# Performance Analysis of Millimeter-Wave UAV Swarm Networks under Blockage Effects

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## Abstract

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## 1. Introduction

- We present the statistics of the distance between an arbitrary UAV BS in a sphere-shaped swarm to the user. To be specific, the probability density function (PDF) of the distance is derived, and its approximate version to obtain the first and second moments in closed forms is also provided.
- Assuming random blockages between the UAV swarm and the receiver, we derive a closed-form expression of the outage rate, which is defined by the likelihood to have no LoS path.
- Using the derived outage rate, we present how it changes with various system parameters. In particular, we show that there exists an optimal value of the size of the UAV swarm to minimize the outage probability. Further, the optimal size of the spherical UAV swarm is derived in a closed-form.
- We present both simulation and theoretical results to show the impact of various system parameters. In addition, by comparing the two results, we validate our analysis.

## 2. Related Work

## 3. System Model

## 4. Distance Distribution and Path Loss Statistics

## 5. Outage Probability Analysis

**Property 1**.

**Property 2**.

**Property 3**.

**Property 4**.

**Property 5**.

**Property 6**.

**Property 7**.

**Property 8**.

**Property 9**.

## 6. Numerical Results

#### 6.1. Impact of R on ${P}_{out}$

#### 6.2. Impacts of $\rho $ and $\beta $ on ${P}_{out}$

#### 6.3. Impacts of $\rho $ and $\lambda $ on ${P}_{out}$

#### 6.4. ${R}_{opt}$ Verus $\rho $

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

5G | Fifth generation |

A2G | Air-to-ground |

AP | Access point |

B5G | Beyond fifth generation |

BS | Base station |

CDF | Cumulative distribution function |

LoS | Line-of-sight |

mmWave | Millimeter-wave |

Probability distribution function | |

PPP | Poisson point process |

SISO | Single-input-single-output |

UAV | Unmanned aerial vehicle |

UDN | Ultra-dense network |

UE | User equipment |

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**Figure 4.**Comparison of the approximate probability density function (PDF) of ${d}_{n}$ and its empirical PDF based on simulation for $R=100$m. (

**a**) $L=300$ m $(\rho =3)$; (

**b**) $L=2$ km $(\rho =20)$.

**Figure 6.**Outage rate versus $\rho =L/R$ with $\lambda ={10}^{-3}$$R=30$m, and $\beta =\{2.5\times {10}^{-2},\phantom{\rule{0.166667em}{0ex}}3.15\times {10}^{-2},\phantom{\rule{0.166667em}{0ex}}3.75\times {10}^{-2}\}$.

**Figure 7.**Outage rate versus $\rho =L/R$ with $\beta =2.5\times {10}^{-2}$, $R=30$ m, and $\lambda =\{0.0025,0.0005,0.0010\}$.

**Figure 8.**Optimal radius ${R}_{opt}$ versus $\rho =L/R$, when $\lambda ={10}^{-3}$ and $\beta =\{2.5\times {10}^{-2},\phantom{\rule{0.166667em}{0ex}}3.15\times {10}^{-2},\phantom{\rule{0.166667em}{0ex}}3.75\times {10}^{-2}\}$.

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**MDPI and ACS Style**

Jung, H.; Lee, I.-H.
Performance Analysis of Millimeter-Wave UAV Swarm Networks under Blockage Effects. *Sensors* **2020**, *20*, 4593.
https://doi.org/10.3390/s20164593

**AMA Style**

Jung H, Lee I-H.
Performance Analysis of Millimeter-Wave UAV Swarm Networks under Blockage Effects. *Sensors*. 2020; 20(16):4593.
https://doi.org/10.3390/s20164593

**Chicago/Turabian Style**

Jung, Haejoon, and In-Ho Lee.
2020. "Performance Analysis of Millimeter-Wave UAV Swarm Networks under Blockage Effects" *Sensors* 20, no. 16: 4593.
https://doi.org/10.3390/s20164593