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Downlink Performance of Cell-Free Massive MIMO for LEO Satellite Mega-Constellation

Xiangyu Li, Bodong Shang

TL;DR

This work analyzes the downlink performance of cell-free mMIMO in a LEO satellite mega-constellation using stochastic geometry. By modeling SAPs and UTs as independent spherical PPPs on concentric spheres and incorporating Nakagami-$m$ fading, the authors derive the distributions of the desired signal and average interference terms to obtain an approximate downlink coverage probability, validated through Monte Carlo simulations. The study demonstrates that larger dome angles, higher orbital altitudes, and denser SAP deployments improve coverage, and it reveals an optimal UT count that maximizes system capacity under given network settings. The results provide design insights for CF-mMIMO LEO SatCom networks and underscore the impact of beamforming and network densification on performance in NTNs.

Abstract

Low-earth orbit (LEO) satellite communication (SatCom) has emerged as a promising technology to improve wireless connectivity in global areas. Cell-free massive multiple-input multiple-output (CF-mMIMO), an architecture proposed for next-generation networks, has yet to be fully explored for LEO satellites. In this paper, we investigate the downlink performance of a CF-mMIMO LEO SatCom network, where multiple satellite access points (SAPs) simultaneously serve the corresponding ground user terminals (UTs). Using tools from stochastic geometry, we model the locations of SAPs and UTs on surfaces of concentric spheres using Poisson point processes (PPPs) and present expressions on transmit and received signals, signal-to-interference-plus-noise ratio (SINR). Then, we derive the coverage probabilities in fading scenarios, considering significant system parameters such as the Nakagami fading parameter, the number of UTs, the number of SAPs, the orbital altitude, and the service range affected by the dome angle. Finally, the analytical model is verified by extensive Monte Carlo simulations. Simulation results indicate that stronger line-of-sight (LoS) effects and a more comprehensive service range of the UT result in a higher coverage probability, despite the presence of multi-user interference (MUI). Moreover, we found that there exist optimal numbers of UTs that maximize system capacity for different orbital altitudes and dome angles, providing valuable insights for system design.

Downlink Performance of Cell-Free Massive MIMO for LEO Satellite Mega-Constellation

TL;DR

This work analyzes the downlink performance of cell-free mMIMO in a LEO satellite mega-constellation using stochastic geometry. By modeling SAPs and UTs as independent spherical PPPs on concentric spheres and incorporating Nakagami- fading, the authors derive the distributions of the desired signal and average interference terms to obtain an approximate downlink coverage probability, validated through Monte Carlo simulations. The study demonstrates that larger dome angles, higher orbital altitudes, and denser SAP deployments improve coverage, and it reveals an optimal UT count that maximizes system capacity under given network settings. The results provide design insights for CF-mMIMO LEO SatCom networks and underscore the impact of beamforming and network densification on performance in NTNs.

Abstract

Low-earth orbit (LEO) satellite communication (SatCom) has emerged as a promising technology to improve wireless connectivity in global areas. Cell-free massive multiple-input multiple-output (CF-mMIMO), an architecture proposed for next-generation networks, has yet to be fully explored for LEO satellites. In this paper, we investigate the downlink performance of a CF-mMIMO LEO SatCom network, where multiple satellite access points (SAPs) simultaneously serve the corresponding ground user terminals (UTs). Using tools from stochastic geometry, we model the locations of SAPs and UTs on surfaces of concentric spheres using Poisson point processes (PPPs) and present expressions on transmit and received signals, signal-to-interference-plus-noise ratio (SINR). Then, we derive the coverage probabilities in fading scenarios, considering significant system parameters such as the Nakagami fading parameter, the number of UTs, the number of SAPs, the orbital altitude, and the service range affected by the dome angle. Finally, the analytical model is verified by extensive Monte Carlo simulations. Simulation results indicate that stronger line-of-sight (LoS) effects and a more comprehensive service range of the UT result in a higher coverage probability, despite the presence of multi-user interference (MUI). Moreover, we found that there exist optimal numbers of UTs that maximize system capacity for different orbital altitudes and dome angles, providing valuable insights for system design.
Paper Structure (23 sections, 3 theorems, 40 equations, 13 figures, 1 table)

This paper contains 23 sections, 3 theorems, 40 equations, 13 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Works
  3. Contributions and Paper Organization
  4. System Model
  5. Spatial Distribution Model
  6. Path-Loss and Channel Model
  7. Uplink Training
  8. Downlink Transmission
  9. Operation Mechanism
  10. Delay and Phase Misalignment
  11. Payload Type and Functional Split
  12. Power Allocation
  13. Performance Analysis for Downlink Transmissions
  14. Statistical Properties
  15. Analytical Expressions
  16. ...and 8 more sections

Key Result

Proposition 1

Based on the perfect CSIT, the CCDF of the DSS received by the typical UT is given in (Formula:CCDF_DS) at the top of the next page, where $s=\frac{A+i2\pi c}{2\sqrt{{{\left| \Phi _{l}^{\rm{U}} \right|}_{\rm{avg}}}} x}$.

Figures (13)

  • Figure 1: An illustration of different satellite constellations.
  • Figure 2: A sketch of stochastic geometry modeling in the system.
  • Figure 3: Statistical Properties for distance relationships.
  • Figure 4: Comparison of coverage probability among PPP model, random initialized Starlink, and fixed initialized Starlink.
  • Figure 5: CCDF of desired signal strength, where $\eta=90^{\circ}$.
  • ...and 8 more figures

Theorems & Definitions (11)

  • Remark 1
  • Remark 2
  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Remark 3
  • Remark 4
  • Theorem 1
  • proof
  • ...and 1 more