Small-Scale Spatial-Temporal Correlation and Degrees of Freedom for Reconfigurable Intelligent Surfaces

TL;DR

This paper investigates the spatial-temporal correlation properties of reconfigurable intelligent surfaces (RIS) in wireless systems, deriving a model and analyzing the degrees of freedom to improve system performance evaluation.

Contribution

It introduces a joint spatial-temporal correlation model for RIS elements and provides an analytical expression for the spatial degrees of freedom considering realistic element spacing.

Findings

Derived a four-dimensional sinc function-based correlation model.

Revisited the spatial degrees of freedom for RIS with practical element spacing.

Provided analytical tools for accurate system performance assessment.

Abstract

The reconfigurable intelligent surface (RIS) is an emerging promising candidate technology for future 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 for an RIS-enabled wireless communication system. Specifically, a joint small-scale spatial-temporal correlation model is derived under isotropic scattering, which can be represented by a four-dimensional sinc function. Furthermore, based upon the spatial-only correlation at a certain time instant, an essential RIS property -- the spatial degrees of freedom (DoF) -- is revisited, and an analytical expression is propounded to characterize the spatial DoF for RISs with realistic hence non-infinitesimal element spacing and finite aperture sizes. The results are vital to the accurate evaluation of various system performance metrics.