面向通信与感知的几何驱动二进制可重构智能表面（RIS）配置优化
Geometry-Informed Optimization of Binary RIS Configurations for Communication and Sensing
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中文总结 AI 辅助
本研究针对1比特RIS的离散配置优化问题，通过几何表征推导全局最优配置的结构特征，开发适配MIMO和SISO系统的高效算法，并将其拓展至ISAC场景，提供统一优化框架。
中文摘要 AI 辅助
实用可重构智能表面（RIS）通常仅支持少量相位状态，其配置本质上是离散的。对于具有 $N$ 个单元的1比特RIS，直接优化需要在 $2^N$ 种二进制配置中搜索。本研究表明，该指数级配置空间并非无结构：通过将1比特RIS优化重新表述为与信道相关向量的符号和范数最大化，我们证明每个全局最优配置必须由其在公共方向上投影的符号诱导。这种几何表征限制了可能包含全局最优的配置类别，并根据信号空间维度产生不同的算法结果。对于通用多输入多输出（MIMO）系统，我们开发了一种几何驱动采样方法，仅评估结构上可接受的配置；对于单输入单输出（SISO）系统，相同原理简化为二维角度划分，可表征完整候选集并通过多项式时间枚举恢复全局最优，仅需在 $2^N$ 种配置中评估至多 $N+1$ 种。最后，我们将相同二进制优化原理应用于集成感知与通信（ISAC）场景，其中通信增强与目标定位可归结为同一底层几何问题。因此，所提框架为在通信与感知功能中利用实用1比特RIS配置的结构提供了统一方法。
英文摘要
Practical Reconfigurable Intelligent Surfaces (RISs) often support only a small number of phase states, making their configuration inherently discrete. For a 1-bit RIS with $N$ elements, direct optimization requires searching among $2^N$ binary configurations. This work shows that this exponential configuration space is not unstructured. By reformulating 1-bit RIS optimization as the maximization of the norm of a signed sum of channel-dependent vectors, we prove that every globally optimal configuration must be induced by the signs of their projections onto a common direction. This geometric characterization restricts the class of configurations that can contain global optima and leads to different algorithmic consequences depending on the signal-space dimension. For general Multiple-Input-Multiple-Output (MIMO) systems, we develop a geometry-informed sampling method that evaluates only structurally admissible configurations. For Single-Input-Single-Output (SISO) systems, the same principle reduces to a two-dimensional angular partition, allowing the complete candidate set to be characterized and the global optimum to be recovered through polynomial-time enumeration, by evaluating at most $N+1$ out of the $2^N$ configurations. Finally, we apply the same binary optimization principle to an Integrated Sensing and Communication (ISAC) scenario, where communication enhancement and target localization reduce to the same underlying geometric problem. The proposed framework therefore provides a unified approach for exploiting the structure of practical 1-bit RIS configurations across communication and sensing functionalities.
