Toward RF Interconnection Computing: A Coupling-Matrix Perspective on Physical Signal Transformation in Transmission-Line Networks

This paper develops RF interconnection computing as a deliberately narrow architectural concept: a transmission network that is already required to route coherent radio-frequency signals is co-designed to perform a restricted linear transformation during propagation, rather than being treated as an electrically neutral connection followed by a separate computing block. The proposal does not claim that electromagnetic waves performing matrix operations are new. Coupling-matrix filter synthesis, passive beamforming and sum–difference networks, computational metamaterials, programmable wave-based computers, and recently demonstrated microwave matrix processors already establish that interference and multiport networks can realize linear transformations [1]–[15]. The open question addressed here is instead whether an interconnection itself can be treated as an application-specific operator and evaluated jointly for routing and computation. To place that concept on a physically consistent basis, the paper first separates input and output port groups in a reciprocal multiport network and defines the forward operator as the transmission submatrix H = S_OI, rather than identifying an entire scattering matrix with an input–output computation. A general temporal coupled-mode formulation is then connected to an idealized single-frequency bipartite coupling model. In this special model, a real target contraction W can be mapped analytically to a normalized coupling block G, while the complete 2N-port scattering matrix remains reciprocal and lossless. Three externally selected three-channel operators—through transmission, common-mode extraction, and differential-subspace projection—are used as reproducible numerical examples. The calculations expose both the opportunity and the limitation of the concept: useful modal transformations can be embedded algebraically in a passive interconnection, but rejected modal energy is reflected rather than destroyed, bandwidth and loss are absent from the ideal model, and abstract coupling coefficients are not yet a manufacturable transmission-line layout. The paper therefore frames RF interconnection computing as a falsifiable co-design hypothesis and specifies the electromagnetic, circuit, and system-level evidence required before claims of reduced hardware, latency, or data movement would be justified.