On the Ergodic Capacity for SIM-Aided Holographic MIMO Communications

2025-12-26

AI Summary

This paper investigates the ergodic capacity lower bound of a holographic MIMO (HMIMO) system enhanced by stacked intelligent metasurfaces (SIM) under Rayleigh fading. Addressing practical finite-antenna and finite-SIM-element scenarios, we derive, for the first time, a tight closed-form capacity lower bound valid across the entire SNR range—overcoming the low-SNR inaccuracy limitation of existing approaches. Leveraging random matrix theory, Rayleigh channel modeling, and electromagnetic response modeling of SIMs, we rigorously derive the bound and analytically characterize its low-SNR asymptotic behavior. The proposed bound is highly tight over the full SNR regime and quantitatively reveals the scaling laws governing the interplay among antenna count, SIM element count, and system capacity. This provides a tractable, analytically optimizable theoretical foundation for co-design of HMIMO-SIM architectures.

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Abstract

We derive a novel closed-form lower bound on the ergodic capacity of holographic multiple-input multiple-output (HMIMO) systems enhanced by stacked intelligent metasurfaces (SIMs) under Rayleigh fading conditions. The proposed expression is valid for systems with a finite number of antennas and SIM elements and exhibits tightness throughout the whole signal-to-noise ratio (SNR) range. Furthermore, we conduct a comprehensive low-SNR analysis, offering meaningful observations on how key system parameters influence the capacity performance.

Problem

• Deriving a lower bound for ergodic capacity in SIM-aided HMIMO systems
• Validating expression for finite antennas and SIM elements across SNR
• Analyzing low-SNR impact of system parameters on capacity performance

Innovation

• Derived closed-form lower bound for HMIMO capacity
• Valid for finite antennas and SIM elements
• Conducted comprehensive low-SNR analysis