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A Generalized Pointing Error Model for FSO Links with Fixed-Wing UAVs for 6G: Analysis and Trajectory Optimization

Hyung-Joo Moon, Chan-Byoung Chae, Kai-Kit Wong, Mohamed-Slim Alouini

TL;DR

This work introduces a generalized pointing-error model for fixed-wing UAVs in FSO links by incorporating 3D jitter across roll, pitch, and yaw axes, deriving a Hoyt distribution for the pointing-angle error with parameters tied to UAV geometry and posture. It integrates this model into an energy-efficiency trajectory optimization framework, solving a nonconvex problem via successive convex approximation and the Dinkelbach method to maximize total ergodic capacity per unit energy under speed, acceleration, and elevation constraints. The approach is validated numerically, showing that UAV posture and 3D jitter significantly influence the optimal trajectory and that the 3D jitter-aware design can yield up to 11.8% higher energy efficiency compared with conventional Gaussian-pointing-error models. The results highlight the importance of UAV-specific jitter modeling for accurate performance evaluation and optimization in 6G NTN FSO backhaul networks.

Abstract

Free-space optical (FSO) communication is a promising solution to support wireless backhaul links in emerging 6G non-terrestrial networks. At the link level, pointing errors in FSO links can significantly impact capacity, making accurate modeling of these errors essential for both assessing and enhancing communication performance. In this paper, we introduce a novel model for FSO pointing errors in unmanned aerial vehicles (UAVs) that incorporates three-dimensional (3D) jitter, including roll, pitch, and yaw angle jittering. We derive a probability density function for the pointing error angle based on the relative position and posture of the UAV to the ground station. This model is then integrated into a trajectory optimization problem designed to maximize energy efficiency while meeting constraints on speed, acceleration, and elevation angle. Our proposed optimization method significantly improves energy efficiency by adjusting the UAV's flight trajectory to minimize exposure to directions highly affected by jitter. The simulation results emphasize the importance of using UAV-specific 3D jitter models in achieving accurate performance measurements and effective system optimization in FSO communication networks. Utilizing our generalized model, the optimized trajectories achieve up to 11.8 percent higher energy efficiency compared to those derived from conventional Gaussian pointing error models.

A Generalized Pointing Error Model for FSO Links with Fixed-Wing UAVs for 6G: Analysis and Trajectory Optimization

TL;DR

This work introduces a generalized pointing-error model for fixed-wing UAVs in FSO links by incorporating 3D jitter across roll, pitch, and yaw axes, deriving a Hoyt distribution for the pointing-angle error with parameters tied to UAV geometry and posture. It integrates this model into an energy-efficiency trajectory optimization framework, solving a nonconvex problem via successive convex approximation and the Dinkelbach method to maximize total ergodic capacity per unit energy under speed, acceleration, and elevation constraints. The approach is validated numerically, showing that UAV posture and 3D jitter significantly influence the optimal trajectory and that the 3D jitter-aware design can yield up to 11.8% higher energy efficiency compared with conventional Gaussian-pointing-error models. The results highlight the importance of UAV-specific jitter modeling for accurate performance evaluation and optimization in 6G NTN FSO backhaul networks.

Abstract

Free-space optical (FSO) communication is a promising solution to support wireless backhaul links in emerging 6G non-terrestrial networks. At the link level, pointing errors in FSO links can significantly impact capacity, making accurate modeling of these errors essential for both assessing and enhancing communication performance. In this paper, we introduce a novel model for FSO pointing errors in unmanned aerial vehicles (UAVs) that incorporates three-dimensional (3D) jitter, including roll, pitch, and yaw angle jittering. We derive a probability density function for the pointing error angle based on the relative position and posture of the UAV to the ground station. This model is then integrated into a trajectory optimization problem designed to maximize energy efficiency while meeting constraints on speed, acceleration, and elevation angle. Our proposed optimization method significantly improves energy efficiency by adjusting the UAV's flight trajectory to minimize exposure to directions highly affected by jitter. The simulation results emphasize the importance of using UAV-specific 3D jitter models in achieving accurate performance measurements and effective system optimization in FSO communication networks. Utilizing our generalized model, the optimized trajectories achieve up to 11.8 percent higher energy efficiency compared to those derived from conventional Gaussian pointing error models.
Paper Structure (26 sections, 4 theorems, 61 equations, 12 figures, 3 tables, 1 algorithm)

This paper contains 26 sections, 4 theorems, 61 equations, 12 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. FSO and Mixed FSO/RF Links
  4. Pointing Error
  5. UAV Trajectory Optimization
  6. Contributions and Paper Organization
  7. System Model
  8. Discrete-Time Coordinate System
  9. Capacity of an FSO Link
  10. Flight Power Consumption Model
  11. Pointing Error Analysis
  12. 3D Jittering Model of Fixed-wing Aircraft
  13. Distribution of the Pointing Error Angle
  14. Trajectory Optimization for Mission Flight
  15. Problem Formulation
  16. ...and 11 more sections

Key Result

Theorem 1

The distribution of $\theta_p$ follows the Hoyt distribution as where $q=\sqrt{\lambda_1/\lambda_2}$ and $\Omega=\lambda_1+\lambda_2$2018ICC. The symbols $\lambda_1$, $\lambda_2$ ($\lambda_1\geq\lambda_2$) are the nonzero eigenvalues of $\bold{\Sigma}^{1/2}\bold{A}\bold{\Sigma}^{1/2}$, where $\bold{A}$ is defined as with the identity matrix $\bold{I}$, and $z={({\hat{\bold{u}}[k]}^T{\hat{\bold{u

Figures (12)

  • Figure 1: GS-centered coordinate system.
  • Figure 2: 3D jittering of the UAV in the UAV-centered coordinate system.
  • Figure 3: Probability density function of the pointing error angle.
  • Figure 4: The energy-efficient trajectories for the mission where the initial and final points are different (moving mission). We vary the parameter values by (a) $\sigma_\text{div} = 1.5$ mrad, (b) $\sigma_\text{div} = 2.0$ mrad, and (c) $\sigma_\text{div} = 2.5$ mrad to compare the impact of the pointing error on the trajectory.
  • Figure 5: The energy-efficient trajectories for the mission where the initial and final points are the same (hovering mission). The parameter is set to $\sigma_\text{div} = 1.5$ mrad, and each of the subfigures varies by the dominant jittering direction.
  • ...and 7 more figures

Theorems & Definitions (4)

  • Theorem 1
  • Lemma 1
  • Theorem 2
  • Lemma 2