Physically Consistent Modeling of Dispersive Time-Modulated Reconfigurable Intelligent Surfaces for Wideband OFDM

Abstract

The elements of a reconfigurable intelligent surface (RIS) are commonly modeled either as frequency-selective time-invariant reflectors or as instantaneous time-varying reflection coefficients. In practice, however, time-modulated metasurfaces exhibit both frequency selectivity and periodic time variation. We develop a physically consistent linear periodically time-varying (LPTV) model that jointly captures these effects and characterizes their impact on wideband orthogonal frequency-division multiplexing (OFDM) communications. From a canonical equivalent circuit of a generic RIS element, we derive a single-resonance model whose physically meaningful parameters determine both the frequency-selective reflection coefficient and the effective impulse-response duration, i.e., the finite memory of the element. The periodically switched dispersive responses are then represented through harmonic transfer functions, leading to a closed-form per-subcarrier OFDM input-output relation. The resulting coupling is generally non-diagonal: each received subcarrier collects contributions from multiple transmitted subcarriers through the RIS harmonics, each weighted by the element response at the corresponding absolute input frequency. We further derive a generalized cyclic-prefix (CP) condition requiring the guard interval to accommodate both the propagation-channel delay spread and the RIS memory. Under this condition, intersymbol interference and out-of-grid spectral leakage are suppressed, while deterministic on-grid harmonic coupling remains. Full-wave simulations of an OpenRIS unit cell designed for a 5G NR channel validate the proposed resonant model and reveal appreciable in-band dispersion despite nearly ideal binary phase switching. Simulations over 3GPP tapped-delay-line (TDL) channels confirm the generalized CP condition and show its relevance for high-quality-factor RIS elements.