A unified framework for STAR-RIS coefficients optimization

Simultaneously Transmitting and Reflecting (STAR) Reconfigurable Intelligent Surface (RIS)—capable of serving users on both sides of the surface—has emerged as a transformative advancement over conventional reflective-only RIS systems. While this innovation holds immense promise, existing research adopts vastly distinct optimization techniques under different STAR-RIS operating modes, presenting challenges for comparing different operating modes under a unified lens. To bridge this gap, we introduce a unified framework to optimize the phase shift design under different STAR-RIS operational modes and it covers both continuous and discrete phase operations. This versatile framework, while applicable to a wide range of STAR-RIS resource allocation problems, will be demonstrated through a downlink sum-rate maximization problem. Our results reveal that algorithms derived from this framework consistently outperform existing methods tailored for specific STAR-RIS scenarios. Remarkably, it is found that STAR-RIS systems with just 4 or even 2 discrete phases achieve near-identical sum-rate performance to those with continuous phase configurations. This challenges the conventional belief that discrete phase is the blame for significant performance loss.