  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.
