超大尺寸非对角可重构智能表面：面向近场通信的低秩模态优化
Extremely Large Beyond-Diagonal RIS: Low-Rank Modal Optimization for Near-Field Communications
中文总结 AI 辅助
本文针对超大尺寸非对角可重构智能表面（XL-BD-RIS），利用近场几何特性提出低秩模态优化方法，仅需少量可重构条目即可达到全连接性能，大幅降低了计算与硬件负担。
中文摘要 AI 辅助
非对角可重构智能表面（BD-RIS）在全连接时性能最优，但代价是优化和硬件负担随单元数呈二次增长，每次迭代的计算复杂度呈三次增长。超大尺寸表面会使这种负担变得难以承受，同时其巨大的孔径会将基站和用户都置于辐射近场中，而远场设计工具在此场景下失效。本文提出超大尺寸BD-RIS（XL-BD-RIS）概念，并表明近场几何特性恰好能让全连接性能在大规模场景下变得经济可行。通过用自由空间格林函数建模级联信道，我们证明孔径场位于由终端位置的球面波响应张成的低维子空间中，并仅利用定位信息在该子空间上设计了一个紧凑的酉模态矩阵，该矩阵可通过几何确定的可重构条目数达到全连接最优，且该条目数与面板尺寸无关。加权最小均方误差（weighted-MMSE）黎曼算法以与面板尺寸无关的代价优化波束成形器和模态矩阵，且收敛具有单调性。数值结果表明，一个24×24单元的面板仅需约200个条目即可达到全连接最优，而不是30万个条目；不匹配的DFT波束空间因球面波前的波束扩展导致条目代价增加60倍，而传统分块架构在任何匹配条目预算下的速率都严格更低。
英文摘要
Beyond-diagonal reconfigurable intelligent surfaces (BD-RIS) achieve their best performance when fully connected, at the price of an optimization and hardware burden that grows quadratically, and per iteration cubically, with the number of elements. Extremely large surfaces make this burden prohibitive, while their sheer aperture places both the base station and the users in the radiative near field, where far-field design tools break down. This paper introduces the extremely large BD-RIS (XL-BD-RIS) concept and shows that near-field geometry is precisely what makes fully connected performance affordable at scale. Modeling the cascade with the free-space Green function, we prove that the aperture fields live in a low-dimensional subspace spanned by the spherical-wave responses of the terminal positions, and we design a compact unitary modal matrix on this subspace, built from localization information alone, that provably attains the fully connected optimum with a number of reconfigurable entries set by the geometry and independent of the panel size. A weighted-MMSE Riemannian algorithm optimizes the beamformers and the modal matrix with monotone convergence at panel-size-independent cost. Numerical results show that a $24\times24$-element panel reaches the fully connected optimum with about two hundred entries instead of three hundred thousand. A mismatched DFT beamspace pays a sixty-fold entry penalty rooted in the beam spread of spherical wavefronts, while the classical block-wise architecture delivers strictly lower rates at any matched entry budget.
