Abstract

This work analyzes the ergodic capacity behavior of reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output (MIMO) systems with a finite and arbitrary number of antennas and RIS elements under Nakagami-m fading conditions. By combining Hadamard’s determinant inequality with the Cauchy–Schwarz inequality, this work derives a dimensionally consistent closed-form upper bound on the ergodic capacity in terms of the Meijer G-function. Subsequently, it is demonstrated that at a high signal-to-noise ratio (SNR), a simplified expression for the capacity upper bound can be derived, enabling an analytical assessment of how the fading parameter influences the ergodic capacity. The study also explores the asymptotic behavior in the large-system regime, where the number of antennas or RIS elements tends to infinity. Monte Carlo (MC) simulations confirm the accuracy of the proposed bound and scaling laws.

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