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Stochastic Geometry-based Analysis of LEO Satellite Communication Systems
Anna Talgat, Mustafa A. Kishk, Mohamed-Slim Alouini
TL;DR
The paper addresses how LEO satellite relaying can improve coverage in rural and remote areas where anchored base stations may be distant. It uses stochastic geometry to derive coverage probability for multi-altitude satellite deployments and ground gateways, finding that gateway density, satellite altitude, and satellite count determine when satellite coverage outperforms the ABS.
Problem
The paper studies coverage enhancement for rural and remote users where the nearest anchored base station is typically far away.
Method
The paper models satellites as binomial point processes on spherical surfaces at multiple altitudes, gateways as a ground PPP, and derives coverage probability using stochastic geometry.
Results
Satellite gateway deployment enhances coverage probability when the nearest ABS exceeds a specific distance threshold, with that threshold affected by gateway density, satellite altitudes, and satellite numbers.
Takeaways & Limitations
Lower satellite altitudes and more satellites reduce the gateway density required to outperform ABS coverage, while satellite coverage improves as the nearest ABS becomes more distant.
Abstract
from arXiv · showhide
This letter studies the performance of a low-earth orbit (LEO) satellite communication system where the locations of the LEO satellites are modeled as a binomial point process (BPP) on a spherical surface. In particular, we study the user coverage probability for a scenario where satellite gateways (GWs) are deployed on the ground to act as a relay between the users and the LEO satellites. We use tools from stochastic geometry to derive the coverage probability for the described setup assuming that LEO satellites are placed at n different altitudes, given that the number of satellites at each altitude ak is Nk for all k. To resemble practical scenarios where satellite communication can play an important role in coverage enhancement, we compare the performance of the considered setup with a scenario where the users are solely covered by a fiber-connected base station (referred to as anchored base station or ABS in the rest of the paper) at a relatively far distance, which is a common challenge in rural and remote areas. Using numerical results, we show the performance gain, in terms of coverage probability, at rural and remote areas when LEO satellite communication systems are adopted. Finally, we draw multiple system-level insights regarding the density of GWs required to outperform the ABS, as well as the number of LEO satellites and their altitudes.
I. INTRODUCTION
The paper analyzes LEO satellite communication as a means to improve coverage in rural and remote areas, modeling satellite and gateway deployments stochastically. It derives coverage expressions and compares satellite relaying with coverage from a distant anchored base station.
- LEO satellites are studied for worldwide coverage, including rural and remote areas, motivated by their relatively low latency and cheaper launching costs.
- The proposed analysis derives coverage probability as a function of satellite altitudes, satellite counts, and gateway density.
- The system compares satellite-based coverage with the nearest ABS, which is typically far from rural and remote users.
- The model uses PPP gateways on the ground and BPP satellites deployed across spherical surfaces, with coverage defined jointly over user-GW and GW-satellite links.
- Satellite-enabled coverage improves over ABS coverage when the nearest ABS lies beyond a specific distance threshold.
II. SYSTEM MODEL
The system model places fixed numbers of LEO satellites on concentric spherical surfaces at multiple altitudes and relays communication through ground gateways. The satellite-gateway link uses propagation loss and shadowed-Rician fading, with its distance and channel parameters explicitly modeled.
- LEO satellites occupy n spherical surfaces, with N_k uniformly distributed satellites on surface S_k at altitude a_k and radius r_k = r_e + a_k.
- Ground gateways follow a PPP with density λ_GW and relay communication between satellites and users.
- A. S-GW Link: The S-GW received signal power is modeled from satellite transmit power, channel fading, and propagation loss.
- A. S-GW Link: The S-GW propagation-loss expression depends on carrier wavelength, GW receiver antenna gain, satellite distance, rain attenuation, beam-pattern phase, and antenna characteristics.
- A. S-GW Link: The S-GW channel uses shadowed-Rician fading whose power distribution is parameterized by m, b_0, and Ω.
B. GW-U Link
The GW-U link models received power using gateway transmission, fading, distance-based path loss, and a path-loss exponent. These ingredients characterize the user-side relay connection.
- The GW-U received signal power is modeled as gateway transmit power multiplied by fading and distance-based path loss.
- The GW-U fading is exponential with unit mean, while R_GW-U denotes gateway-user distance and α is the path-loss exponent.
C. Association Policy
Coverage requires both the S-GW and GW-U links to meet their respective SNR thresholds under nearest-GW and nearest-satellite association.
- Users associate with their nearest GW, while each GW associates with its nearest LEO satellite.
- A user is covered only when the S-GW SNR exceeds γg and the GW-U SNR exceeds γu.
A. Distance Distribution
The satellite contact distance is random because satellites are uniformly located across multiple spherical surfaces, and its distribution is characterized through a CCDF and PDF.
- Random satellite locations on the spherical surfaces {Sk} make the contact distance D a random variable.
- Lemma 1 gives the contact-distance distribution through the complementary CDF of each distance Di.
- The CCDF is piecewise, including a zero-probability region for distances beyond dmax(i, 0).
- The distance geometry includes the term 2reai + a_i^2, and the PDF fDi(d) is defined over the stated interval and zero otherwise.
B. Coverage Analysis
The coverage analysis combines the GW-U link with the S-GW link, using a known GW-U result and deriving the S-GW coverage expression as the paper’s main theorem.
- The overall coverage calculation requires deriving the component coverage probability P S−GW_cov.
- The GW-U coverage probability is presented as a literature-established result using the distance density fR_GW−U(r).
- The main analytical contribution is the derivation of the S-GW link coverage probability.
- The S-GW coverage expression is stated in Theorem 1, with its proof deferred to Appendix A.
- Figure 2 frames satellite communication as a means to enhance coverage in underserved remote and rural areas.
C. Coverage Enhancement in Remote locations
The remote-area comparison uses a distant nearest ABS as the no-satellite benchmark, whose large distance leads to relatively low coverage probability.
- In rural and remote areas, the nearest ABS is modeled at distance R, which is typically large and yields relatively low coverage probability.
- The no-satellite benchmark is the ABS-user coverage probability under Rayleigh fading, with ABS transmit power ρa.
IV. NUMERICAL RESULTS
The numerical results validate the analytical expressions through Monte Carlo simulations and examine how thresholds, satellite altitude and count, gateway density, and ABS distance affect coverage. Lower satellite altitudes, more satellites, and sufficient gateway density improve the satellite system's coverage relative to the ABS.
- Simulation validation: Markers match Monte Carlo simulations represented by solid lines, validating the derived analytical results.The simulations use γg = γu = γth and ρs = ρg = ρa.
- Threshold effects: At low γth, S-U coverage is limited by GW-U coverage; at higher γth, it is limited by S-U coverage.
- Satellite parameters: Lower satellite altitude improves coverage probability when the satellite count is fixed.This result is shown for n = 1 while varying a1.
- Satellite parameters: Coverage improvement saturates beyond a specific satellite count when altitude is fixed.The saturation is reported for the n = 1 scenario.
- Gateway density: The gateway density required to outperform ABS decreases as satellite altitude decreases or satellite count increases.The altitude comparison fixes the satellite count, while the satellite-count comparison fixes altitude.
- ABS comparison: Satellite communication improves coverage at remote locations as the distance to the nearest ABS increases.
V. CONCLUSION
The conclusion presents a stochastic-geometry model for randomly located LEO satellites on spherical surfaces and derives coverage probability for ground gateways modeled by a PPP. Analytical expressions fit Monte Carlo simulations, while the framework quantifies effects of satellite altitudes, satellite numbers, gateway density, and ABS distance.
- Model and analysis: The paper models LEO satellite locations stochastically and analyzes satellite communication performance for satellites randomly located on spherical surfaces.
- Coverage derivation: The derived coverage probability applies to ground satellite gateways distributed according to a PPP.
- Validation: The derived expressions show a perfect fit with Monte Carlo simulations.
- System insights: The framework studies how satellite altitudes, satellite numbers, and gateway density affect system performance.
- Extension: The framework can be extended to more general integrated satellite-aerial-terrestrial network setups.
APPENDIX
The appendix contains a proof conclusion and a displayed expression involving the distribution of a distance-related quantity.
- Appendix: A displayed expression uses f_D(√y) within an integral involving √y.
- Appendix: The appendix ends the proof after presenting the displayed expression.