On the Universal Approximation Capability of Stacked Intelligent Metasurfaces

Abstract

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.