Small-Scale Spatial-Temporal Correlation Modeling for Reconfigurable Intelligent Surfaces

The reconfigurable intelligent surface (RIS) is an emerging promising candidate technology for the sixth-generation wireless networks, where the element spacing is usually of sub-wavelength. Only limited knowledge, however, has been gained about the spatial-temporal correlation behavior among the elements in an RIS. In this paper, we investigate the joint spatial-temporal correlation models for an RIS in a wireless communication system. Joint small-scale spatial-temporal correlation functions are provided and analyzed for both ideal isotropic scattering and more practical non-isotropic scattering environments, where the latter is studied by employing an angular distribution derived from real-world millimeter-wave measurements. Analytical and simulation results demonstrate that the joint spatial-temporal correlation can be represented by a four-dimensional sinc function under isotropic scattering, while the correlation is generally stronger with more fluctuation for non-isotropic scattering with various motion directions.