Mutual Coupling (MC) emerges as an inherent feature in Reconfigurable Intelligent Surfaces (RISs), particularly, when they are fabricated with sub-wavelength inter-element spacing. Hence, any physically-consistent model of the RIS operation needs to accurately describe MC-induced effects. In addition, the design of the ElectroMagnetic (EM) transmit/receive radiation patterns constitutes another critical factor for efficient RIS operation. The latter two factors lead naturally to the emergence of non-local RIS structures, whose operation can be effectively described via non-diagonal phase shift matrices. In this paper, we focus on jointly optimizing MC and the radiation patterns in multi-user MIMO communication systems assisted by non-local RISs, which are modeled via the scattering parameters. We particularly present a novel problem formulation for the joint optimization of MC, radiation patterns, and the active and passive beamforming in a physically-consistent manner, considering either reflective or transmissive RIS setups. Differently from the current approaches that design the former two parameters on the fly, we present an offline optimization method which is solved for both considered RIS functionalities. Our extensive simulation results, using both parametric and geometric channel models, showcase the validity of the proposed optimization framework over benchmark schemes, indicating that improved performance is achievable without the need for optimizing MC and the radiation patterns of the RIS on the fly, which can be rather cumbersome.

翻译：互耦效应是可重构智能表面（RIS）的固有特性，尤其当RIS采用亚波长单元间距制造时更为显著。因此，任何物理一致的RIS工作模型都需要准确描述互耦引发的效应。此外，电磁收发辐射方向图的设计是影响RIS高效运行的另一个关键因素。上述两个因素自然导致非局部RIS结构的出现，其工作特性可通过非对角相位偏移矩阵有效描述。本文聚焦于联合优化非局部RIS辅助多用户MIMO通信系统中的互耦效应与辐射方向图，该系统通过散射参数进行建模。我们特别提出了一种新颖的问题公式化方法，以物理一致的方式联合优化互耦、辐射方向图以及有源/无源波束赋形，并同时考虑反射型与透射型RIS配置。与现有在线实时设计前两个参数的方法不同，我们提出了一种离线优化方法，可针对两种RIS功能分别求解。通过采用参数化信道模型与几何信道模型的广泛仿真结果，验证了所提优化框架相比基准方案的优越性，表明无需在线优化互耦与RIS辐射方向图（该过程相当繁琐）即可实现更优性能。