发表机构
Università di Bologna; National Laboratory of Wireless Communications (WiLab), CNIT（博洛尼亚大学; CNIT无线通信国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对堆叠智能超表面（SIM）提出通用逼近理论，给出其作为复线性变换通用逼近器的充要闭式条件，填补了该领域理论空白。
AI 中文摘要
波域处理是一种新兴范式，其中信号处理操作部分从数字域转移到电磁（EM）域，以降低下一代无线系统的复杂度、能耗和延迟。堆叠智能超表面（SIM）是实现波操控的一种有前景的技术。尽管大量研究针对特定任务对SIM进行了数值设计，但尚无理论结果确定给定的SIM架构能否逼近任意的复线性映射，即其是否具备通用逼近能力。为解决此问题，本文建立了基本定理，给出了给定SIM架构作为复线性变换通用逼近器的充要闭式条件。
英文摘要
Wave-domain processing is an emerging paradigm in which signal-processing operations are partially shifted from the digital domain to the electromagnetic (EM) domain to reduce complexity, energy consumption, and latency in next-generation wireless systems. Stacked intelligent metasurfaces (SIMs) are a promising technology for wave manipulation. Although numerous studies have addressed the numerical design of SIMs for specific tasks, no theoretical results have yet established whether a prescribed SIM architecture can approximate an arbitrary complex linear mapping, i.e., whether it possesses a universal approximation capability. To address this question, this paper establishes fundamental theorems that provide necessary and sufficient closed-form conditions under which a given SIM architecture can serve as a universal approximator of complex linear transformations.
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