⚡ electrical engineering

Coverage Analysis in Terahertz Clustered HetNets

This paper analyzes the coverage performance of Terahertz clustered heterogeneous networks using stochastic geometry, demonstrating that modeling base stations and users with a Poisson Cluster Process yields higher coverage probabilities compared to traditional Poisson Point Process models, particularly when small base stations exhibit a moderate spatial spread.

Original authors: Hadeel Obaid

Published 2026-07-03

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Hadeel Obaid

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ 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 the future of the internet as a high-speed train system. The Terahertz (THz) band is like a brand-new, ultra-fast train that can carry massive amounts of data (like thousands of movies at once). However, this train has a major flaw: it can only travel a very short distance before it runs out of steam. It also gets easily blocked by walls, trees, or even the humidity in the air. If you tried to build a network using only these short-range trains, you'd have huge gaps in coverage, especially in crowded cities.

This paper proposes a clever solution: Clustered Heterogeneous Networks (HetNets). Think of this not as a uniform grid of trains, but as a system of "hubs" or "hotspots."

Here is how the paper breaks it down using simple analogies:

1. The Problem: The "Short-Range Train"

The authors explain that while THz technology offers incredible speed, its signal is weak and easily absorbed. It's like trying to shout a message across a large, foggy field; the sound dies out quickly. If you just scatter radio towers randomly (which mathematicians call a Poisson Point Process or PPP), you end up with many people standing far away from a tower, unable to hear the signal clearly.

2. The Solution: The "VIP Club" Model

Instead of scattering towers randomly, the paper suggests grouping them. Imagine a city where people naturally gather in specific spots (like a concert venue or a busy cafe).

The Cluster: The paper models these groups as Poisson Cluster Processes (PCP). Think of a "parent" point (the center of the hotspot) that spawns a group of "children" (Small Base Stations or SBSs) and users around it.
The Layout: The Small Base Stations (SBSs) are like security guards or Wi-Fi routers placed specifically around these crowded areas. The users are also clustered there.
The Macro Station: There are also large, powerful towers (MBSs) scattered randomly across the whole city to cover the gaps, but the real action happens in the clusters.

3. The "Line of Sight" Rule

Because THz signals are so fragile, they need a clear path, like a laser beam. If a building blocks the path, the signal is lost. The paper treats buildings like random obstacles (like furniture in a room) that block the view. The system is designed so that a user only connects to a tower if there is a clear, unobstructed line of sight.

4. The Mathematical "Map"

To prove this works, the authors used a branch of math called Stochastic Geometry.

Imagine trying to predict the weather. You can't know exactly where every raindrop will fall, but you can use probability to predict how much rain will hit a specific area.
The authors used this math to calculate the odds of a user finding a clear path to a tower, the amount of "noise" (interference) from other towers, and the likelihood of a successful connection. They derived complex formulas to map out exactly how likely a user is to get a good signal in this clustered setup versus a random setup.

5. The Findings: Why Clustering Wins

The paper ran simulations (computer experiments) to test their theory. Here is what they found:

Clusters are better: The "VIP Club" model (PCP) provides much better coverage than the random "scattered" model (PPP). By keeping the towers and users close together in groups, the signal doesn't have to travel as far, and it's less likely to get blocked.
The "Goldilocks" Zone: The paper discovered that the spacing of the small towers matters.
- If the towers are too close together (clumped tightly), they interfere with each other, like too many people shouting in a small room.
- If they are too far apart, the signal gets weak.
- Just right: A "moderate spread" of towers around the cluster center works best. It balances the need for a strong signal with the need to avoid interference.
Building Density: The more buildings (blockages) there are, the harder it is to get a signal, which makes sense.

Summary

In short, the paper argues that to make the super-fast, short-range Terahertz internet work in the real world, we shouldn't just scatter towers randomly. Instead, we should group them around where people actually are. This "clustered" approach keeps the distance short, ensures a clear line of sight, and results in a much more reliable connection for everyone in the hotspot.

Technical Summary: Coverage Analysis in Terahertz Clustered HetNets

Problem Statement
Terahertz (THz) transmission technologies offer vast bandwidths essential for ultra-broadband, low-latency 6G communications. However, THz signals face significant deployment challenges, including limited transmission ranges, high free-space attenuation, and molecular absorption. These factors make achieving universal coverage with standalone THz base stations difficult, particularly in urban environments where conventional wide-area deployments result in coverage gaps. Furthermore, user distribution in real-world scenarios is rarely uniform; users tend to cluster around traffic hotspots. The paper addresses the need to evaluate THz performance within a clustered heterogeneous network (HetNet) architecture that aligns with these spatial realities, moving beyond the standard assumption of uniformly distributed nodes.

Methodology
The paper employs a stochastic geometry framework to model and analyze a two-tier THz HetNet consisting of Macro Base Stations (MBS) and Small Base Stations (SBS).

Network Modeling: The MBS tier is modeled as a homogeneous Poisson Point Process (PPP). In contrast, to capture user clustering and network hotspots, both the SBS tier and the user distribution are modeled using a Poisson Cluster Process (PCP). Specifically, the SBSs follow a Thomas cluster process (TCP), where cluster centers form a PPP, and SBSs are distributed as offspring points around these centers. Users are similarly clustered around the same parent points.
Channel and Propagation: The model incorporates a sectored antenna gain model to compensate for high path loss. Environmental blockages are modeled using a Boolean scheme of rectangles distributed via PPP. The propagation model accounts for molecular absorption (exponential power loss) and distinguishes between Line-of-Sight (LoS) and Non-Line-of-Sight (NLoS) links, considering only LoS connections due to the significant power gap. Small-scale fading is modeled using Nakagami- $m$ distribution.
Analytical Derivation: The authors derive analytical expressions for user association probabilities, the Laplace transform of aggregate interference, and the downlink coverage probability. The analysis considers interference from three sources depending on the serving tier: intra-tier interference, intra-cluster interference, and inter-cluster interference.

Key Contributions

Novel Modeling Approach: Unlike prior works that typically model THz networks using independent PPPs for all tiers, this paper introduces a PCP-based framework for both SBSs and users. This approach explicitly addresses the spatial correlation between users and base stations in hotspot scenarios.
Comprehensive Performance Analysis: The paper derives closed-form analytical expressions for the coverage probability in a clustered THz HetNet, accounting for blockage effects, molecular absorption, and directional antenna gains.
Interference Characterization: The study provides detailed derivations for the Laplace transform of interference, distinguishing between intra-cluster and inter-cluster interference components, which are critical in clustered topologies.

Numerical Results
The analytical results are validated against Monte Carlo simulations ( $10^5$ iterations). Key findings include:

Clustered vs. Uniform: The coverage probability in the proposed THz PCP-HetNet is consistently higher than in a THz PPP-based HetNet. The uniform distribution in PPP models increases the average serving distance and reduces LoS probability, whereas clustering brings users closer to serving nodes, enhancing signal quality.
Spatial Spread ( $\sigma_s$ ): The coverage probability exhibits a non-monotonic behavior with respect to the spatial spread of SBSs ( $\sigma_s$ ). Coverage initially increases as $\sigma_s$ grows (reaching a peak at $\sigma_s = 20$ m in the simulation) and then decreases. This suggests that a moderate spatial spread is optimal; too little spread causes intense intra-cluster interference, while too much spread increases the distance to the serving node.
User Spread ( $\sigma_u$ ): Generally, increasing the user-cluster spread reduces coverage as users move further from the hotspot center. However, a moderate spread can slightly improve coverage by mitigating severe intra-cluster interference before distance effects dominate.
Blockage and Density: Increasing building density ( $\lambda_B$ ) consistently reduces coverage due to the higher likelihood of NLoS links. Conversely, a moderate number of SBSs per cluster ( $n_s$ ) improves coverage by increasing the chance of a nearby LoS link, though gains saturate or slightly decline at very high densities due to interference.

Significance
The paper claims that its stochastic-geometry framework provides a more realistic performance evaluation for THz communications in clustered environments. By demonstrating that clustered deployment (PCP) outperforms uniform deployment (PPP) in terms of coverage, the study offers practical guidance for network planners. Specifically, it suggests that leveraging the natural clustering of users and deploying SBSs with a moderate spatial spread can effectively mitigate the inherent range and attenuation limitations of THz signals in next-generation networks.