[Paper Review] Optimal Beamwidth and Altitude for Maximal Uplink Coverage in Satellite Networks

Bassel Al Homssi, Akram Al‐Hourani|arXiv (Cornell University)|Oct 13, 2021

Satellite Communication Systems14 references44 citations

TL;DR

This paper proposes an analytical framework using stochastic geometry to jointly optimize satellite constellation altitude and antenna beamwidth for maximal uplink coverage in dense low Earth orbit (LEO) satellite networks. By modeling user traffic demand and interference, it derives closed-form expressions for uplink coverage probability, showing that optimal beamwidth and altitude can significantly enhance network capacity—with results closely matching real-world constellations like Walker-delta and Walker-star.

ABSTRACT

Dense satellite constellations recently emerged as a prominent solution to complementing terrestrial networks in attaining true global coverage. As such, analytic optimization techniques can be adopted to rapidly maximize the benefits of such satellite networks. The paper presents a framework that relies on two primary tuning parameters to optimize the uplink performance; (i) the constellation altitude and (ii) the satellite antenna beamwidth. The framework leverages tools from stochastic geometry to derive analytical models that formulate a parametric uplink coverage problem which also includes user traffic demand as an input. This allows operators to devise uplink expansion strategies to cater for expanding user demand. The framework demonstrates that fine-tuning of these parameters can significantly enhance the network capacity. We show that the optimization of random constellations provides a close match to that of practical satellite constellations such as Walker-delta and Walker-star.

Motivation & Objective

• Address the challenge of maximizing uplink coverage in dense satellite constellations serving massive IoT and rural users.
• Overcome limitations of conventional simulation-based optimization, which is computationally expensive for large-scale constellations.
• Develop an analytical framework that enables rapid, scalable optimization of uplink performance under dynamic user demand.
• Enable network expansion strategies by identifying optimal beamwidth and altitude combinations for future deployment or retrofitting.
• Provide a tractable model that captures interference, user distribution, and satellite availability for realistic performance evaluation.

Proposed method

• Models satellite and user locations as independent homogeneous Binomial Point Processes (BPP) on a spherical Earth.
• Derives the effective beamwidth ψ using geometric constraints from satellite and user antenna beamwidths and Earth occlusion, with ψ = min[ψs, 2 arcsin(α sin(ψt/2))], where α = R⊕/(R⊕+h).
• Uses stochastic geometry to model the contact angle ϕo (zenith angle to the nearest satellite) and derives its CDF and PDF: Fϕo(ϕ) = 1 − exp(−N/2 (1 − cos ϕ)).
• Models uplink signal power using free-space path loss and antenna gains, with Pr = Pt Gs Gt l(ϕ) ζ, where l(ϕ) depends on the zenith angle and carrier frequency.
• Analytically computes average interference using Campbell’s theorem over a spherical annular region, accounting for all interfering users.
• Derives the uplink coverage probability as P(γ > γ₀) = ∫₀^{ϕm} [1 − Fζ(γ₀(Ī + W)/(Pt Gt Gs l(ϕ)))] fϕo(ϕ) dϕ, incorporating noise and interference.

Experimental results

Research questions

• RQ1 What is the optimal combination of satellite altitude and beamwidth that maximizes uplink coverage probability in dense LEO constellations?
• RQ2 How does user traffic demand (density) influence the optimal beamwidth and coverage performance?
• RQ3 Can a stochastic geometry-based analytical model accurately predict coverage performance for practical constellations like Walker-delta and Walker-star?
• RQ4 How does joint optimization of altitude and beamwidth compare to optimizing only one parameter in terms of coverage gain?
• RQ5 To what extent does beamwidth adaptation alone enable network scalability without adding new satellites?

Key findings

• Joint optimization of altitude and beamwidth yields a significant coverage probability gain—up to 30% improvement over non-optimized configurations, as shown in Fig. 5.
• The optimal beamwidth varies with altitude: for a 10,000-satellite constellation, the optimal beamwidth ranges from ~30° at 200 km to ~60° at 2000 km, as shown in Fig. 4.
• Random constellations provide a close match to practical Walker-delta and Walker-star constellations in terms of optimal beamwidth vs. altitude, validating the model’s accuracy.
• Beamwidth optimization alone can support up to 40% more ground users without infrastructure expansion, as demonstrated in Fig. 3 and Fig. 5.
• Coverage probability exhibits a non-monotonic response to beamwidth: it increases with beamwidth up to a peak, then degrades due to rising interference, confirming a trade-off between availability and interference.
• The analytical model closely matches simulation results across all tested configurations (e.g., N=1000, N=10,000), with negligible deviation in coverage probability curves (Figs. 2, 5).