# A Service-Constrained Positioning Strategy for an Autonomous Fleet of Airborne Base Stations

^{*}

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## Abstract

**:**

## 1. Introduction

## 2. System Overview

#### 2.1. Scenario

#### 2.2. Channel Model

## 3. Single Cell User Scheduling

#### 3.1. Round Robin Scheduler

#### 3.2. Equal Rate Scheduler

## 4. Positioning and Communication for a Fleet of UAVs

#### 4.1. Problem Formulation

#### 4.2. Derivation of the UAV Trajectories

#### 4.2.1. Gradient of the Cost Function

#### 4.2.2. Gradient of the Wireless Backhaul Constraint Functions

Algorithm 1 Positioning Strategy. | |

1: | Start iteration $\left[n\right]$ |

2: | for $i=1:P$ do |

3: | if ${\left(\right)}_{\overline{R}}{R}_{i}$ then |

4: | Add index i to the unfulfilled constraints vector $\mathbf{w}$ |

5: | end if |

6: | end for |

7: | if${\sum}_{j=1}^{P}{B}_{j}^{BH}\ge {B}_{BH}^{total}$then |

8: | Add the index $P+1$ to $\mathbf{w}$ |

9: | end if |

10: | if$\mathbf{w}$ is empty then |

11: | go to 20 |

12: | else |

13: | Randomly select one constraint of $\mathbf{w}$ |

14: | end if |

15: | if selected $i\le P$ then |

16: | go to 24 |

17: | else [the selected index is $P+1$] |

18: | go to 27 |

19: | end if |

20: | Calculate $\overline{R}$ for each region using Equation (22) |

21: | Identify the region ${i}_{0}$ with the lowest $\overline{R}$ |

22: | Find the UAVs to be moved |

23: | Update the positions of the selected UAVs using Equation (28) and taking into account the restrictions imposed by the maximum feasible velocities. Then, go to 29 |

24: | Find the UAVs to be moved |

25: | Update the positions of the selected UAVs using Equation (32) and taking into account the restrictions imposed by the maximum feasible velocities |

26: | Update ${B}_{i}^{BH}$ using Equation (33) and go to 28 |

27: | Subtract a portion from all the bandwidths ${B}_{i}^{BH}$ |

28: | Empty $\mathbf{w}$ |

29: | End iteration $\left[n\right]$ |

#### 4.3. Practical Implementation Aspects

## 5. Energy Consumption

#### 5.1. Vertical Flight

#### 5.2. Forward Flight

## 6. Evaluation and Results

#### 6.1. Scheduling Evaluation

#### 6.2. Positioning Strategy Evaluation

#### 6.3. Comparison to Previous Works

#### 6.3.1. Spiral Algorithm

#### 6.3.2. k-Means Algorithm

#### 6.3.3. Comparison

#### 6.4. Non-Static Scenarios

#### 6.4.1. One UAV Decays

#### 6.4.2. Displacement of the Concentration of Users

#### 6.4.3. Scattering of the Concentration of Users

#### 6.5. Energy Consumption Evaluation

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Example of a complete scenario: three ABBSs linked through a wireless connection to a backhaul ground station.

**Figure 2.**Aggregated rate of the round robin (RR) and the equal rate (ER) schedulers as a function of the cell side.

**Figure 3.**Initial UAV positions and service areas (

**top left**); after 500 iterations (

**top right**); after 1000 iterations (

**center left**); after 1500 iterations (

**center right**); after 2000 iterations (

**bottom left**); and after 3000 iterations (

**bottom right)**.

**Figure 4.**Evolution of the rate per user, for all coverage areas. Each color represents one coverage area using the same colors as the ones assigned to letters in Figure 3.

**Figure 6.**Rearrangement of UAVs when one UAV decays: positions and coverage areas (

**top**); and evolution of the rate per user in each coverage area (

**bottom**). Each color in the bottom figure represents one coverage area using the same colors as the ones assigned to letters in the top figure.

**Figure 7.**Rearrangement of UAVs when subscribers move: positions and coverage areas (

**top**); and evolution of the rate per user in each coverage area (

**bottom**). Each color in the bottom figure represents one coverage area using the same colors as the ones assigned to letters in the top figure.

**Figure 8.**Rearrangement of UAVs when subscribers density returns to uniform: positions and coverage areas (

**top**); and evolution of the rate per user in each coverage area (

**bottom**). Each color in the bottom figure represents one coverage area using the same colors as the ones assigned to letters in the top figure.

**Figure 10.**Evolution of the individual energy consumptions vs the numbers of iterations for: one UAV decays (

**top**); displacement of users (

**center**); and scattering of users (

**bottom**). Each color in the figures represents one UAV using the same colors as the ones assigned to letters in the previous figures in this section.

Parameter | ${\mathit{P}}_{\mathit{T}}$ | ${\mathit{P}}_{{\mathit{T}}_{\mathit{B}\mathit{H}}}$ | ${\mathit{f}}_{\mathit{c}}$ | $\mathit{B}{\mathit{W}}_{\mathit{A}}$ | ${\mathit{G}}_{\mathit{T}}$ | ${\mathit{G}}_{\mathit{R}}$ | ${\mathit{k}}_{\mathit{b}}$ | T | F | $\mathit{\alpha}$ |
---|---|---|---|---|---|---|---|---|---|---|

Value | 25 dBm | 28 dBm | 2 GHz | 20 MHz | 3 | 3 | 1.38 $\times {10}^{23}$ J/K | 290 K | 5 dB | 9.6 |

Parameter | $\beta $ | ${\xi}_{LOS}$ | ${\xi}_{NLOS}$ | $\mu $ | ${\mu}_{BH}$ | Δ | ${B}_{BH}^{total}$ | $\gamma $ | ${T}_{it}$ | $grid$ |

Value | 0.28 | 1 dB | 20 dB | 3 | 5 $\times {10}^{5}$ | 52 m | 180 MHz | 14 kHz | 0.3 s | 50 m/unit |

Parameter | ${\mathit{F}}_{\mathit{m}}$ | ${\mathit{C}}_{\mathit{D}}$ | $\mathsf{\Omega}$ | ${\mathit{\alpha}}_{\mathit{P}}$ | M |
---|---|---|---|---|---|

Value | 0.75 | 1.3 | 20 rad/s | 10${}^{\circ}$ | 2 Kg |

Parameter | n | m | r | a | ${\mathit{V}}_{\mathit{F}}^{\mathit{Max}}$ | ${\mathit{V}}_{\mathit{V}}^{\mathit{Max}}$ | ${\mathit{V}}_{\mathit{V}}^{\mathit{Min}}$ |
---|---|---|---|---|---|---|---|

Value | 6 | 9.6 Kg | 0.267 m | 1.99 m${}^{2}$ | 18 m/s | 5 m/s | −3 m/s |

Algorithm | $\overline{{\mathbf{R}}_{\mathbf{T}}}$ (kbps) | Fairness | TSBB (MHz) |
---|---|---|---|

Proposed | 9.29 | 0.99999 | 179.94 |

Spiral | 9.40 | 0.72860 | 200.64 |

k-Means | 9.47 | 0.86724 | 187.86 |

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**MDPI and ACS Style**

José-Torra, F.; Pascual-Iserte, A.; Vidal, J.
A Service-Constrained Positioning Strategy for an Autonomous Fleet of Airborne Base Stations. *Sensors* **2018**, *18*, 3411.
https://doi.org/10.3390/s18103411

**AMA Style**

José-Torra F, Pascual-Iserte A, Vidal J.
A Service-Constrained Positioning Strategy for an Autonomous Fleet of Airborne Base Stations. *Sensors*. 2018; 18(10):3411.
https://doi.org/10.3390/s18103411

**Chicago/Turabian Style**

José-Torra, Ferran, Antonio Pascual-Iserte, and Josep Vidal.
2018. "A Service-Constrained Positioning Strategy for an Autonomous Fleet of Airborne Base Stations" *Sensors* 18, no. 10: 3411.
https://doi.org/10.3390/s18103411