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Ergodic Mutual Information and Outage Probability for SIM-Assisted Holographic MIMO Communications

Anastasios Papazafeiropoulos, Pandelis Kourtessis, Dimitra I. Kaklamani, Iakovos S. Venieris

TL;DR

This work derives the ergodic mutual information and outage probability for SIM-assisted holographic MIMO using large-system random matrix theory under statistical CSI. It develops a closed-form EMI approximation $\bar{C}(\rho)$, proves a CLT for MI fluctuations, and provides a Gaussian-based outage approximation $P_{\text{out}}(R)$. A projected gradient descent method jointly optimizes transmitter and receiver SIM phase shifts, achieving faster convergence than alternating optimization. The analysis also yields a finite-SNR DMT, illustrating how SIM size and layering improve diversity and multiplexing, with numerical results confirming the theoretical predictions and highlighting practical gains over conventional RIS setups.

Abstract

Stacked intelligent metasurface (SIM) is a promising enabler for next-generation high-capacity networks that exhibit better performance compared to its single-layer counterpart by means of just wave propagation. However, the study of ergodic mutual information (EMI) and outage probability for SIM-assisted multiple-input-multiple-output (MIMO) systems is not available in the literature. To this end, we obtain the distribution of the MI by using large random matrix theory (RMT) tools. Next, we derive a tight closed-form expression for the outage probability based on statistical channel state information (CSI). Moreover, we apply the gradient descent method for the minimization of the outage probability. Simulation results verify the analytical results and provide fundamental insights such as the performance enhancements compared to conventional MIMO systems and the single-layer counterpart. Notably the proposed optimization algorithm is faster than the alternating optimization (AO) benchmark by saving significant overhead.

Ergodic Mutual Information and Outage Probability for SIM-Assisted Holographic MIMO Communications

TL;DR

This work derives the ergodic mutual information and outage probability for SIM-assisted holographic MIMO using large-system random matrix theory under statistical CSI. It develops a closed-form EMI approximation , proves a CLT for MI fluctuations, and provides a Gaussian-based outage approximation . A projected gradient descent method jointly optimizes transmitter and receiver SIM phase shifts, achieving faster convergence than alternating optimization. The analysis also yields a finite-SNR DMT, illustrating how SIM size and layering improve diversity and multiplexing, with numerical results confirming the theoretical predictions and highlighting practical gains over conventional RIS setups.

Abstract

Stacked intelligent metasurface (SIM) is a promising enabler for next-generation high-capacity networks that exhibit better performance compared to its single-layer counterpart by means of just wave propagation. However, the study of ergodic mutual information (EMI) and outage probability for SIM-assisted multiple-input-multiple-output (MIMO) systems is not available in the literature. To this end, we obtain the distribution of the MI by using large random matrix theory (RMT) tools. Next, we derive a tight closed-form expression for the outage probability based on statistical channel state information (CSI). Moreover, we apply the gradient descent method for the minimization of the outage probability. Simulation results verify the analytical results and provide fundamental insights such as the performance enhancements compared to conventional MIMO systems and the single-layer counterpart. Notably the proposed optimization algorithm is faster than the alternating optimization (AO) benchmark by saving significant overhead.
Paper Structure (22 sections, 9 theorems, 73 equations, 9 figures, 1 algorithm)

This paper contains 22 sections, 9 theorems, 73 equations, 9 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Architecture and Modeling of SIM-Based HMIMO
  3. System Model
  4. Channel Model
  5. Comparison between SIM and RIS in Holographic MIMO
  6. EMI Analysis Using Large RMT
  7. Mutual Information
  8. The CLT for the MI
  9. Special Case
  10. Outage Analysis and Joint SIM Optimization
  11. Problem Formulation and Optimization
  12. Proposed Algorithm
  13. Derivation of Gradients
  14. Finite-SNR Trade-offs in SIM-Assisted Systems
  15. Key Factors Driving SIM Superiority over Single-Layer RIS
  16. ...and 7 more sections

Key Result

Theorem 1

Given the Assumptions as1-as3, the average throughput $\mathbb{E}\{C(\rho)\}$ obeys to In our case, where $\tilde{{\mathbf{G}}}$ is Gaussian, it holds that where $\bar{C}(\rho)$ is given by Note that $(\delta(\rho),e(\rho))$ forms the unique positive solution of the following system of equations where

Figures (9)

  • Figure 1: A SIM-assisted HMIMO system.
  • Figure 2: EMI with respect to the number of SIM layers of the receiver SIM.
  • Figure 3: EMI with respect to the number of metasurface elements of the transmitter SIM.
  • Figure 4: EMI with respect to the number of iterations.
  • Figure 5: Outage probability with respect to the transmit power.
  • ...and 4 more figures

Theorems & Definitions (21)

  • Remark 1
  • Theorem 1: Couillet2011a
  • Remark 2
  • Theorem 2
  • proof
  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Theorem 3
  • ...and 11 more