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Satellite-Terrestrial Routing or Inter-Satellite Routing? A Stochastic Geometry Perspective

Ruibo Wang, Mustafa A. Kishk, Howard H. Yang, Mohamed-Slim Alouini

TL;DR

This work uses a spherical stochastic geometry framework to compare satellite-terrestrial routing (STR) and inter-satellite routing (ISR) in LEO constellations, introducing energy efficiency as the objective under a space-ground price ratio $\beta$. The authors derive ideal relay-position bounds, develop two routing-relay selection algorithms, and provide analytical expressions for routing availability and energy efficiency, validated by numerical results. The findings show that ISR generally offers higher routing availability, while STR can be more energy-efficient under favorable altitude and price conditions; both approaches can approach an energy-efficiency upper bound through the proposed global optimization, substantially reducing reliance on extensive link-level simulations. The results offer practical design insights for constellation planning and routing protocols, and point to future work integrating more detailed channel modeling and advanced antenna techniques within the SG framework.

Abstract

The design and comparison of satellite-terrestrial routing (STR) and inter-satellite routing (ISR) in low Earth orbit satellite constellations is a widely discussed topic. The signal propagation distance under STR is generally longer than that under ISR, resulting in greater path loss. The global deployment of gateways introduces additional costs for STR. In contrast, transmissions under ISR rely on the energy of satellites, which could be more costly. Additionally, ISLs require more complex communication protocol design, extra hardware support, and increased computational power. To maximize energy efficiency, we propose two optimal routing relay selection algorithms for ISR and STR, respectively. Furthermore, we derive the analytical expressions for the routing availability probability and energy efficiency, quantifying the performance of the algorithms. The analyses enable us to assess the performance of the proposed algorithms against existing methods through numerical results, compare the performance of STR and ISR, and provide useful insights for constellation design.

Satellite-Terrestrial Routing or Inter-Satellite Routing? A Stochastic Geometry Perspective

TL;DR

This work uses a spherical stochastic geometry framework to compare satellite-terrestrial routing (STR) and inter-satellite routing (ISR) in LEO constellations, introducing energy efficiency as the objective under a space-ground price ratio . The authors derive ideal relay-position bounds, develop two routing-relay selection algorithms, and provide analytical expressions for routing availability and energy efficiency, validated by numerical results. The findings show that ISR generally offers higher routing availability, while STR can be more energy-efficient under favorable altitude and price conditions; both approaches can approach an energy-efficiency upper bound through the proposed global optimization, substantially reducing reliance on extensive link-level simulations. The results offer practical design insights for constellation planning and routing protocols, and point to future work integrating more detailed channel modeling and advanced antenna techniques within the SG framework.

Abstract

The design and comparison of satellite-terrestrial routing (STR) and inter-satellite routing (ISR) in low Earth orbit satellite constellations is a widely discussed topic. The signal propagation distance under STR is generally longer than that under ISR, resulting in greater path loss. The global deployment of gateways introduces additional costs for STR. In contrast, transmissions under ISR rely on the energy of satellites, which could be more costly. Additionally, ISLs require more complex communication protocol design, extra hardware support, and increased computational power. To maximize energy efficiency, we propose two optimal routing relay selection algorithms for ISR and STR, respectively. Furthermore, we derive the analytical expressions for the routing availability probability and energy efficiency, quantifying the performance of the algorithms. The analyses enable us to assess the performance of the proposed algorithms against existing methods through numerical results, compare the performance of STR and ISR, and provide useful insights for constellation design.
Paper Structure (23 sections, 11 theorems, 48 equations, 8 figures, 1 table, 3 algorithms)

This paper contains 23 sections, 11 theorems, 48 equations, 8 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Contribution
  4. System Model
  5. Spatial Configuration
  6. Channel Model
  7. Performance Metric
  8. Routing Algorithm Design and Performance Analysis
  9. Problem Formulation
  10. Preliminaries
  11. Routing Algorithms
  12. Performance Evaluation
  13. Numerical Results
  14. Routing Availiability Probability
  15. Routing Energy Efficiency
  16. ...and 8 more sections

Key Result

Proposition 1

Given the number of hops $N_{\mathrm{STR}}$, the ideal relay positions in the spherical coordinate system of STR are where $\theta_{{\mathrm{STR}},1}$ and $\theta_{{\mathrm{STR}},2}$ represent the central angles of odd hops and even hops in STR, respectively, satisfying $\Theta = \frac{N_{\mathrm{STR}}}{2} (\theta_{{\mathrm{STR}},1} + \theta_{{\mathrm{STR}},2})$.

Figures (8)

  • Figure 1: An illustrative comparison between the satellite-terrestrial routing and inter-satellite routing approaches.
  • Figure 2: A schematic diagram of the spatial configuration.
  • Figure 3: Routing availability probability with different numbers of GWs and satellites.
  • Figure 4: Routing energy efficiency of STR with different constellation configurations.
  • Figure 5: Routing energy efficiency of ISR with different constellation configurations.
  • ...and 3 more figures

Theorems & Definitions (16)

  • Definition 1: Routing Energy Efficiency
  • Definition 2: Central Angle
  • Proposition 1
  • Proposition 2
  • Lemma 1
  • Proposition 3
  • Definition 3: Distance Scaling Factor
  • Lemma 2
  • Remark 1
  • Definition 4: Routing Availability Probability
  • ...and 6 more