Meta Distribution of the SIR in a Narrow-Beam LEO Uplink

Ilari Angervuori; Martin Haenggi; Risto Wichman

doi:10.1109/TCOMM.2025.3547734

Meta Distribution of the SIR in a Narrow-Beam LEO Uplink

Ilari Angervuori^*
, Martin Haenggi
, Risto Wichman

^*Corresponding author for this work

University of Notre Dame

Research output: Contribution to journal › Article › Scientific › peer-review

1 Citation (Scopus)

2 Downloads (Pure)

Abstract

We focus on stochastic geometry analysis of a low Earth orbit (LEO) narrowband terrestrial-satellite uplink with satellite base stations (SBSs) in a uniform constellation equipped with narrow Gaussian beams. The served and interfering omnidirectional user equipments (UEs) are distributed on the Earth’s surface according to a homogeneous Poisson point process (HPPP) with Nakagami faded signals. This study presents a detailed but comprehensive mathematical analysis of several key metrics: the signal-to-interference ratio (SIR), the SIR meta distribution (MD), the signal-to-interference-plus-noise ratio (SINR), and the average throughput. Many results are presented in simple analytical and closed forms containing more insight than the expressions proposed in prior works. The results indicate an optimal UE density depending on the altitude, elevation angle, and the width of the antenna gain, maximizing the average throughput. However, this optimal density leads to a significant variance in the user experience regarding link quality (i.e., the users are not treated fairly).

Original language	English
Pages (from-to)	8260-8273
Number of pages	14
Journal	IEEE Transactions on Communications
Volume	73
Issue number	9
DOIs	https://doi.org/10.1109/TCOMM.2025.3547734
Publication status	Published - 2025
MoE publication type	A1 Journal article-refereed

Funding

Received 10 December 2024; accepted 17 February 2025. Date of publication 4 March 2025; date of current version 18 September 2025. The work was supported by the Research Council of Finland Grant 339446 and the Vilho, Yrjö and Kalle Väisälä Foundation. The associate editor coordinating the review of this article and approving it for publication was N. Mokari. (Corresponding author: Ilari Angervuori.) Ilari Angervuori and Risto Wichman are with the Department of Electrical Engineering, Aalto University, 02150 Espoo, Finland (e-mail: [email protected]; [email protected]).

Keywords

average throughput
coverage probability
Lomax distribution
Low Earth orbit
meta distribution
stochastic geometry

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Cite this

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title = "Meta Distribution of the SIR in a Narrow-Beam LEO Uplink",

abstract = "We focus on stochastic geometry analysis of a low Earth orbit (LEO) narrowband terrestrial-satellite uplink with satellite base stations (SBSs) in a uniform constellation equipped with narrow Gaussian beams. The served and interfering omnidirectional user equipments (UEs) are distributed on the Earth{\textquoteright}s surface according to a homogeneous Poisson point process (HPPP) with Nakagami faded signals. This study presents a detailed but comprehensive mathematical analysis of several key metrics: the signal-to-interference ratio (SIR), the SIR meta distribution (MD), the signal-to-interference-plus-noise ratio (SINR), and the average throughput. Many results are presented in simple analytical and closed forms containing more insight than the expressions proposed in prior works. The results indicate an optimal UE density depending on the altitude, elevation angle, and the width of the antenna gain, maximizing the average throughput. However, this optimal density leads to a significant variance in the user experience regarding link quality (i.e., the users are not treated fairly).",

keywords = "average throughput, coverage probability, Lomax distribution, Low Earth orbit, meta distribution, stochastic geometry",

author = "Ilari Angervuori and Martin Haenggi and Risto Wichman",

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year = "2025",

doi = "10.1109/TCOMM.2025.3547734",

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AU - Angervuori, Ilari

AU - Haenggi, Martin

AU - Wichman, Risto

PY - 2025

Y1 - 2025

N2 - We focus on stochastic geometry analysis of a low Earth orbit (LEO) narrowband terrestrial-satellite uplink with satellite base stations (SBSs) in a uniform constellation equipped with narrow Gaussian beams. The served and interfering omnidirectional user equipments (UEs) are distributed on the Earth’s surface according to a homogeneous Poisson point process (HPPP) with Nakagami faded signals. This study presents a detailed but comprehensive mathematical analysis of several key metrics: the signal-to-interference ratio (SIR), the SIR meta distribution (MD), the signal-to-interference-plus-noise ratio (SINR), and the average throughput. Many results are presented in simple analytical and closed forms containing more insight than the expressions proposed in prior works. The results indicate an optimal UE density depending on the altitude, elevation angle, and the width of the antenna gain, maximizing the average throughput. However, this optimal density leads to a significant variance in the user experience regarding link quality (i.e., the users are not treated fairly).

AB - We focus on stochastic geometry analysis of a low Earth orbit (LEO) narrowband terrestrial-satellite uplink with satellite base stations (SBSs) in a uniform constellation equipped with narrow Gaussian beams. The served and interfering omnidirectional user equipments (UEs) are distributed on the Earth’s surface according to a homogeneous Poisson point process (HPPP) with Nakagami faded signals. This study presents a detailed but comprehensive mathematical analysis of several key metrics: the signal-to-interference ratio (SIR), the SIR meta distribution (MD), the signal-to-interference-plus-noise ratio (SINR), and the average throughput. Many results are presented in simple analytical and closed forms containing more insight than the expressions proposed in prior works. The results indicate an optimal UE density depending on the altitude, elevation angle, and the width of the antenna gain, maximizing the average throughput. However, this optimal density leads to a significant variance in the user experience regarding link quality (i.e., the users are not treated fairly).

KW - average throughput

KW - coverage probability

KW - Lomax distribution

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KW - stochastic geometry

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Meta Distribution of the SIR in a Narrow-Beam LEO Uplink

Abstract

Funding

Keywords

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ILOSAT: Integrated low earth orbit satellite and terrestrial networks

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Meta Distribution of the SIR in a Narrow-Beam LEO Uplink

Abstract

Funding

Keywords

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Projects

ILOSAT: Integrated low earth orbit satellite and terrestrial networks

Cite this