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Outage Probability Analysis of Uplink Heterogeneous Non-terrestrial Networks: A Novel Stochastic Geometry Model

Wen-Yu Dong, Shaoshi Yang, Wei Lin, Wei Zhao, Jia-Xing Gui, Sheng Chen

TL;DR

This work addresses uplink outage in heterogeneous non-terrestrial networks comprising two UAV groups and a satellite, focusing on challenging environments. It introduces a novel Matérn hard-core cluster process (MHCCP) to model clustered UAV deployments alongside a binomial point process for the other group, and derives closed-form outage probability expressions under directional beamforming and shadowed-Rician fading, with FDMA-induced interference. The key contributions include the MHCCP construction, an interference analysis framework for SR fading, and a tractable outage bound validated by Monte Carlo simulations, providing design guidance for network deployment and resource allocation in NTNs. The results offer practical insights into how node density, minimum inter-cluster distance, channelization, and transmit power impact link reliability in uplink aerial-to-satellite communications.

Abstract

In harsh environments such as mountainous terrain, dense vegetation areas, or urban landscapes, a single type of unmanned aerial vehicles (UAVs) may encounter challenges like flight restrictions, difficulty in task execution, or increased risk. Therefore, employing multiple types of UAVs, along with satellite assistance, to collaborate becomes essential in such scenarios. In this context, we present a stochastic geometry based approach for modeling the heterogeneous non-terrestrial networks (NTNs) by using the classical binomial point process and introducing a novel point process, called Mat{é}rn hard-core cluster process (MHCCP). Our MHCCP possesses both the exclusivity and the clustering properties, thus it can better model the aircraft group composed of multiple clusters. Then, we derive closed-form expressions of the outage probability (OP) for the uplink (aerial-to-satellite) of heterogeneous NTNs. Unlike existing studies, our analysis relies on a more advanced system configuration, where the integration of beamforming and frequency division multiple access, and the shadowed-Rician (SR) fading model for interference power, are considered. The accuracy of our theoretical derivation is confirmed by Monte Carlo simulations. Our research offers fundamental insights into the system-level performance optimization of NTNs.

Outage Probability Analysis of Uplink Heterogeneous Non-terrestrial Networks: A Novel Stochastic Geometry Model

TL;DR

This work addresses uplink outage in heterogeneous non-terrestrial networks comprising two UAV groups and a satellite, focusing on challenging environments. It introduces a novel Matérn hard-core cluster process (MHCCP) to model clustered UAV deployments alongside a binomial point process for the other group, and derives closed-form outage probability expressions under directional beamforming and shadowed-Rician fading, with FDMA-induced interference. The key contributions include the MHCCP construction, an interference analysis framework for SR fading, and a tractable outage bound validated by Monte Carlo simulations, providing design guidance for network deployment and resource allocation in NTNs. The results offer practical insights into how node density, minimum inter-cluster distance, channelization, and transmit power impact link reliability in uplink aerial-to-satellite communications.

Abstract

In harsh environments such as mountainous terrain, dense vegetation areas, or urban landscapes, a single type of unmanned aerial vehicles (UAVs) may encounter challenges like flight restrictions, difficulty in task execution, or increased risk. Therefore, employing multiple types of UAVs, along with satellite assistance, to collaborate becomes essential in such scenarios. In this context, we present a stochastic geometry based approach for modeling the heterogeneous non-terrestrial networks (NTNs) by using the classical binomial point process and introducing a novel point process, called Mat{é}rn hard-core cluster process (MHCCP). Our MHCCP possesses both the exclusivity and the clustering properties, thus it can better model the aircraft group composed of multiple clusters. Then, we derive closed-form expressions of the outage probability (OP) for the uplink (aerial-to-satellite) of heterogeneous NTNs. Unlike existing studies, our analysis relies on a more advanced system configuration, where the integration of beamforming and frequency division multiple access, and the shadowed-Rician (SR) fading model for interference power, are considered. The accuracy of our theoretical derivation is confirmed by Monte Carlo simulations. Our research offers fundamental insights into the system-level performance optimization of NTNs.

Paper Structure

This paper contains 12 sections, 2 theorems, 13 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Topology Model
  4. Deployment of $A_1$ and $A_2$
  5. Multi-access Mechanism
  6. Channel Model
  7. Directional Beamforming Modeling
  8. Channel Fading
  9. SINR Model
  10. Performance Analysis
  11. Numerical Results
  12. Conclusions

Key Result

Theorem 1

The outage probability for an arbitrarily located aerial node under the SR fading channel is given by where $\Psi (k)=\frac{(-1)^{k} \kappa \delta^{k}}{(k!)^{2}}{\rm Ps}(1-q)_{k}$, $s=\frac{t \zeta (\beta -\delta) T d_{m}^{\alpha}}{p_m D_m}$ and $\zeta = (\Gamma (k+2))^{-\frac{1}{k+1}}$.

Figures (6)

  • Figure 1: Illustration of the heterogeneous NTN system.
  • Figure 2: Illustration of node positions in heterogeneous aircraft network.
  • Figure 3: Outage probability as function of SINR threshold $T$, given different transmit power $p_m$ of target node.
  • Figure 4: Outage probability as function of target node transmit power $p_m$, given different values of spherical space's radius $R_1$.
  • Figure 5: Outage probability as function of target node transmit power $p_m$, given different numbers of frequency channels $K$.
  • ...and 1 more figures

Theorems & Definitions (5)

  • Theorem 1
  • proof
  • Lemma 1
  • proof
  • Remark 1