Static Grouping Strategy Design for Beyond Diagonal Reconfigurable Intelligent Surfaces
Matteo Nerini, Shanpu Shen, Bruno Clerckx
TL;DR
This work addresses BD-RIS with group-connected architectures by introducing a static grouping strategy $\pi$ designed offline from channel statistics, paired with online reconfiguration of the intra-group scattering $\bar{\boldsymbol{\Theta}}$ per channel realization. The authors formulate bi-level optimization problems for single- and multi-user scenarios, derive tractable surrogates, and propose Alg. 1-based local-search methods to find $\pi$ while leveraging closed-form or Ner22-based updates for $\bar{\boldsymbol{\Theta}}$. The key contributions include a complete BD-RIS model with static grouping, offline grouping optimization, online block-wise Theta optimization, and demonstrated gains up to $60\%$ in sum rate for highly correlated channels, plus notable power gains, all achieved without increasing circuit complexity. The results suggest that careful static grouping can substantially narrow the performance gap between group-connected and fully-connected BD-RIS while maintaining a low-complexity hardware design, making it pragmatic for real deployments in correlated-rich channels.
Abstract
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.