Low-Earth Orbit Satellite Network Analysis: Coverage under Distance-Dependent Shadowing

Abstract

This paper offers a thorough analysis of the coverage performance of Low Earth Orbit (LEO) satellite networks using a strongest satellite association approach, with a particular emphasis on shadowing effects modeled through a Poisson point process (PPP)-based network framework. We derive an analytical expression for the coverage probability, which incorporates key system parameters and a distance-dependent shadowing probability function, explicitly accounting for both line-of-sight and non-line-of-sight propagation channels. To enhance the practical relevance of our findings, we provide both lower and upper bounds for the coverage probability and introduce a closed-form solution based on a simplified shadowing model. Our analysis reveals several important network design insights, including the enhancement of coverage probability by distance-dependent shadowing effects and the identification of an optimal satellite altitude that balances beam gain benefits with interference drawbacks. Notably, our PPP-based network model shows strong alignment with other established models, confirming its accuracy and applicability across a variety of satellite network configurations. The insights gained from our analysis are valuable for optimizing LEO satellite deployment strategies and improving network performance in diverse scenarios.

Figures (10)

• Figure 1: Satellites are assumed to be distributed on the surface of the satellite sphere with radius of $R_{\sf S} = R_{\sf E} + h$ where $h$ is the satellite altitude and $R_{\sf E}$ is the radius of Earth. A typical user is located at $(0,0,R_{\sf E})$ and can only be served by satellites on the typical spherical cap $\hbox{$\mathcal{A}$}$.
• Figure 2: Satellites have different LOS and NLOS channel probability depending on the distance to the typical user. In addition, they also have different beam gain depending on the distance to the typical user.
• Figure 3: The numerical and analytical coverage probabilities versus the target SIR $\gamma$ for $\alpha_{\sf L} = 2$, $\alpha_{\sf N} =3$, $h = 700$ km, $m=3$, $K=10$, and $\beta \in \{0.048, 0.2, 0.57\}$.
• Figure 4: The numerical coverage probability and analytical bounds versus the target SIR $\gamma$ for $\alpha_{\sf L} = 2$, $\alpha_{\sf N} =3$, $h = 700$ km, $m=3$, $K=10$, and $\beta \in \{0.048, 0.57\}$.
• Figure 5: The simulation coverage probability and analytical approximation versus the target SIR $\gamma$ for the simplified LOS probability and beam gain functions with $\alpha_{\sf L} = 2$, $\alpha_{\sf N} =4$, $h = 700$ km, $m=3$, $K=10$, $R_{\sf los} \in \{1500, 1700, 2300\}$ km, $\kappa =(m!)^{-\frac{1}{m}}$, and $\epsilon = 0.6$

Theorems & Definitions (16)

• Remark 1: Nakagami-$m$ and shadowed-Rician fading
• Lemma 1: Interference Laplace
• Theorem 1: Coverage probability
• proof
• Theorem 2
• proof
• Proposition 1
• proof
• Proposition 2
• proof