一种用于BD-RIS辅助多用户波束成形的低维黎曼交替优化算法
A Low-Dimensional Riemannian Alternating Optimization Algorithm for BD-RIS-Assisted Multiuser Beamforming
- Beijing University of Posts and Telecommunications（北京邮电大学）
- Imperial College London（伦敦帝国理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对BD-RIS辅助多用户波束成形，提出低维黎曼交替优化算法，降低计算复杂度，性能与SOTA相当。
AI中文摘要：
本文研究了一种由全连接超对角可重构智能表面（BD-RIS）辅助的多用户下行链路系统中的联合有源和无源波束成形问题。由于可调组件的数量随RIS元件数量的平方增长，直接优化全散射矩阵的计算成本越来越高。为了解决这一挑战，我们首先推导出一个等效的低维公式，用列数等于用户数的变量替代全散射矩阵。我们进一步在等效可行集的稠密子集上建立了一个光滑流形结构，并在此基础上开发了一种低维黎曼交替优化（LD-RAO）算法，其中无源变量在每次迭代中使用单步黎曼梯度上升更新。在温和假设下建立了LD-RAO的收敛性。数值结果表明，所提出的算法在显著减少CPU时间的情况下，实现了与现有最先进（SOTA）全维方法相同的性能，特别是在大规模BD-RIS场景中。
英文摘要：
This paper investigates joint active and passive beamforming for a multiuser downlink system assisted by a fully-connected beyond-diagonal reconfigurable intelligent surface (BD-RIS). Since the number of tunable components grows quadratically with the number of RIS elements, directly optimizing the full scattering matrix becomes increasingly computationally expensive. To address this challenge, we first derive an equivalent low-dimensional formulation that replaces the full scattering matrix with a variable whose number of columns equals the number of users. We further establish a smooth manifold structure on a dense subset of the equivalent feasible set, based on which we develop a low-dimensional Riemannian alternating optimization (LD-RAO) algorithm, where the passive variable is updated using a single Riemannian gradient ascent step at each iteration. The convergence of LD-RAO is established under mild assumptions. Numerical results demonstrate that the proposed algorithm achieves the same performance as the existing state-of-the-art (SOTA) full-dimensional methods with significantly less CPU time, particularly for large-scale BD-RIS.
