Reconfigurable intelligent surface (RIS) is a promising technology for future wireless communication systems. Conventional RIS is constrained to a diagonal scattering matrix, which limits its flexibility. Recently, beyond-diagonal RIS (BD-RIS) has been proposed as a more general RIS architecture class that allows inter-element connections and shows great potential for performance improvement. Despite extensive progress on BD-RIS, most existing studies rely on simplified channel models that ignore practical electromagnetic (EM) effects such as mutual coupling and impedance mismatching. To address this gap, this paper investigates the architecture design and optimization of BD-RIS under the general physics-consistent model derived with multiport network theory in recent literature. Building on a compact reformulation of this model, we show that band-connected RIS achieves the same channel-shaping capability as fully-connected RIS, which extends existing results obtained for conventional channel models. We then develop optimization methods under the general physics-consistent model; specifically, we derive closed-form solutions for single-input single-output (SISO) systems, propose a globally optimal semidefinite relaxation (SDR)-based algorithm for single-stream multi-input multi-output (MIMO) systems, and design an efficient alternating direction method of multipliers (ADMM)-based algorithm for multiuser MIMO systems. Using the proposed algorithms, we conduct comprehensive simulations to evaluate the impact of various EM effects and approximations. The results indicate that the commonly adopted unilateral approximation provides sufficient accuracy in RIS-aided systems and can therefore be readily adopted to simplify the channel model, whereas mutual coupling among RIS elements should be properly taken into account in channel modeling.

翻译：可重构智能表面（RIS）是未来无线通信系统的一项前景广阔的技术。传统RIS受限于对角散射矩阵，这限制了其灵活性。近年来，超越对角RIS（BD-RIS）作为一种更通用的RIS架构类别被提出，它允许单元间互连，并展现出巨大的性能提升潜力。尽管BD-RIS研究取得了广泛进展，但现有大多数研究依赖于简化的信道模型，忽略了诸如互耦和阻抗失配等实际电磁（EM）效应。为弥补这一不足，本文基于近期文献中利用多端口网络理论推导出的通用物理一致模型，研究了BD-RIS的架构设计与优化。基于对该模型的紧凑重构，我们证明了带连接RIS实现了与全连接RIS相同的信道成形能力，这扩展了在传统信道模型下获得的现有结果。随后，我们在通用物理一致模型下开发了优化方法；具体而言，我们推导了单输入单输出（SISO）系统的闭式解，为单流多输入多输出（MIMO）系统提出了一种基于半定松弛（SDR）的全局最优算法，并为多用户MIMO系统设计了一种高效的基于交替方向乘子法（ADMM）的算法。利用所提出的算法，我们进行了全面的仿真，以评估各种电磁效应和近似的影响。结果表明，通常采用的单向近似在RIS辅助系统中提供了足够的精度，因此可以方便地用于简化信道模型，而RIS单元间的互耦应在信道建模中予以适当考虑。