Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Joint Beam Scheduling and Beamforming Design for Cooperative Positioning in Multi-beam LEO Satellite Networks

Hongtao Xv, Yaohua Sun, Yafei Zhao, Mugen Peng, Shijie Zhang

TL;DR

The paper tackles cooperative Time Difference of Arrival positioning in multi-beam LEO satellite networks, addressing inter-beam interference and geometry-driven accuracy. It introduces a two-layer approach: a dynamic SINR threshold-based beamforming (DSTA) with SDR in the inner problem and a fast heuristic beam scheduling (HBS) in the outer problem, enabling joint optimization under per-beam power and beam-count constraints. The key contributions are a monotonicity-based beamforming design tied to SINR, a low-complexity HBS algorithm that accounts for channel correlation and topology geometry, and extensive simulations showing significant improvements in average positioning accuracy (e.g., up to around 17–18% over baselines and substantial gains over GDOP-based scheduling). The results demonstrate practical potential for positioning-enhanced cooperative LEO networks, offering a scalable and effective path to improved navigation and location-based services in next-generation satellite constellations.

Abstract

Cooperative positioning with multiple low earth orbit (LEO) satellites is promising in providing location-based services and enhancing satellite-terrestrial communication. However, positioning accuracy is greatly affected by inter-beam interference and satellite-terrestrial topology geometry. To select the best combination of satellites from visible ones and suppress inter-beam interference, this paper explores the utilization of flexible beam scheduling and beamforming of multi-beam LEO satellites that can adjust beam directions toward the same earth-fixed cell to send positioning signals simultaneously. By leveraging Cramér-Rao lower bound (CRLB) to characterize user Time Difference of Arrival (TDOA) positioning accuracy, the concerned problem is formulated, aiming at optimizing user positioning accuracy under beam scheduling and beam transmission power constraints. To deal with the mixed-integer-nonconvex problem, we decompose it into an inner beamforming design problem and an outer beam scheduling problem. For the former, we first prove the monotonic relationship between user positioning accuracy and its perceived signal-to-interference-plus-noise ratio (SINR) to reformulate the problem, and then semidefinite relaxation (SDR) is adopted for beamforming design. For the outer problem, a heuristic low-complexity beam scheduling scheme is proposed, whose core idea is to schedule users with lower channel correlation to mitigate inter-beam interference while seeking a proper satellite-terrestrial topology geometry. Simulation results verify the superior positioning performance of our proposed positioning-oriented beamforming and beam scheduling scheme, and it is shown that average user positioning accuracy is improved by $17.1\%$ and $55.9\%$ when the beam transmission power is 20 dBw, compared to conventional beamforming and beam scheduling schemes, respectively.

Joint Beam Scheduling and Beamforming Design for Cooperative Positioning in Multi-beam LEO Satellite Networks

TL;DR

The paper tackles cooperative Time Difference of Arrival positioning in multi-beam LEO satellite networks, addressing inter-beam interference and geometry-driven accuracy. It introduces a two-layer approach: a dynamic SINR threshold-based beamforming (DSTA) with SDR in the inner problem and a fast heuristic beam scheduling (HBS) in the outer problem, enabling joint optimization under per-beam power and beam-count constraints. The key contributions are a monotonicity-based beamforming design tied to SINR, a low-complexity HBS algorithm that accounts for channel correlation and topology geometry, and extensive simulations showing significant improvements in average positioning accuracy (e.g., up to around 17–18% over baselines and substantial gains over GDOP-based scheduling). The results demonstrate practical potential for positioning-enhanced cooperative LEO networks, offering a scalable and effective path to improved navigation and location-based services in next-generation satellite constellations.

Abstract

Cooperative positioning with multiple low earth orbit (LEO) satellites is promising in providing location-based services and enhancing satellite-terrestrial communication. However, positioning accuracy is greatly affected by inter-beam interference and satellite-terrestrial topology geometry. To select the best combination of satellites from visible ones and suppress inter-beam interference, this paper explores the utilization of flexible beam scheduling and beamforming of multi-beam LEO satellites that can adjust beam directions toward the same earth-fixed cell to send positioning signals simultaneously. By leveraging Cramér-Rao lower bound (CRLB) to characterize user Time Difference of Arrival (TDOA) positioning accuracy, the concerned problem is formulated, aiming at optimizing user positioning accuracy under beam scheduling and beam transmission power constraints. To deal with the mixed-integer-nonconvex problem, we decompose it into an inner beamforming design problem and an outer beam scheduling problem. For the former, we first prove the monotonic relationship between user positioning accuracy and its perceived signal-to-interference-plus-noise ratio (SINR) to reformulate the problem, and then semidefinite relaxation (SDR) is adopted for beamforming design. For the outer problem, a heuristic low-complexity beam scheduling scheme is proposed, whose core idea is to schedule users with lower channel correlation to mitigate inter-beam interference while seeking a proper satellite-terrestrial topology geometry. Simulation results verify the superior positioning performance of our proposed positioning-oriented beamforming and beam scheduling scheme, and it is shown that average user positioning accuracy is improved by and when the beam transmission power is 20 dBw, compared to conventional beamforming and beam scheduling schemes, respectively.
Paper Structure (13 sections, 2 theorems, 42 equations, 9 figures, 4 tables, 2 algorithms)

This paper contains 13 sections, 2 theorems, 42 equations, 9 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. System Model
  4. Channel Model
  5. Problem Formulation
  6. Dynamic UT SINR Threshold Adjustment Based Satellite Beamforming
  7. Beam Scheduling Algorithm Design
  8. SIMULATION RESULTS
  9. The Effectiveness of DSTA-based Beamforming
  10. The Impact of Beam Transmission Power Budget on The Performance of DSTA-based Beamforming
  11. The Impact of The Number of Visible Satellites on The Performance of DSTA-based Beamforming
  12. Performance Evaluation of The Proposed Heuristic Beam Scheduling
  13. CONCLUSION

Key Result

Proposition 1

$F_c$ is monotonically decreasing with respect to $\text{SINR}_{i,c}$ with the gradient of $F_c$ with respect to $\text{SINR}_{i,c}$ given by where satellite $i$ is the $\widehat{i}$-th satellite in set $\mathcal{I}_c$ serving UT $c$, $\mathbf{A_c}$ is a column full rank matrix with probability one and $\mathbf{R_c}$ is positive definite.

Figures (9)

  • Figure 1: The multi-beam LEO satellite system scenario for cooperative UT positioning.
  • Figure 2: Spatial relationships among UT $c$ and satellites.
  • Figure 3: The CDFs of UT positioning accuracy under different beamforming schemes when $I=21$, $I_{\text{TDOA}}=4$, and $P=26$ dBw.
  • Figure 4: The CDFs of UT SINR under different beamforming schemes when $I=21$, $I_{\text{TDOA}}=4$, and $P=26$ dBw.
  • Figure 5: The CDFs of positioning accuracy with DSTA-based beamforming under different satellite transmission power budgets when $I=21$ and $I_{\text{TDOA}}=4$.
  • ...and 4 more figures

Theorems & Definitions (4)

  • Proposition 1
  • proof
  • Proposition 2
  • proof