Reconfigurable intelligent surface (RIS) is a key technology to control the communication environment in future wireless networks. Recently, beyond diagonal RIS (BD-RIS) emerged as a generalization of RIS achieving larger coverage through additional tunable impedance components interconnecting the RIS elements. However, conventional RIS and BD-RIS can effectively serve only users in their proximity, resulting in limited coverage. To overcome this limitation, in this paper, we investigate distributed RIS, whose elements are distributed over a wide region, in opposition to localized RIS commonly considered in the literature. The scaling laws of distributed BD-RIS reveal that it offers significant gains over distributed conventional RIS and localized BD-RIS, enabled by its interconnections allowing signal propagation within the BD-RIS. To assess the practical performance of distributed BD-RIS, we model and optimize BD-RIS with lossy interconnections through transmission line theory. Our model accounts for phase changes and losses over the BD-RIS interconnections arising when the interconnection lengths are not much smaller than the wavelength. Numerical results show that the performance of localized BD-RIS is only slightly impacted by losses, given the short interconnection lengths. Besides, distributed BD-RIS can achieve orders of magnitude of gains over conventional RIS, even in the presence of low losses.

翻译：可重构智能表面（RIS）是未来无线网络中控制通信环境的关键技术。近年来，超越对角RIS（BD-RIS）作为RIS的推广形式出现，通过额外可调阻抗组件互联RIS单元，实现了更广覆盖范围。然而，传统RIS和BD-RIS仅能有效服务其邻近用户，导致覆盖范围受限。为克服这一局限，本文研究分布式RIS——其单元分布在广阔区域，与文献中常见的局部化RIS形成对比。分布式BD-RIS的缩放定律表明，得益于允许信号在BD-RIS内部传播的互联结构，相较于分布式传统RIS和局部化BD-RIS，它能带来显著增益。为评估分布式BD-RIS的实际性能，我们通过传输线理论对含损耗互联的BD-RIS进行建模与优化。该模型计及互联长度与波长相当时，由BD-RIS互联引起的相位变化和损耗。数值结果表明，由于互联长度较短，损耗对局部化BD-RIS性能影响较小；此外，即便存在低损耗，分布式BD-RIS相较于传统RIS仍能实现数量级增益。