SCALING EFFECTS ON SPATIAL DEGREES OF FREEDOM AND CHANNEL HARDENING IN RIS‑ASSISTED WIRELESS LINKS

Abstract

This study addresses how the spatial configuration and statistical environment of reconfigurable intelligent surfaces affect the capacity and reliability of wireless channels. A theoretical and simulation-based framework is established, constructing the RIS correlation matrix using a sinc function over a two-dimensional passive element lattice, and evaluating Rayleigh, Rician, and Nakagami fading models with large-scale Monte Carlo analysis. Key system metrics, including eigenvalue spectra, effective spatial degrees of freedom, SNR, and capacity, are quantified for varying array sizes and element spacings. Results reveal that expanding the RIS array from 16×16 to 32×32 elements increases the mean SNR from 176 dB to 188 dB and mean capacity from 58.5 to 62.5 bps/Hz, while changes in element spacing and fading models exert minimal influence. The spatial degrees of freedom scale rapidly with array size, and the capacity distribution exhibits pronounced channel hardening across all scenarios. These findings confirm that array aperture governs the achievable multiplexing and reliability gains, supporting the use of large-scale RIS for robust, high-capacity wireless communication.