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

^{*}

^{†}

## 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 ${\left.\overline{R}\right|}_{{R}_{i}}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{N}_{i}\ge {R}_{i}^{BH}$ 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

- Ahmed, N.; Kanhere, S.S.; Jha, S. On the importance of link characterization for aerial wireless sensor networks. IEEE Commun. Mag.
**2016**, 54, 52–57. [Google Scholar] [CrossRef] - Feng, Q.; McGeehan, J.; Tameh, E.K.; Nix, A.R. Path loss models for air-to-ground radio channels in urban environments. In Proceedings of the 2006 IEEE 63rd Vehicular Technology Conference (VTC), Melbourne, Australia, 7–10 May 2006; pp. 2901–2905. [Google Scholar]
- Al-Hourani, A.; Kandeepan, S.; Jamalipour, A. Modeling air-to-ground path loss for low altitude platforms in urban environments. In Proceedings of the 2014 IEEE Global Communications Conference (GLOBECOM), Austin, TX, USA, 8–12 December 2014; pp. 2898–2904. [Google Scholar]
- Mozaffari, M.; Saad, W.; Bennis, M.; Debbah, M. Drone small cells in the clouds: Design, deployment and performance analysis. In Proceedings of the 2015 IEEE Global Communications Conference (GLOBECOM), San Diego, CA, USA, 6–10 December 2015; pp. 1–6. [Google Scholar]
- Chandrasekharan, S.; Gomez, K.; Al-Hourani, A.; Kandeepan, S.; Rasheed, T.; Goratti, L.; Reynaud, L.; Grace, D.; Bucaille, I.; Wirth, T.; et al. Designing and implementing future aerial communication networks. IEEE Commun. Mag.
**2016**, 54, 26–34. [Google Scholar] [CrossRef] [Green Version] - Holis, J.; Pechac, P. Elevation dependent shadowing model for mobile communications via high altitude platforms in built-up areas. IEEE Trans. Antennas Propag.
**2008**, 56, 1078–1084. [Google Scholar] [CrossRef] - Hourani, A.; Chandrasekharan, S.; Kaandorp, G.; Glenn, W.; Jamalipour, A.; Sithamparanathan, K. Coverage and rate analysis of aerial base stations. IEEE Trans. Aerosp. Electron. Syst.
**2016**, 52, 3077–3081. [Google Scholar] [CrossRef] - Bor-Yaliniz, R.I.; El-Keyi, A.; Yanikomeroglu, H. Efficient 3-D placement of an aerial base station in next generation cellular networks. In Proceedings of the 2016 IEEE International Conference on Communications (ICC), Kuala Lumpur, Malaysia, 22–27 May 2016; pp. 1–5. [Google Scholar] [CrossRef]
- Xiao, Z.; Xia, P.; Xia, X. Enabling UAV cellular with millimeter-wave communication: potentials and approaches. IEEE Commun. Mag.
**2016**, 54, 66–73. [Google Scholar] [CrossRef] [Green Version] - Fotouhi, A.; Ding, M.; Hassan, M. Dynamic base station repositioning to improve performance of drone small cells. In Proceedings of the 2016 IEEE Global Communications Conference (GLOBECOM), Washington, DC, USA, 4–8 December 2016; pp. 1–6. [Google Scholar]
- Jeong, S.; Simeone, O.; Kang, J. Mobile Edge Computing via a UAV-Mounted Cloudlet: Optimization of Bit Allocation and Path Planning. IEEE Trans. Veh. Technol.
**2018**, 67, 2049–2063. [Google Scholar] [CrossRef] [Green Version] - Lyu, J.; Zeng, Y.; Zhang, R.; Lim, T.J. Placement Optimization of UAV-Mounted Mobile Base Stations. IEEE Commun. Lett.
**2016**. [Google Scholar] [CrossRef] - Koulali, S.; Sabir, E.; Taleb, T.; Azizi, M. A green strategic activity scheduling for UAV networks: A sub-modular game perspective. IEEE Commun. Mag.
**2016**, 54, 58–64. [Google Scholar] [CrossRef] - Van Der Bergh, B.; Chiumento, A.; Pollin, S. LTE in the sky: trading off propagation benefits with interference costs for aerial nodes. IEEE Commun. Mag.
**2016**, 54, 44–50. [Google Scholar] [CrossRef] - Merwaday, A.; Guvenc, I. UAV assisted heterogeneous networks for public safety communications. In Proceedings of the 2015 IEEE Wireless Communications and Networking Conference (WCNC), New Orleans, LA, USA, 9–12 March 2015; pp. 329–334. [Google Scholar]
- Galkin, B.; Kibilda, J.; DaSilva, L.A. Deployment of UAV-mounted access points according to spatial user locations in two-tier cellular networks. In Proceedings of the 2016 IEEE Wireless Days (WD), Toulouse, France, 23–25 March 2016; pp. 1–6. [Google Scholar]
- Anderberg, M.R. Cluster Analysis for Applications, 1st ed.; Academic Press: New York, NY, USA, 1973. [Google Scholar]
- Rosati, S.; Krużelecki, K.; Heitz, G.; Floreano, D.; Rimoldi, B. Dynamic routing for flying ad hoc networks. IEEE Trans. Veh. Technol.
**2016**, 65, 1690–1700. [Google Scholar] [CrossRef] - Friis, H.T. A note on a simple transmission formula. Proc. IEEE
**1946**, 34, 254–256. [Google Scholar] [CrossRef] - Zeng, Y.; Zhang, R.; Lim, T.J. Wireless communications with unmanned aerial vehicles: opportunities and challenges. IEEE Commun. Mag.
**2016**, 54, 36–42. [Google Scholar] [CrossRef] [Green Version] - Mylin, A.K. A Communication Link Reliability Study for Small Unmanned Aerial Vehicles. Master’s Thesis, University of Kentucky, Lexington, KY, USA, 2007. [Google Scholar]
- Cheng, C.; Hsiao, P.; Kung, H.; Vlah, D. Maximizing throughput of UAV-relaying networks with the load-carry-and-deliver paradigm. In Proceedings of the 2007 IEEE Wireless Communications and Networking Conference (WCNC), Hong Kong, China, 11–15 March 2007; pp. 4420–4427. [Google Scholar]
- 3GPP TR 36.814, Technical Specification Group Radio Access Network. Evolved Universal Terrestrial Radio Access (E-UTRA), Further Advancements for E-UTRA Physical Layer Aspects; Technical Report; 3rd Generation Partnership Project (3GPP): Valbonne, France, March 2010. [Google Scholar]
- Biglieri, E.; Taricco, G. Transmission and Reception with Multiple Antennas: Theoretical Foundations; Now Publishers Inc.: Delft, The Netherlands, 2004. [Google Scholar]
- Maeng, S.J.; Park, H.I.; Cho, Y.S. Preamble Design Technique for GMSK-Based Beamforming System with Multiple Unmanned Aircraft Vehicles. IEEE Trans. Veh. Technol.
**2017**, 66, 7098–7113. [Google Scholar] [CrossRef] - Boyd, S.; Vandenberghe, L. Convex Optimization; Cambridge University Press: Cambridge, UK, 2004. [Google Scholar]
- Boyd, S.; Mutapcic, A. Subgradient Methods; Lecture Notes of EE364b; Stanford University: Stanford, CA, USA, 23 January 2007. [Google Scholar]
- Auer, G.; Blume, O.; Giannini, V.; Godor, I.; Imran, M.; Jading, Y.; Katranaras, E.; Olsson, M.; Sabella, D.; Skillermark, P.; et al. D2. 3: Energy Efficiency Analysis of the Reference Systems, Areas of Improvements and Target Breakdown; Technical Report INFSO-ICT-247733 EARTH; Earth Project: Durham, NC, USA, 31 December 2010. [Google Scholar]
- Di Franco, C.; Buttazzo, G. Energy-aware coverage path planning of UAVs. In Proceedings of the 2015 IEEE International Conference on Autonomous Robot Systems and Competitions (ICARSC), Vila Real, Portugal, 8–10 April 2015; pp. 111–117. [Google Scholar]
- Morbidi, F.; Cano, R.; Lara, D. Minimum-energy path generation for a quadrotor UAV. In Proceedings of the 2016 IEEE International Conference on Robotics and Automation (ICRA), Stockholm, Sweden, 16–21 May 2016; pp. 1492–1498. [Google Scholar]
- Dorling, K.; Heinrichs, J.; Messier, G.G.; Magierowski, S. Vehicle routing problems for drone delivery. IEEE Trans. Syst. Man Cybern. Syst.
**2017**, 47, 70–85. [Google Scholar] [CrossRef] - Filippone, A. Flight Performance of Fixed and Rotary Wing Aircraft, 1st ed.; Elsevier: Amsterdam, The Netherlands, 2006. [Google Scholar]
- Sankar, L.N. Helicopter Aerodynamics and Performance. Available online: https://studylib.net/doc/9642416/helicopter-aerodynamics-and-performance (accessed on 5 June 2018).
- Lee, A.Y.; Bryson, A.E.; Hindson, W.S. Optimal landing of a helicopter in autorotation. J. Guid. Control Dyn.
**1988**, 11, 7–12. [Google Scholar] [CrossRef] [Green Version] - Mozaffari, M.; Saad, W.; Bennis, M.; Debbah, M. Mobile unmanned aerial vehicles (UAVs) for energy-efficient Internet of Things communications. arXiv, 2017; arXiv:1703.05401. [Google Scholar]
- Grigorie, T.; Dinca, L.; Corcau, J.I.; Grigorie, O. Aircrafts’ Altitude Measurement Using Pressure Information: Barometric Altitude and Density Altitude. WSEAS Trans. Circuits Syst.
**2010**, 9, 503–512. [Google Scholar] - Jain, R.; Chiu, D.M.; Hawe, W.R. A Quantitative Measure of Fairness and Discrimination For Resource Allocation in Shared Computer System; Technical Report DEC-TR-301: Hudson, MA, USA, 26 September 1984. [Google Scholar]
- DJI Matrice 600 Specifications. Available online: http://www.dji.com/matrice600/info#specs (accessed on 5 June 2018).
- NanoLTE: High Speed Coverage Where It Is Needed Most. Available online: https://fccid.io/pdf.php?id=3068683 (accessed on 5 June 2018).

**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 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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