arXiv subjects

Chang-Sik Choi

Publications and source records attributed to Chang-Sik Choi.

15 recordsLinked to original sources

arXiv2026

Satellite Infrastructure Sharing: Orbit-Structured Stochastic Geometry Modeling and Connectivity Analysis in Heterogeneous Satellite Networks

This paper develops an analytical framework to evaluate the feasibility and performance of satellite infrastructure sharing among multiple low Earth orbit (LEO) satellite operators. Motivated by the growing demand for universal connectivity under limited satellite resources, the proposed model captures uncoordinated deployments where independently operated constellations coexist without predefined orbital agreements. To describe such heterogeneous configurations, the spherical Cox point process is employed to jointly generate orbital structures and satellites. Then, each satellite is further assigned a random communication range, reflecting variations in coverage capability across operators. The overall coverage region is modeled through a spherical Cox-Boolean model that captures the spatial overlap of individual satellite spherical footprints on Earth. Using the proposed framework, the feasibility and benefits of satellite infrastructure sharing are mathematically analyzed, and closed-form expressions are derived for key performance metrics such as the connection probability, connection number, and downlink signal characteristics including the nearest serving distance, total received signal power, and the signal-to-interference ratio (SIR) distribution in the interference-limited regime. The analytical results, validated through system-level simulations, provide a tractable characterization of how orbital geometry governs coverage, connectivity, and interference, and reveal the inherent trade-offs induced by coverage overlap in heterogeneous satellite constellations.

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arXiv2026

Dynamical System Characterization of Heterogeneous Walker Satellite Networks: An Orbit-Aware Stochastic Geometry Perspective

Heterogeneous and in particular multi-altitude low Earth orbit (LEO) satellite constellations exhibit complex spatial and temporal structures, which require new modeling tools for their performance analysis. In this paper, we develop an orbit-aware stochastic geometry framework modeling today's LEO satellites on various orbits and various altitudes. In particular, we characterize such a system as the superposition of multiple Walker point processes and formulate it as a dynamical system determined by an initial condition and the rotation speeds of satellites and Earth. We show that when the speeds are rationally commensurable, the proposed satellite system is periodic. Then, we show that the system is ergodic when the speeds are rationally independent, establishing a theoretical link between time averages of the system and the expectation of it under the invariant measure. We derive the nearest-satellite distance distribution of a typical receiver at a given latitude and analyze the signal to interference-plus-noise ratio (SINR) coverage probability of the typical receiver. We then derive the ergodic throughput of the downlink communication to the typical receiver. Overall, the proposed framework offers a rigorous and tractable tool for analyzing downlink performance in Walker-type heterogeneous LEO satellite networks.

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arXiv2025

Stochastic Geometry and Dynamical System Analysis of Walker Satellite Constellations

In practice, low Earth orbit (LEO) and medium Earth orbit (MEO) satellite networks consist of multiple orbits which are populated with many satellites. A widely used spatial architecture for LEO or MEO satellites is the Walker constellation, where the longitudes of orbits are evenly spaced and the satellites are equally spaced along the orbits. In this paper, we develop a stochastic geometry model for the Walker constellations. This proposed model enables an analysis based on dynamical system theory, which allows one to address essential structural properties such as periodicity and ergodicity. It also enables a stochastic geometry analysis under which we derive the performance of downlink communications of a typical user at a given latitude, as a function of the key constellation parameters.

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arXiv2024

Leveraging Aerial Platforms for Downlink Communications in Sparse Satellite Networks

Although a significant number satellites are deemed essential for facilitating diverse applications of satellite networks, aerial platforms are emerging as excellent alternatives for enabling reliable communications with fewer satellites. In scenarios with sparse satellite networks, aerial platforms participate in downlink communications, serving effectively as relays and providing comparable or even superior coverage compared to a large number of satellites. This paper explores the role of aerial platforms in assisting downlink communications, emphasizing their potential as an alternative to dense satellite networks. Firstly, we account for the space-time interconnected movement of satellites in orbits by establishing a stochastic geometry framework based on an isotropic satellite Cox point process. Using this model, we evaluate space-and-time performance metrics such as the number of orbits, the number of communicable satellites, and the connectivity probability, primarily assessing the geometric impact of aerial platforms. Subsequently, we analyze signal-to-noise ratio (SNR) coverage probability, end-to-end throughput, and association delay. Through examination of these performance metrics, we explicitly demonstrate how aerial platforms enhance downlink communications by improving various key network performance metrics that would have been achieved only by many satellites, thereby assessing their potential as an excellent alternative to dense satellite networks.

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arXiv2024

Stochastic Geometry Analysis of RIS-Assisted Cellular Networks with Reflective Intelligent Surfaces on Roads

Reconfigurable intelligent surfaces (RISs) provide alternative routes for reflected signals to network users, offering numerous applications. This paper explores an innovative approach of strategically deploying RISs along road areas to leverage various propagation and blockage conditions present in cellular networks with roads. To address the local network geometries shown by such networks, we use a stochastic geometry framework, specifically the Cox point processes, to model the locations of RISs and vehicle users. Then, we define the coverage probability as the chance that either a base station or an RIS is in line of sight (LOS) of the typical user and that the LOS signal has a signal-to-noise ratio (SNR) greater than a threshold. We derive the coverage probability as a function of key parameters such as RIS density and path loss exponent. We observe that the network geometry highly affects the coverage and that the proposed RIS deployment effectively leverages the underlying difference of attenuation and blockage, significantly increasing the coverage of vehicle users in the network. With experimental results addressing the impact of key variables to network performance, this work serves as a versatile tool for designing, analyzing, and optimizing RIS-assisted cellular networks with many vehicles.

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arXiv2024

Analysis of a Delay-Tolerant Data Harvest Architecture Leveraging Low Earth Orbit Satellite Networks

Reaching all regions of Earth, low Earth orbit (LEO) satellites can harvest delay-tolerant data from remotely located users on Earth without ground infrastructure. This work aims to assess a data harvest network architecture where users generate data and LEO satellites harvest data from users when passing by. By developing a novel stochastic geometry Cox point process model that simultaneously generates orbits and the motion of LEO satellite harvesters on them, we analyze key performance indices of such a network by deriving the following: (i) the average fraction of time that the typical user is served by LEO satellite harvesters, (ii) the average amount of data uploaded per each satellite pass, (iii) the maximum harvesting capacity of the proposed network model, and (iv) the delay distribution in the proposed network. These key metrics are given as functions of key network variables such as $λ$ the mean number of orbits and $μ$ the mean number of satellites per orbit. Providing rich comprehensive analytical results and practical interpretations of these results, this work assesses the potential of the delay-tolerant use of LEO satellites and also serves as a versatile framework to analyze, design, and optimize delay-tolerant LEO satellite networks.

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arXiv2024

Modeling and Analysis of Downlink Communications in a Heterogeneous LEO Satellite Network

Low Earth Orbit (LEO) satellite networks connect millions of devices on Earth and offer various services, such as data communications, remote sensing, and data harvesting. As the number of services increases, LEO satellite networks will continue to grow, and many LEO satellite network operators will share the same spectrum resources. We aim to examine the coexistence of such a future heterogeneous LEO satellite network by proposing a tractable spatial model and analyzing the basic performance of downlink communications. We model a heterogeneous LEO satellite network as Cox point processes, ensuring satellites are located on various orbits. Then, we analyze two different access technologies for such a heterogeneous satellite network: closed access and open access. For both cases, we derive the coverage probability and prove that the coverage probability of the open access scenario outperforms that of the closed access, and this coverage enhancement applies to all users. By providing essential network performance statistics as key distributional parameters and by presenting the fact that the Cox point process approximates a forthcoming future constellation with slight variation, the developed framework and analysis will serve as a tractable instrument to design, evaluate, and optimize heterogeneous LEO satellite networks with numerous constellations.

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arXiv2024

A Novel Analytical Model for LEO and MEO Satellite Networks based on Cox Point Processes

This work develops an analytical framework for downlink low Earth orbit (LEO) or medium Earth orbit (MEO) satellite communications, leveraging tools from stochastic geometry. We propose a tractable approach to the analysis of such satellite communication systems, accounting for the fact that satellites are located on circular orbits. We accurately incorporate this geometric property of LEO or MEO satellite constellations by developing a Cox point process model that jointly produces orbits and satellites on these orbits. Our work contrasts with previous modeling studies that presumed satellite locations to be entirely random, thereby overlooking the fundamental fact that satellites are jointly positioned on orbits. Employing this Cox model, we analyze the network performance experienced by users located on Earth. Specifically, we evaluate the no-satellite probability of the proposed network and the Laplace transform of the interference created by such a network. Using it, we compute its SIR (signal-to-interference) distribution, namely its coverage probability. By presenting fundamental network performance as functions of key parameters, this model allows one to assess the statistical properties of downlink LEO or MEO satellite communications and can thus be used as a system-level design tool to operate and optimize forthcoming complex LEO or MEO satellite networks.

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arXiv2024

Cox Point Processes for Multi Altitude LEO Satellite Networks

To model existing or future low Earth orbit (LEO) satellite networks leveraging multiple constellations, we propose a simple analytical approach to represent the clustering of satellites on orbits. More precisely, we develop a variable-altitude Poisson orbit process that effectively captures the geometric fact that satellites are always positioned on orbits, and these orbits may vary in altitude. Conditionally on the orbit process, satellites situated on these orbits are modeled as linear Poisson point processes, thereby forming a Cox point process. For this model, we derive useful statistics, including the distribution of the distance from the typical user to its nearest visible satellite, the outage probability, the Laplace functional of the proposed Cox satellite point process, and the Laplace transform of the interference power from the Cox-distributed satellites under general fading. The derived statistics enable the evaluation of the performance of such LEO satellite communication systems as functions of network parameters.

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arXiv2024

Analysis of a Spatially Correlated Vehicular Network Assisted by Cox-distributed Vehicle Relays

In vehicle-to-all (V2X) communications, roadside units (RSUs) play an essential role in connecting various network devices. In some cases, users may not be well-served by RSUs due to congestion, attenuation, or interference. In these cases, vehicular relays associated with RSUs can be used to serve those users. This paper uses stochastic geometry to model and analyze a spatially correlated heterogeneous vehicular network where both RSUs and vehicular relays serve network users such as pedestrians or other vehicles. We present an analytical model where the spatial correlation between roads, RSUs, relays, and users is systematically modeled via Cox point processes. Assuming users are associated with either RSUs or relays, we derive the association probability and the coverage probability of the typical user. Then, we derive the user throughput by considering interactions of links unique to the proposed network. This paper gives practical insights into designing spatially correlated vehicular networks assisted by vehicle relays. For instance, we express the network performance such as the user association, SIR coverage probability, and the network throughput as the functions of network key geometric variables. In practice, this helps one to optimize the network so as to achieve ultra reliability or maximum user throughput of a spatially correlated vehicular networks by varying key aspects such as the relay density or the bandwidth for relays.

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arXiv2023

LOS Coverage Area in Vehicular Networks with Cox distributed Roadside Units and Relays

We develop an analytical framework to examine the line-of-sight (LOS) coverage area in vehicular networks with roadside units (RSU) and vehicle relays. In practical deployment scenarios, RSUs and vehicle relays are spatially correlated and we characterize this by employing Cox point processes to model the locations of RSUs and vehicle relays simultaneously. Leveraging the random blockage model, we model the LOS coverage area as Boolean models on these Cox point processes. The LOS coverage area is then evaluated by its area fraction. We show that relays can increase the area fraction of LOS coverage by nearly 50\% even when RSUs and relays are spatially correlated. By presenting a stochastic geometry model for a vehicular network with RSUs and relays and then by providing a tool to capture its LOS coverage, our work assesses the viability of vehicle relays for modern vehicular networks exploiting LOS coverage.

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arXiv2021

A Random Geometric Model of Blockages in Vehicular Networks

This paper presents a novel spatially consistent approach for modeling line-of-sight (LOS) paths in vehicular networks. We use stochastic geometry to model transmitters, obstacles, and receivers located in three parallel lines, respectively. Their geometric interactions are leveraged to characterize the existence of LOS paths. Specifically, the proposed approach focuses on the role of obstacles in blocking one or more LOS paths, which has been overlooked in most statistical models for blockage. Under the proposed framework, we derive the probability that a typical vehicle is in LOS with respect to transmitters with received signal-to-noise ratios greater than a threshold. The proposed framework and LOS coverage analysis are instrumental to the analysis of LOS-critical applications such as positioning or mmWave communications in vehicular networks.

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arXiv2018

Poisson Cox Point Processes for Vehicular Networks

This paper analyzes statistical properties of the Poisson line Cox point process useful in the modeling of vehicular networks. The point process is created by a two-stage construction: a Poisson line process to model road infrastructure and independent Poisson point processes, conditionally on the Poisson lines, to model vehicles on the roads. We derive basic properties of the point process, including the general quadratic position of the points, the nearest distance distribution, the Laplace functional, the densities of facets of the Cox-Voronoi tessellation, and the asymptotic behavior of the typical Voronoi cell under vehicular densification. These properties are closely linked to features that are important in vehicular networks.

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arXiv2017

An Analytical Framework for Coverage in Cellular Networks Leveraging Vehicles

This paper analyzes an emerging architecture of cellular network utilizing both planar base stations uniformly distributed in Euclidean plane and base stations located on roads. An example of this architecture is that where, in addition to conventional planar cellular base stations and users, vehicles also play the role of both base stations and users. A Poisson line process is used to model the road network and, conditionally on the lines, linear Poisson point processes are used to model the vehicles on the roads. The conventional planar base stations and users are modeled by independent planar Poisson point processes. The joint stationarity of the elements in this model allows one to use Palm calculus to investigate statistical properties of such a network. Specifically, this paper discusses two different Palm distributions, with respect to the user point processes depending on its type: planar or vehicular. We derive the distance to the nearest base station, the association of the typical users, and the coverage probability of the typical user in terms of integral formulas. Furthermore, this paper provides a comprehensive characterization of the performance of all possible cellular transmissions in this setting, namely vehicle-to-vehicle (V2V), vehicle-to-infrastructure (V2I), infrastructure-to-vehicle (I2V), and infrastructure-to-infrastructure (I2I) communications.

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arXiv2017

An Analytical Framework for Modeling a Spatially Repulsive Cellular Network

We propose a new cellular network model that captures both deterministic and random aspects of base station deployments. Namely, the base station locations are modeled as the superposition of two independent stationary point processes: a random shifted grid with intensity $λ_g$ and a Poisson point process (PPP) with intensity $λ_p$. Grid and PPP deployments are special cases with $λ_p \to 0$ and $λ_g \to 0$, with actual deployments in between these two extremes, as we demonstrate with deployment data. Assuming that each user is associated with the base station that provides the strongest average received signal power, we obtain the probability that a typical user is associated with either a grid or PPP base station. Assuming Rayleigh fading channels, we derive the expression for the coverage probability of the typical user, resulting in the following observations. First, the association and the coverage probability of the typical user are fully characterized as functions of intensity ratio $ρ_λ= λ_p/λ_g$. Second, the user association is biased towards the base stations located on a grid. Finally, the proposed model predicts the coverage probability of the actual deployment with great accuracy.

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