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Analysis of SINR Coverage in LEO Satellite Networks through Spatial Network Calculus

Yuting Tang, Yufan He, Yi Zhong, Xijun Wang, Tony Q. S. Quek, Howard H. Yang

TL;DR

A new analytical framework, developed based on the spatial network calculus, for performance assessment of Low Earth Orbit (LEO) satellite networks, is introduced, which model the satellites'spatial positions as a strong ball-regulated point process on the sphere.

Abstract

We introduce a new analytical framework, developed based on the spatial network calculus, for performance assessment of Low Earth Orbit (LEO) satellite networks. Specifically, we model the satellites' spatial positions as a strong ball-regulated point process on the sphere. Under this model, proximal points in space exhibit a locally repulsive property, reflecting the fact that intersatellite links are protected by a safety distance and would not be arbitrarily close. Subsequently, we derive analytical lower bounds on the conditional coverage probabilities under Nakagami-$m$ and Rayleigh fading, respectively. These expressions have a low computational complexity, enabling efficient numerical evaluations. We validate the effectiveness of our theoretical model by contrasting the coverage probability obtained from our analysis with that estimated from a Starlink constellation. The results show that our analysis provides a tight lower bound on the actual value and, surprisingly, matches the empirical simulations almost perfectly with a 1 dB shift. This demonstrates our framework as an appropriate theoretical model for LEO satellite networks.

Analysis of SINR Coverage in LEO Satellite Networks through Spatial Network Calculus

TL;DR

A new analytical framework, developed based on the spatial network calculus, for performance assessment of Low Earth Orbit (LEO) satellite networks, is introduced, which model the satellites'spatial positions as a strong ball-regulated point process on the sphere.

Abstract

We introduce a new analytical framework, developed based on the spatial network calculus, for performance assessment of Low Earth Orbit (LEO) satellite networks. Specifically, we model the satellites' spatial positions as a strong ball-regulated point process on the sphere. Under this model, proximal points in space exhibit a locally repulsive property, reflecting the fact that intersatellite links are protected by a safety distance and would not be arbitrarily close. Subsequently, we derive analytical lower bounds on the conditional coverage probabilities under Nakagami- and Rayleigh fading, respectively. These expressions have a low computational complexity, enabling efficient numerical evaluations. We validate the effectiveness of our theoretical model by contrasting the coverage probability obtained from our analysis with that estimated from a Starlink constellation. The results show that our analysis provides a tight lower bound on the actual value and, surprisingly, matches the empirical simulations almost perfectly with a 1 dB shift. This demonstrates our framework as an appropriate theoretical model for LEO satellite networks.

Paper Structure

This paper contains 11 sections, 19 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Prior Art
  3. Contributions
  4. System Model
  5. Network Configuration
  6. Performance Metric
  7. Analysis
  8. Regulated Spherical Point Processes
  9. Coverage Analysis
  10. Simulation and Numerical Results
  11. Conclusion

Figures (5)

  • Figure 1: A snapshot of the satellite downlink network model. A user is located on the Earth's surface. The blue icon represents the serving satellite, while the red icons denote the interfering satellites within the shaded visible cap.
  • Figure 2: Illustration of a Fibonacci lattice point distribution, showing both the global spherical view (left) and a regional projection (right).
  • Figure 3: Coverage probability under simulations and analysis, with the number of visible satellites $N_{vis}=16$, a minimum elevation angle $\omega_{\min}=25\degree$, and a Nakagami-m fading parameter of $m=2$.
  • Figure 4: Coverage probability versus the decoding threshold, $\theta$, comparing the analytical results of Theorem \ref{['thm:P_Nakagami']} (with $m=1$) and Corollary \ref{['cor:P_Rayleigh']} with simulations for two density scenarios: $N_{vis}=10$ (with $H=650$ km) and $N_{vis}=50$ (with $H=287$ km).
  • Figure 5: The coverage probability for various Nakagami-m fading parameters ($m \in \{1, 2, 4\}$) and a fixed number of visible satellites of $N_{vis}=50$.