Beyond diagonal reconfigurable intelligent surface (BD-RIS) extends conventional RIS through novel architectures, such as group-connected RIS, with scattering matrix not restricted to being diagonal. However, it remains unexplored how to optimally group the elements in group-connected RISs to maximize the performance while maintaining a low-complexity circuit. In this study, we propose and model BD-RIS with a static grouping strategy optimized based on the channel statistics. After formulating the corresponding problems, we design the grouping in single- and multi-user systems. Numerical results reveal the benefits of grouping optimization, i.e., up to 60% sum rate improvement, especially in highly correlated channels.

翻译：超越对角可重构智能表面（BD-RIS）通过新颖架构（如分组连接型RIS）扩展了传统RIS，其散射矩阵不局限于对角形式。然而，如何在分组连接型RIS中最优地分组元件以最大化性能并保持低复杂度电路仍待探索。本研究提出并建模了基于信道统计优化的静态分组策略BD-RIS。在制定相应问题后，我们设计了单用户与多用户系统中的分组方案。数值结果揭示了分组优化的优势，即在高度相关信道中可实现高达60%的和速率提升。