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）通过新型架构（如组连接型RIS）扩展了传统RIS，其散射矩阵不受限于对角形式。然而，如何在组连接型RIS中优化元素分组，在保持低复杂度电路的同时最大化性能，仍是未解难题。本研究针对基于信道统计的静态分组策略，提出并建模了BD-RIS。在公式化相应问题后，我们分别设计了单用户与多用户系统的分组方案。数值结果表明，分组优化可带来显著的性能提升，在高度相关信道中尤其突出，最高可实现60%的和速率增益。