[Paper Review] Performance Analysis of Satellite Communication System Under the Shadowed-Rician Fading: A Stochastic Geometry Approach

Dong‐Hyun Jung, Joon-Gyu Ryu+2 more|arXiv (Cornell University)|Apr 27, 2021

Satellite Communication SystemsEngineering38 references125 citations

TL;DR

This paper proposes a stochastic geometry-based performance analysis of downlink low Earth orbit (LEO) satellite communications under shadowed-Rician fading, modeling satellite distribution via a homogeneous binomial point process (BPP). It derives exact and approximated outage probability expressions using the Poisson limit theorem and formulates a throughput maximization problem with visibility and outage constraints, solved via an iterative algorithm that achieves near-optimal performance with low complexity.

ABSTRACT

In this paper, we consider downlink low Earth orbit (LEO) satellite communication systems where multiple LEO satellites are uniformly distributed over a sphere at a certain altitude according to a homogeneous binomial point process (BPP). Based on the characteristics of the BPP, we analyze the distance distributions and the distribution cases for the serving satellite. We analytically derive the exact outage probability, and its approximated expression is obtained using the Poisson limit theorem. With these derived expressions, the system throughput maximization problem is formulated under the satellite-visibility and outage constraints. To solve this problem, we reformulate it with bounded feasible sets and propose an iterative algorithm to obtain near-optimal solutions. Simulation results perfectly match the derived exact expressions for the outage probability and system throughput. The analytical results of the approximated expressions are fairly close to those of the exact ones. It is also shown that the proposed algorithm for the throughput maximization is very close to the optimal performance obtained by a two-dimensional exhaustive search.

Motivation & Objective

• To analyze system performance in downlink LEO satellite communications under shadowed-Rician fading with finite, uniformly distributed satellites.
• To model the spatial distribution of LEO satellites using a homogeneous binomial point process (BPP) for accurate finite-node system modeling.
• To derive exact and approximated expressions for outage probability under the BPP and shadowed-Rician fading for mathematical tractability.
• To formulate and solve a system throughput maximization problem under satellite-visibility and outage constraints.
• To propose an iterative algorithm that achieves near-optimal throughput with significantly reduced complexity compared to exhaustive search.

Proposed method

• Models LEO satellite constellations as a homogeneous binomial point process (BPP) to capture finite, uniformly distributed satellites at a fixed altitude.
• Derives exact distance distributions to the nearest and serving satellites based on BPP geometry and beam pattern constraints (main lobe and side lobe sectors).
• Uses the Poisson limit theorem to derive approximated expressions for outage probability, enabling tractable analysis.
• Introduces a system model with directional beamforming and fixed beam antennas aligned toward the subsatellite point.
• Reformulates the throughput maximization problem over bounded feasible sets to enable convergence of the iterative algorithm.
• Proposes an iterative algorithm to jointly optimize transmission rate and minimum elevation angle, achieving near-optimal performance with low computational cost.

Experimental results

Research questions

• RQ1 How does the finite number of LEO satellites affect the distance distribution and serving satellite selection in a downlink satellite system?
• RQ2 What are the exact and approximated expressions for outage probability under shadowed-Rician fading when satellites are modeled via a BPP?
• RQ3 How does beam pattern (main lobe vs. side lobe) impact system performance in BPP-based LEO satellite networks?
• RQ4 What is the optimal trade-off between transmission rate and minimum elevation angle to maximize system throughput under visibility and outage constraints?
• RQ5 How close is the performance of the proposed iterative algorithm to the optimal solution obtained via exhaustive search?

Key findings

• The exact outage probability expressions derived via BPP-based geometry perfectly match simulation results, validating the analytical model.
• The approximated outage probability expressions, derived using the Poisson limit theorem, show close agreement with exact results, enabling low-complexity system analysis.
• The proposed iterative algorithm for throughput maximization achieves performance within 1% of the optimal solution obtained via two-dimensional exhaustive search.
• System throughput increases with the number of satellites S due to improved visibility and reduced outage probability, with saturation observed at high S due to minimum distance constraints.
• Beam-pointing errors (e.g., 1°) and rain attenuation (e.g., g = -3 dB) significantly degrade system performance, reducing throughput.
• Computational complexity of the exact outage probability is O(S²N²τ), dominated by the number of satellites S, while the approximated version is O(N²τ), showing high efficiency for large-scale systems.