Reconfigurable intelligent surfaces (RISs) are envisioned as a promising technology for future wireless communication systems due to their ability to control the propagation environment in a hardware- and energy-efficient way. Recently, the concept of RISs has been extended to beyond diagonal RISs (BD-RISs), which unlock the full potential of RISs thanks to the presence of tunable interconnections between RIS elements. While various algorithms have been proposed for specific BD-RIS architectures, a universal optimization framework applicable to arbitrary architectures is still lacking. In this paper, we bridge this research gap by proposing an architecture-independent framework for BD-RIS optimization, with the main focus on sum-rate maximization and transmit power minimization in multiuser multi-input single-output (MU-MISO) systems. Specifically, we first incorporate BD-RIS architectures into the models by connecting the scattering matrix with the admittance matrix and introducing appropriate constraints to the admittance matrix. The formulated problems are then solved by our custom-designed partially proximal alternating direction method of multipliers (pp-ADMM) algorithms. The pp-ADMM algorithms are computationally efficient, with each subproblem either admitting a closed-form solution or being easily solvable. We further explore the extension of the proposed framework to general utility functions and multiuser multi-input multi-output (MU-MIMO) systems. Simulation results demonstrate that the proposed approaches achieve a better trade-off between performance and computational efficiency compared to existing methods. We also compare the performance of various BD-RIS architectures in MU-MISO systems using the proposed approach, which has not been explored before due to the lack of an architecture-independent framework.

翻译：可重构智能表面（RIS）因其能够以硬件和能源高效的方式控制传播环境，被视作未来无线通信系统的关键技术。近年来，RIS概念已扩展至超对角可重构智能表面（BD-RIS），通过引入RIS单元间的可调互连结构，充分释放了RIS的潜力。尽管已有多种针对特定BD-RIS架构的优化算法被提出，但适用于任意架构的通用优化框架仍然缺失。本文通过提出一种架构无关的BD-RIS优化框架来填补这一研究空白，主要聚焦于多用户多输入单输出（MU-MISO）系统中的和速率最大化与发射功率最小化问题。具体而言，我们首先通过将散射矩阵与导纳矩阵相关联，并对导纳矩阵施加适当的约束条件，将不同BD-RIS架构纳入系统模型。随后，采用我们专门设计的部分近端交替方向乘子法（pp-ADMM）算法求解所构建的优化问题。该pp-ADMM算法具有较高的计算效率，其每个子问题要么存在闭式解，要么易于求解。我们进一步探讨了所提框架向通用效用函数及多用户多输入多输出（MU-MIMO）系统的扩展。仿真结果表明，与现有方法相比，所提方案在性能与计算效率之间取得了更好的平衡。此外，基于所提出的架构无关框架，我们首次系统比较了MU-MISO系统中不同BD-RIS架构的性能表现，这一比较此前因缺乏通用框架而尚未被深入研究。