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 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 via employing an angular distribution derived from real-world millimeter-wave measurements. Furthermore, for the special case of spatial-only correlation under isotropic scattering, an analytical expression is proposed to characterize the spatial degrees of freedom (DoF) for RISs with finite element spacing and aperture sizes in practice. Analytical and numerical 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 and significantly fewer dominant eigenvalues hence smaller DoF for non-isotropic scattering.