Static Grouping Strategy Design for beyond Diagonal Reconfigurable Intelligent Surfaces

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.