AI 中文总结
研究互易群连接 BD-RIS 辅助 MIMO 系统和速率最大化问题，基于可行空间为黎曼流形的结果，扩展为乘积流形，提出群扩展框架，逐块执行操作并保持组间耦合，涵盖特殊架构，实现性能与复杂性灵活折衷。
AI 中文摘要
可重构智能表面（RIS）通过可配置多端口散射网络为工程无线传播信道提供了灵活手段。在其架构中，群连接非对角 RIS（BD-RIS）通过将表面划分为相互连接的组，在散射灵活性和硬件复杂性之间实现了实际折衷。在互易和无损实现中，每个组散射块必须是对称且酉的。本文研究了在这种结构约束下，互易群连接 BD-RIS 辅助的多输入多输出（MIMO）系统的和速率最大化问题。具体而言，基于最近的一个结果，将由对称和酉约束确定的可行空间表征为黎曼流形，并将其扩展为对称酉块流形的乘积流形，从而将流形相位优化方法扩展到群连接设置中。因此，所提出的群扩展框架逐块执行切空间投影和高木收缩，同时通过公共 MIMO 等效信道保持所有组之间的耦合。该公式自然地将单连接和全连接互易 BD-RIS 架构作为特殊情况包含在内，并通过组大小实现了灵活的性能-复杂性折衷。
英文摘要
Reconfigurable intelligent surfaces (RISs) provide a flexible means of engineering wireless propagation channels through configurable multiport scattering networks. Among their architectures, group-connected beyond-diagonal RISs (BD-RISs) offer a practical tradeoff between scattering flexibility and hardware complexity by partitioning the surface into inter-connected groups. In reciprocal and lossless implementations, each group scattering block must be symmetric and unitary. In this paper, we investigate sum-rate maximization for reciprocal group-connected BD-RIS-assisted multiple-input multiple-output (MIMO) systems under such structural constraints. In particular, we build on a recent result where the feasible space determined by the symmetry and unitary constraints was characterized as a Riemannian manifold, extending it into a product manifold of symmetric-unitary block manifolds, thus expanding the approach to manifold phase optimization in the group-connected setting. As a consequence, the proposed group-extended framework performs tangent-space projections and Takagi retractions block-wise, while preserving the coupling among all groups through the common MIMO equivalent channel. The formulation naturally includes single-connected and fully connected reciprocal BD-RIS architectures as special cases and enables a flexible performance-complexity tradeoff through the group size.
