⚡ electrical engineering

Impact of Terrestrial Blockage on the Coverage of Integrated Satellite-Terrestrial Networks

This paper presents a stochastic geometry-based analytical framework using a Boolean blockage model to demonstrate that terrestrial blockages in integrated satellite-terrestrial networks can simultaneously attenuate signals and suppress interference, ultimately enhancing downlink coverage probability across diverse urban and open environments.

Original authors: Joon-Young Park, Byungju Lim, Young-Chai Ko

Published 2026-05-14

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CC0 1.0

Original authors: Joon-Young Park, Byungju Lim, Young-Chai Ko

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to listen to a radio station while driving through a city. Sometimes, you get a clear signal from a distant tower (the Satellite). Other times, you get a strong signal from a local cell tower on a nearby building (the Terrestrial Network).

In the future (specifically for 6G), these two systems will work together to make sure you never lose your connection. But there's a problem: buildings. Skyscrapers and walls can block your view of the sky or the local tower.

This paper is like a math-heavy detective story that figures out exactly how these buildings affect your ability to stay connected when you have both a satellite and a cell tower to choose from.

Here is the breakdown of their findings using simple analogies:

1. The Two-Headed Monster: Blockages

The authors discovered that buildings (blockages) have a weird, double-sided personality. They act like a shield and a wall at the same time.

The Bad Wall: If a building stands between you and the signal you want, it blocks it. This is bad. It's like someone standing in front of a stage, blocking your view of the singer.
The Good Shield: If a building stands between you and a different radio tower that is making noise (interference), it blocks that noise. This is good! It's like putting a soundproof wall between you and a noisy neighbor.

The paper's big discovery is that in a crowded city, having some buildings might actually help your connection because they silence the "noise" from other towers, even if they occasionally block your main signal.

2. The Curved Earth Problem

Most math models for cell towers pretend the Earth is flat. But the Earth is a giant ball.

The Analogy: Imagine you are looking at a lighthouse from the beach. If you walk a little further down the beach, the curve of the Earth makes the lighthouse look lower.
The Paper's Insight: The authors realized that because the Earth is round, buildings far away from you look "shorter" relative to the sky than buildings right next to you. A skyscraper 10 miles away might not block a satellite signal because the Earth's curve dips below the line of sight. They created a new math formula to account for this "curved world" effect, which changes how likely a satellite signal is to get blocked.

3. The "Best Friend" Strategy (The Integrated Network)

The paper tests a strategy where your phone is smart enough to switch between the Satellite and the Cell Tower.

The Scenario: Imagine you are in a dense city. The local cell towers are jammed with interference (too many people talking at once).
The Result: If you rely only on the cell tower, you might lose connection. If you rely only on the satellite, a tall building might block your view of the sky.
The Win: By combining them, the system acts like a safety net. If the cell tower is too noisy, the phone switches to the satellite. If the satellite is blocked by a building, the phone switches to the cell tower. The paper shows that this "dual-option" approach works best in the middle ground—where neither system is perfect on its own.

4. The "Goldilocks" Zone for Buildings

The paper found that the number of buildings matters, but not in a simple "more is better" way.

Too few buildings: There is too much noise (interference) from other towers.
Too many buildings: You get blocked too often, and your signal dies.
Just right: There is a "sweet spot" where there are enough buildings to silence the noisy neighbors (interference) but not so many that they block your main signal.

Summary

The paper doesn't promise that buildings will magically appear to help you. Instead, it provides a mathematical map showing that Integrated Satellite-Terrestrial Networks are a robust way to stay connected in cities. It proves that by understanding how buildings block signals (and how the Earth's curve changes that), we can design networks that use both space and ground towers to keep us online, even when the city is full of obstacles.

In short: It's about using the sky and the ground together so that if a building blocks one, the other is there to save the day, while realizing that a few buildings can actually help by quieting down the radio noise.

Technical Summary: Impact of Terrestrial Blockage on the Coverage of Integrated Satellite-Terrestrial Networks

Problem Statement
The integration of Non-Terrestrial Networks (NTNs), specifically Low Earth Orbit (LEO) satellite networks, with Terrestrial Networks (TNs) is a critical enabler for ubiquitous connectivity in sixth-generation (6G) systems. While existing literature has analyzed satellite-terrestrial networks, most studies assume dominant Line-of-Sight (LoS) links or neglect the geometric impact of urban blockages on the joint performance of these heterogeneous layers. In practical scenarios, terrestrial structures (e.g., skyscrapers) frequently obstruct direct signal paths, converting LoS links to Non-Line-of-Sight (NLoS) or causing outages. There is a lack of rigorous quantification regarding how terrestrial blockages affect the coverage probability of an Integrated Satellite-Terrestrial Network (ISTN), particularly considering the unique geometric constraints of satellite links (Earth's curvature) versus terrestrial links.

Methodology
The authors develop a stochastic geometry-based analytical framework to characterize the downlink coverage probability of an ISTN in the presence of terrestrial blockages. The key modeling components include:

Network Geometry:
- Satellite Layer: Modeled as a homogeneous Spherical Poisson Point Process (SPPP) on a shell at altitude $h$ . The Earth is modeled as a sphere with radius $R_E$ .
- Terrestrial Layer: Modeled using a local planar approximation (tangent plane) for the terrestrial base stations (TBSs) and users, justified by the short distances relative to Earth's curvature.
- Blockages: Terrestrial blockages are modeled using a Boolean scheme with rectangular footprints. Blockage centers follow a homogeneous PPP, with heights following a Rayleigh distribution and random orientations.
Channel Model:
- Satellite Links: Utilize a two-state availability model (LoS or blocked). Blocked links are treated as outages. The fading for LoS links follows a Shadowed-Rician model, approximated by a Gamma random variable for analytical tractability.
- Terrestrial Links: Explicitly model both LoS and NLoS propagation with distinct path-loss exponents. Small-scale fading follows Nakagami- $m$ for LoS and Rayleigh for NLoS.
- Interference: Cross-tier interference is neglected (orthogonal carriers). Aggregate interference is derived using the Probability Generating Functional (PGFL) of the PPP.
Geometric Analysis:
- A critical innovation is the derivation of a curvature-dependent scaling factor ( $\eta(\psi_S)$ ) for satellite links. Unlike flat-Earth models, this factor accounts for how Earth's curvature reduces the effective height of blockages relative to the satellite user link as the geocentric angle increases.
- The framework derives the LoS probability for both satellite and terrestrial links as a function of distance and blockage density, incorporating the Boolean blockage model.

Key Contributions

Unified Analytical Framework: The paper presents a stochastic geometry framework for ISTN downlink coverage that explicitly incorporates a Boolean blockage model and Earth's curvature.
Curvature-Dependent Blockage Modeling: The authors derive a geometric condition for satellite link blockage, introducing a scaling factor that quantifies how Earth's curvature diminishes the obstructive capability of terrestrial blockages at larger geocentric angles. This leads to a tractable characterization of the LoS satellite process.
Dual Role of Blockages: The analysis reveals that terrestrial blockages have a competing dual effect: they attenuate desired signals (causing outages) but also act as spatial shields that suppress aggregate interference.
Coverage Gain Characterization: The paper quantifies the overall ISTN coverage gain by comparing the integrated system against standalone terrestrial or satellite networks, identifying specific regimes where integration significantly improves reliability.

Results
Numerical results and simulations validate the analytical framework and highlight several key findings:

Blockage Density Impact: Blockages exhibit a non-monotonic effect on coverage. At low densities, interference is high, and coverage is low. As density increases, blockages suppress interference, improving coverage. However, at very high densities, the desired signal is frequently blocked, degrading coverage. An optimal blockage density exists that maximizes coverage.
Satellite vs. Terrestrial Differences:
- For satellite networks, the optimal blockage density increases with the number of visible satellites (due to higher interference) and decreases with blockage height (taller blockages are more effective at suppression).
- For terrestrial networks, coverage typically follows a three-regime pattern: improvement due to interference suppression, degradation as the serving link becomes NLoS, and a rebound when interference mitigation dominates.
ISTN Performance: The integration of satellite and terrestrial layers provides significant coverage gains, particularly in intermediate Signal-to-Interference-plus-Noise Ratio (SINR) regimes where standalone networks offer only mediocre performance. The ISTN architecture stabilizes coverage probability by providing an alternative association path when one layer fails.
Blockage Size Sensitivity: The "beneficial" size of blockages depends on the SINR threshold. At low thresholds, smaller blockages are preferred to maintain LoS availability. At high thresholds (interference-limited), larger blockages are beneficial for suppressing interference.

Significance and Claims
The paper claims that its primary contribution is the rigorous quantification of the geometric impact of terrestrial blockages on ISTN performance, a gap previously unaddressed in the literature. By explicitly accounting for Earth's curvature and the dual nature of blockages (signal attenuation vs. interference shielding), the proposed framework offers a mathematically tractable approach for system design.

The authors assert that their findings highlight the necessity of blockage-aware modeling and joint satellite-terrestrial design to achieve reliable connectivity in future 6G systems. The results suggest that ISTN is a resilient architecture capable of maintaining connectivity under heterogeneous blockage conditions, offering a practical solution for environments where terrestrial infrastructure is sparse or heavily obstructed. The paper modestly notes that the independence approximation used for the combined coverage probability serves as a baseline and that future work could extend the framework to models with spatially correlated blockages.