems equipped with different modes of STAR-RIS and the performance degradation caused by the constraints involving discrete selection, this paper proposes a unified optimization framework for handling the STAR-RIS operating mode and discrete phase constraints. With a judiciously introduced penalty term, this framework transforms the original problem into two iterative subproblems, with one containing the selection-type constraints, and the other subproblem handling other wireless resource. Convergent point of the whole algorithm is found to be at least a stationary point under mild conditions. As an illustrative example, the proposed framework is applied to a sum-rate maximization problem in the downlink transmission. Simulation results show that the algorithms from the proposed framework outperform other existing algorithms tailored for different STAR-RIS scenarios. Furthermore, it is found that 4 or even 2 discrete phases STAR-RIS could achieve almost the same sum-rate performance as the continuous phase setting, showing for the first time that discrete phase is not necessarily a cause of significant performance degradation.