Beyond diagonal reconfigurable intelligent surface (BD-RIS) is a family of RIS architectures more flexible than conventional RIS. While BD-RIS has been primarily analyzed assuming uni-polarized systems, modern wireless deployments are dual-polarized. To address this gap, this paper investigates the fundamental limits of dual-polarized BD-RIS-aided systems. We derive the scaling laws governing the performance of BD-RIS and the Pareto frontier of the trade-off between performance and circuit complexity enabled by BD-RIS. Theoretical results show that the group-connected RIS with group size 2 provides remarkable gains over conventional RIS in both Rayleigh and line-of-sight (LoS) channels, while maintaining a reduced circuit complexity.

翻译：超对角可重构智能表面（BD-RIS）是一类比传统RIS架构更灵活的可重构智能表面体系。尽管现有研究主要在单极化系统假设下分析BD-RIS，现代无线部署实际采用双极化架构。为填补这一研究空白，本文探究了双极化BD-RIS辅助系统的基本性能极限。我们推导了支配BD-RIS性能的缩放定律，以及BD-RIS在性能与电路复杂度之间权衡的帕累托前沿。理论结果表明：在瑞利信道和视距（LoS）信道中，分组规模为2的组连接RIS相较于传统RIS均能实现显著性能增益，同时保持较低的电路复杂度。