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Modeling UAV-aided Roadside Cell-Free Networks with Matérn Hard-Core Point Processes

Chenrui Qiu, Yongxu Zhu, Bo Tan, George K. Karagiannidis, Tasos Dagiuklas

TL;DR

This work develops a stochastic-geometry framework for UAV-aided road-constrained cell-free vehicular networks. Roads are modeled by a Poisson Line Process, ground APs are deployed along roads via multi-layer 1-D PPPs, and UAVs form a 3-D Matérn Hard-Core tier to maintain safety spacing. A distance-based power control scheme is introduced to enable tractable aggregation of signals from multiple APs, and coverage probability is analyzed using Gamma approximations and interference Laplace transforms. The paper derives association probabilities, serving-distance distributions, and a practical SINR-based coverage expression, validated by simulations that reveal how UAV density, altitude, and policy parameters affect performance. The results provide deployment guidelines for UAV-assisted roadside CF networks in realistic road topologies.

Abstract

This paper investigates a uncrewed aerial vehicles (UAV)-assisted cell-free architecture for vehicular networks in road-constrained environments. Roads are modeled using a Poisson Line Process (PLP), with multi-layer roadside access points (APs) deployed via 1-D Poisson Point Process (PPP). Each user forms a localized cell-free cluster by associating with the nearest AP in each layer along its corresponding road. This forms a road-constrained cell-free architecture. To enhance coverage, UAV act as an aerial tier, extending access from 1-D road-constrained layouts (embedded in 2-D) to 3-D. We employ a Matérn Hard-Core (MHC) point process to model the spatial distribution of UAV base stations, ensuring a minimum safety distance between them. In order to enable tractable analysis of the aggregate signal from multiple APs, a distance-based power control scheme is introduced. Leveraging tools from stochastic geometry, we have studied the coverage probability. Furthermore, we analyze the impact of key system parameters on coverage performance, providing useful insights into the deployment and optimization of UAV-assisted cell-free vehicular networks.

Modeling UAV-aided Roadside Cell-Free Networks with Matérn Hard-Core Point Processes

TL;DR

This work develops a stochastic-geometry framework for UAV-aided road-constrained cell-free vehicular networks. Roads are modeled by a Poisson Line Process, ground APs are deployed along roads via multi-layer 1-D PPPs, and UAVs form a 3-D Matérn Hard-Core tier to maintain safety spacing. A distance-based power control scheme is introduced to enable tractable aggregation of signals from multiple APs, and coverage probability is analyzed using Gamma approximations and interference Laplace transforms. The paper derives association probabilities, serving-distance distributions, and a practical SINR-based coverage expression, validated by simulations that reveal how UAV density, altitude, and policy parameters affect performance. The results provide deployment guidelines for UAV-assisted roadside CF networks in realistic road topologies.

Abstract

This paper investigates a uncrewed aerial vehicles (UAV)-assisted cell-free architecture for vehicular networks in road-constrained environments. Roads are modeled using a Poisson Line Process (PLP), with multi-layer roadside access points (APs) deployed via 1-D Poisson Point Process (PPP). Each user forms a localized cell-free cluster by associating with the nearest AP in each layer along its corresponding road. This forms a road-constrained cell-free architecture. To enhance coverage, UAV act as an aerial tier, extending access from 1-D road-constrained layouts (embedded in 2-D) to 3-D. We employ a Matérn Hard-Core (MHC) point process to model the spatial distribution of UAV base stations, ensuring a minimum safety distance between them. In order to enable tractable analysis of the aggregate signal from multiple APs, a distance-based power control scheme is introduced. Leveraging tools from stochastic geometry, we have studied the coverage probability. Furthermore, we analyze the impact of key system parameters on coverage performance, providing useful insights into the deployment and optimization of UAV-assisted cell-free vehicular networks.
Paper Structure (14 sections, 2 theorems, 28 equations, 5 figures)

This paper contains 14 sections, 2 theorems, 28 equations, 5 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Channel Model
  4. Association Policy
  5. SINR and Coverage Probability
  6. Evaluation of Performance Metrics
  7. Association Probability
  8. Serving Distance Distribution
  9. Coverage Probability
  10. Numerical Results
  11. Conclusion
  12. Proof of Lemma 1
  13. Proof of Lemma 2
  14. Proof of Coverage Probability

Key Result

Lemma 1

We denote that typical receiver connects to UAV (tier-1) as event $\mathcal{E}_1$, to APs (tier-2) as event $\mathcal{E}_2$. The probability of the event $\mathcal{E}_1$ and $\mathcal{E}_2$ defined as where $\mathcal{A}_{v}^1, v\in \{\rm {L,NL}\}$ means UE biased received power at LoS or NLoS UAV-UE link is larger than from APs, could be expressed as where $\rho(r_2) = \max\left( 0, \xi_{21}^{ -

Figures (5)

  • Figure 1: Architecture of vehicular Cell-free Network integrated with UAV base stations.
  • Figure 2: Coverage probability versus SNR threshold.
  • Figure 3: Coverage probability versus UAV density. ($\gamma_0 =0 \rm{dB}$)
  • Figure 4: Coverage probability versus safety distance $d$ with different bias $B_{\rm U}$ in $\rm dB$ ($\gamma_0 =0 \rm{dB}$).
  • Figure 5: Coverage probability versus LoS and NLoS path loss exponent ($\gamma_0 =0 \rm{dB}$).

Theorems & Definitions (7)

  • Definition 1
  • Definition 2
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • proof