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Optical Intelligent Reflecting Surfaces Empowering Non-Terrestrial Communications

Shunyuan Shang, Emna Zedini, Abla Kammoun, Mohamed-Slim Alouini

TL;DR

The paper tackles urban LOS challenges in optical non-terrestrial networks by proposing a three-hop system that couples a High-Altitude Platform (HAP) with an Optical Intelligent Reflecting Surface (OIRS) to create a robust OGS→HAP→OIRS→User link. It develops a comprehensive channel model: attenuative Beer-Lambert losses, Gamma-Gamma atmospheric turbulence, and a 3D Hoyt-based Geometric Misalignment Loss, for both the OGS→HAP and HAP→User hops, and derives end-to-end SNR statistics under fixed-gain AF relaying. Closed-form and asymptotic expressions for outage probability, BER, and ergodic capacity are obtained using advanced mathematical tools (Meijer-G and Fox-H functions) along with practical approximations, enabling diversity-order analysis in the high-SNR regime. The results offer practical insights into OIRS deployment, beam alignment tolerances, and AF vs DF relay trade-offs, demonstrating that AF can approach DF performance with significantly reduced complexity and power—an appealing option for resource-constrained aerial platforms in urban environments.keywords": ["Optical Intelligent Reflecting Surface (OIRS)", "High-Altitude Platform (HAP)", "Gamma-Gamma turbulence", "Hoyt-based Geometric Misalignment Loss (GML)", "Fixed-gain AF relay", "Meijer-G", "Fox-H function", "End-to-end outage probability", "Ergodic capacity"]

Abstract

In this work, we propose an innovative system that combines high-altitude platforms (HAPs) and optical intelligent reflecting surfaces (OIRS) to address line-of-sight (LOS) challenges in urban environments. Our three-hops system setup includes an optical ground station (OGS), a HAP, an OIRS, and a user. Signals are transmitted from the OGS to the HAP via a free space optical (FSO) link, with the HAP functioning as an amplify-and-forward (AF) relay that redirects signals through an OIRS, effectively bypassing obstacles such as buildings and trees to improve connectivity for non-line-of-sight (NLOS) User. For the OIRS link, we address key channel impairments, including atmospheric turbulence, pointing errors, attenuation, and geometric and misalignment losses (GML). An accurate approximation for the Hoyt-distributed GML model is derived, enabling us to obtain closed-form expressions for outage probability (OP) and various performance metrics, such as average bit error rate (BER) and channel capacity of the OIRS-assisted FSO link. Furthermore, we analyze the end-to-end signal-to-noise ratio (SNR) and derive closed-form expressions for OP and performance metrics. Asymptotic expressions are provided for high-SNR regimes, allowing the system's diversity order to be calculated.

Optical Intelligent Reflecting Surfaces Empowering Non-Terrestrial Communications

TL;DR

The paper tackles urban LOS challenges in optical non-terrestrial networks by proposing a three-hop system that couples a High-Altitude Platform (HAP) with an Optical Intelligent Reflecting Surface (OIRS) to create a robust OGS→HAP→OIRS→User link. It develops a comprehensive channel model: attenuative Beer-Lambert losses, Gamma-Gamma atmospheric turbulence, and a 3D Hoyt-based Geometric Misalignment Loss, for both the OGS→HAP and HAP→User hops, and derives end-to-end SNR statistics under fixed-gain AF relaying. Closed-form and asymptotic expressions for outage probability, BER, and ergodic capacity are obtained using advanced mathematical tools (Meijer-G and Fox-H functions) along with practical approximations, enabling diversity-order analysis in the high-SNR regime. The results offer practical insights into OIRS deployment, beam alignment tolerances, and AF vs DF relay trade-offs, demonstrating that AF can approach DF performance with significantly reduced complexity and power—an appealing option for resource-constrained aerial platforms in urban environments.keywords": ["Optical Intelligent Reflecting Surface (OIRS)", "High-Altitude Platform (HAP)", "Gamma-Gamma turbulence", "Hoyt-based Geometric Misalignment Loss (GML)", "Fixed-gain AF relay", "Meijer-G", "Fox-H function", "End-to-end outage probability", "Ergodic capacity"]

Abstract

In this work, we propose an innovative system that combines high-altitude platforms (HAPs) and optical intelligent reflecting surfaces (OIRS) to address line-of-sight (LOS) challenges in urban environments. Our three-hops system setup includes an optical ground station (OGS), a HAP, an OIRS, and a user. Signals are transmitted from the OGS to the HAP via a free space optical (FSO) link, with the HAP functioning as an amplify-and-forward (AF) relay that redirects signals through an OIRS, effectively bypassing obstacles such as buildings and trees to improve connectivity for non-line-of-sight (NLOS) User. For the OIRS link, we address key channel impairments, including atmospheric turbulence, pointing errors, attenuation, and geometric and misalignment losses (GML). An accurate approximation for the Hoyt-distributed GML model is derived, enabling us to obtain closed-form expressions for outage probability (OP) and various performance metrics, such as average bit error rate (BER) and channel capacity of the OIRS-assisted FSO link. Furthermore, we analyze the end-to-end signal-to-noise ratio (SNR) and derive closed-form expressions for OP and performance metrics. Asymptotic expressions are provided for high-SNR regimes, allowing the system's diversity order to be calculated.

Paper Structure

This paper contains 29 sections, 10 theorems, 63 equations, 13 figures, 3 tables.

Table of Contents

  1. Introduction
  2. System models for two single links
  3. System model from OGS to HAP
  4. Channel Model
  5. SNR Statistics from OGS to HAP
  6. System model from HAP to User
  7. Channel Model
  8. SNR Statistics from HAP to User
  9. Performance Analysis
  10. END-TO-END SYSTEM PERFORMANCE
  11. End-to-End SNR Statistics
  12. Performance Analysis
  13. Outage Probability
  14. Average Bit-Error Rate
  15. Ergodic Capacity
  16. ...and 14 more sections

Key Result

Theorem 1

The PDF of $h_{g2}$ can be approximated as where $\mathcal{N} = \left\{ \sum_{k=0}^{N_k} \frac{2 q_g \Gamma(1 + 2k)}{k! \Gamma(1 + k)(1 + q_g^2)} \left[ \frac{(1 - q_g^2)\varpi}{2(1 + q_g^2)\varpi} \right]^{2k} \right\}^{-1}$.

Figures (13)

  • Figure 1: HAP-Ground Integrated Communication System with Optical Intelligent Reflecting Surfaces.
  • Figure 2: Precise Positioning of the Integrated HAP-Ground Communication System with OIRS.
  • Figure 3: Schematic diagram of the OIRS System.
  • Figure 4: Comparison plot of the exact and approximate PDF of GML under varying fluctuation conditions.
  • Figure 5: Convergence behavior of the truncated series approximation for the PDF of GML under different incident angles $\theta_i$.
  • ...and 8 more figures

Theorems & Definitions (21)

  • Theorem 1
  • proof
  • Corollary 1.1
  • proof
  • Theorem 2
  • proof
  • Corollary 2.1
  • proof
  • Corollary 2.2
  • proof
  • ...and 11 more