# Dynamic Repositioning of Aerial Base Stations for Enhanced User Experience in 5G and Beyond

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

- This paper proposes a novel idea of potential candidate positions, a subset of which will be chosen for the placement of ABSs based on user density.
- This paper formulates the problem of optimal ABS placement at a subset of the candidate positions to maximize received power and SIR.
- This paper develops solutions for the formulated problems to determine the optimal placement of ABSs.

## 2. Related Works

## 3. System Model

_{u}} be the set of ABSs and S = {1, 2,3, …,N

_{s}} be the set of users. Let L = {1,2,3, …,N

_{l}} be the set of N

_{l}candidate locations for UAV placement. There are more candidate locations than the number of UAVs, i.e., N

_{l}> N

_{u}. All ABSs have the same transmission power P

_{s}. We assume that the main source of noise for a user is the interference caused by ABSs other than the one with which the user is associated and that the thermal noise is negligible.

#### 3.1. Aerial Base Stations

#### 3.2. Candidate Locations for ABSs

#### 3.3. Path Loss Model

_{LoS}and η

_{NLoS}represent the additional losses in the cases of LoS and NLoS, respectively. The value for d is given by $\sqrt{{h}^{2}+{r}^{2}}$, where h and r are the altitudes of the UAV and its horizontal distance from the receiver, respectively. P(LoS) is given by

## 4. Problem Formulation

_{i}be a zero–one indicator variable with A

_{i}= 1 if an ABS is deployed at candidate location i; otherwise, A

_{i}= 0. Similarly, let B

_{i,j}be a zero–one indicator variable with B

_{i,j}= 1 if user j is connected to the ABS at candidate location i; otherwise, B

_{i,j}= 0. Let P

_{i,j}be the power received by user j from the ABS at location i. If user j is connected to the ABS at location r, then the signal-to-interference noise ratio at user j will be:

_{j}be the power received by a user j from the candidate location to which it is assigned; then,

_{i}controls where to place an ABS and B

_{i,j}controls to which location to assign a user such that the corresponding summation is maximized.

_{i}= 1. This means:

_{u}is the number of ABSs, the following constraint should be satisfied:

#### 4.1. Maximizing the Sum of Received Powers

_{i}B

_{i,j}= 1,∀j ∈ S

#### 4.2. Maximizing the Sum of SIRs

_{i}B

_{i,j}= 1, ∀j ∈ S

## 5. Solution Modeling

_{eq}, B

_{eq}) produces a vector X whose entries are binary values and a variable Val = F

^{T}X, which is the value that is minimized; F

^{T}represents the transpose of F. The arguments A

_{eq}and B

_{eq}are used for equality constraints such that A

_{eq}X = B

_{eq}, whereas A and B are used for inequality constraints such that AX ≤ B. A

_{eq}is a matrix whose number of rows should equal the number of equality constraints and whose columns should equal to the number of 0–1 variables.

_{s}-by-N

_{l}matrix P, where P

_{i,j}represents the power received by user i from candidate location j.

_{eq}is an (N

_{s}+ 1)-by-(N

_{s}+ 1)N

_{l}matrix, whereas B

_{eq}is an (N

_{s}+ 1)-by-1 vector. This means that there are N

_{s}+ 1 equality constraints. The first equality constraint ensures that exactly N

_{u}UAVs (small cells are deployed and the remaining N

_{s}constraints ensure that each user is assigned to exactly one candidate location. (Note that we ensure through inequality constraints that each user is assigned to a candidate location with a deployed small cell; we will discuss this shortly). F is an (N

_{s}+ 1)N

_{l}-by-1 vector and is constructed such that the first N

_{l}entries are set to zero and entries iN

_{l}+ 1 through (i + 1)N

_{l}are set to the received powers of user i from all candidate locations: 1 through N

_{l}. A

_{eq}is constructed as given in Algorithm 1.

Algorithm 1: Construction of matrix A_{eq} for received power maximization |

Input: Number of users, N_{s} and Number of candidate positions, N_{l} |

Output: Matrix A_{eq} |

for i = 1 upto N_{s} + 1A _{eq}[i][(i − 1)N_{l} + 1:(i − 1) N_{l} + N_{l}] = 1end |

_{eq}is constructed as B

_{eq}= [N

_{u}O]

^{T}, where N

_{u}is the number of ABSs and O is row vector of size N

_{s}and each of its entries is 1. Moreover, A is an N

_{s}N

_{l}by (N

_{s}+ 1)N

_{l}matrix, whereas b is an N

_{s}N

_{l-}by-1 vector. Then, for the inequality constraint, the matrix is constructed as given in Algorithm 2.

Algorithm 2: Construction of matrix A for received power maximization |

Input: Number of users, N_{s} and Number of candidate positions, N_{l} |

Output: Matrix A |

for i = 1 upto N_{s}for j = 1 upto N_{l}A[(i − 1)N _{l} + j][j]=1A[(i − 1)N _{l} + j][iN_{l} + j] = −1endend |

_{s}N

_{l}-by-1 column vector and is initialized to all zero entries; that is, B[1:N

_{s}N

_{l}] = 0. The matrix F is constructed as shown in Algorithm 3.

Algorithm 3: Construction of vector F for received power maximization |

Input: Number of users, N_{s}, Number of candidate positions, N_{l} and Matrix of received powers, P |

Output: Vector F |

F[1:N_{l}] = 0for i = 1 upto N_{s}F[iN _{s} + 1: (i + 1)N_{s}] = P[i][:]endF = F ^{T} |

_{eq}is constructed as given in Algorithm 4.

Algorithm 4: Construction of matrix A_{eq} for SIR maximization |

Input: Number of users, N_{s} and Number of candidate positions, N_{l} |

Output: Matrix A_{eq} |

Take two auxiliary matrices T and Z, each of dimensions (N_{s} + 1)-by-(N_{s} N_{l} + N_{l}) of all zero entriesfor i = 1 upto N_{s} + 1T[i][(i − 1)N _{l} + 1:(i − 1) N_{l} + N_{l}] = 1end${\mathrm{A}}_{\mathrm{eq}}=\left[\begin{array}{cc}T& Z\\ Z& T\end{array}\right]$ A _{eq}[1][ N_{l} + 1:2(N_{s} N_{l} + N_{l})] = 0 |

_{eq}is constructed as B

_{eq}= [N

_{u}O N

_{u}(N

_{u}− 1)O]

^{T}, where O is a row vector of size N

_{s}containing all ones.

Algorithm 5: Construction of matrix A for SIR maximization |

Input: Number of users, N_{s} and Number of candidate positions, N_{l} |

Output: Matrix A |

Take four auxiliary amatrices A_{1}, A_{2}, A_{3} and A_{4} each of dimensions NsNl-by-(N_{s} + 1)N_{l}Initialize A_{1}, A_{2}, A_{3} and A_{4} to zero (that is, make all their entries zero)for i = 1 upto N_{s}for j = 1 upto N_{l}A _{1}[(i − 1)N_{l} + j][j] = 1A _{1} [(i − 1)N_{l} + j][iN_{l} + j] = −1A _{2}[(i − 1)N_{l} + j][j] = 1A _{3}[(i − 1)N_{l}+j][iN_{l} + j] = −1 endend$\mathrm{A}=\left[\begin{array}{cc}{A}_{1}& {A}_{4}\\ {A}_{2}& {A}_{3}\end{array}\right]$ |

_{s}N

_{l}+ N

_{l})-by-1 column vector and is initialized to all zero entries.

Algorithm 6: Construction of vector F for received power maximization |

Input: Number of users, N_{s}, Number of candidate positions, N_{l} and Matrix of received powers, P |

Output: Vector F |

F_{1}[1:N_{l}] = 0;for i = 1 upto N_{s}F _{1}[iN_{s} + 1: (i + 1)N_{s}] = P[i][:]F _{1} = F_{1}^{T}$\mathrm{F}=\left[\begin{array}{c}\mathrm{F}1\\ -\mathrm{F}1\end{array}\right]$ |

## 6. Results and Discussion

^{2}. The heights of candidate positions (and hence those of the ABSs) were maintained between 50 and 100 m. The transmit power of the ABSs was kept at 30 dBm. User positions were generated using the Poisson point process and Poisson cluster process. A Poisson cluster process is a mathematical model used to describe the spatial distribution of points in a given region. In this process, points are grouped into clusters, where each cluster is generated independently according to a Poisson distribution. The superposition of these clusters allows for individual points to be random and have the tendency to cluster together in certain regions. Candidate positions for ABSs were generated using evenly spaced grid points. A suburban environment was considered with the parameters given in Table 1.

#### 6.1. Results

#### 6.2. Discussion

## 7. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Harald, B.; Blennerud, G.; Burstedt, F.; Chaisatien, W.; Karikyt, M. Ericsson Mobility Report; Tech. Rep.: Stockholm, Sweden, 2022. [Google Scholar]
- Andrews, J.G.; Buzzi, S.; Choi, W.; Hanly, S.V.; Lozano, A. What will 5g be? IEEE J. Sel. Areas Commun.
**2014**, 32, 1065–1082. [Google Scholar] [CrossRef] - Khodabandelou, G.; Gauthier, V.; Fiore, M.; El-Yacoubi, M.A. Estimation of static and dynamic urban populations with mobile network metadata. IEEE Trans. Mob. Comput.
**2019**, 18, 2034–2047. [Google Scholar] [CrossRef] [Green Version] - Rahman, S.U.; Kim, G.-H.; Cho, Y.-Z.; Khan, A. Positioning of UAVs for throughput maximization in software-defined disaster UAV communication networks. J. Commun. Netw.
**2018**, 20, 452–463. [Google Scholar] [CrossRef] - Liu, X.; Li, Z.; Zhao, N.; Meng, W.; Gui, G. Transceiver design and multihop d2d for UAV IoT coverage in disasters. IEEE Internet Things J.
**2019**, 6, 1803–1815. [Google Scholar] [CrossRef] [Green Version] - Horváth, D.; Gazda, J.; Šlapak, E.; Maksymyuk, T.; Dohler, M. Evolutionary coverage optimization for a self-organizing UAV-based wireless communication system. IEEE Access
**2021**, 9, 145066–145082. [Google Scholar] [CrossRef] - Zhang, Q.; Saad, W.; Bennis, M.; Lu, X.; Debbah, M. Predictive deployment of UAV base stations in wireless networks: Machine learning meets contract theory. IEEE Trans. Wirel. Commun.
**2021**, 20, 637–652. [Google Scholar] [CrossRef] - Zeng, Y.; Guvenc, I.; Zhang, R.; Geraci, G.; Matolak, D. UAV Communications for 5G and Beyond; John Wiley and Sons Inc.: Hoboken, NJ, USA, 2020. [Google Scholar]
- Rahman, S.U.; Cho, Y.Z. UAV positioning for throughput maximization. EURASIP J. Wirel. Commun. Netw.
**2018**, 2018, 31. [Google Scholar] [CrossRef] - Munaye, Y.Y.; Lin, H.-P.; Adege, A.B.; Tarekegn, G.B. UAV positioning for throughput maximization using deep learning approaches. Sensors
**2019**, 19, 2775. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Li, L.; Chang, T.-H.; Cai, S. UAV positioning and power control for two-way wireless relaying. IEEE Trans. Wirel. Commun.
**2020**, 19, 1008–1024. [Google Scholar] [CrossRef] [Green Version] - Rosário, D.; Filho, J.A.; do Rosário, D.; Santos, A.; Gerla, M.L. A relay placement mechanism based on UAV mobility for satisfactory video transmissions. In Proceedings of the 16th Annual Mediterranean Ad Hoc Networking Workshop, Med-Hoc-Net, Budva, Montenegro, 28 June 2017. [Google Scholar]
- Al-Hourani, A.; Kandeepan, S.; Lardner, S. Optimal lap altitude for maximum coverage. IEEE Wirel. Commun. Lett.
**2014**, 3, 569–572. [Google Scholar] [CrossRef] [Green Version] - Bor-Yaliniz, I.; Yanikomeroglu, H. The new frontier in ran heterogeneity: Multi-tier drone-cells. Comm. Mag.
**2016**, 54, 48–55. [Google Scholar] [CrossRef] [Green Version] - Guo, W.; and Farrell, T.O. Relay deployment in cellular networks: Planning and optimization. IEEE J. Sel. Areas Commun.
**2013**, 31, 1597–1606. [Google Scholar] - Kalantari, E.; Shakir, M.Z.; Yanikomeroglu, H.; Yongaçoglu, A. Backhaul-aware robust 3D drone placement in 5G+ wireless networks. arXiv
**2017**, arXiv:1702.08395. [Google Scholar] - Dixon, C.; Frew, E.W. Optimizing cascaded chains of unmanned aircraft acting as communication relays. IEEE J. Sel. Areas Commun.
**2012**, 30, 883–898. [Google Scholar] [CrossRef] - Chen, Y.; Feng, W.; Zheng, G. Optimum placement of UAVs as relays. IEEE Commun. Lett.
**2018**, 22, 248–251. [Google Scholar] [CrossRef] [Green Version] - Alzenad, M.; El-Keyi, A.; Yanikomeroglu, H. 3-d placement of an unmanned aerial vehicle base station for maximum coverage of users with different QoS requirements. IEEE Wirel. Commun. Lett.
**2018**, 7, 38–41. [Google Scholar] [CrossRef] [Green Version] - Cheng, F.; Zhang, S.; Li, Z.; Chen, Y.; Zhao, N. UAV trajectory optimization for data offloading at the edge of multiple cells. IEEE Trans. Veh. Technol.
**2018**, 67, 6732–6736. [Google Scholar] [CrossRef] [Green Version] - Zhan, P.; Yu, K.; Swindlehurst, A.L. Wireless relay communications with unmanned aerial vehicles: Performance and optimization. IEEE Trans. Aerosp. Electron. Syst.
**2011**, 47, 2068–2085. [Google Scholar] [CrossRef] - Al-Hourani, A.; Kandeepan, S.; Jamalipour, A. Modeling air-toground path loss for low altitude platforms in urban environments. In Proceedings of the IEEE Global Communications Conference, Austin, TX, USA, 8 December 2014. [Google Scholar]
- Filo, M.; Foh, C.H.; Vahid, S.; Tafazolli, R. Performance impact of antenna height in ultra-dense cellular networks. In Proceedings of the IEEE International Conference on Communications Workshops (ICC Workshops), Paris, France, 3 July 2017. [Google Scholar]
- Lin, Z.; Lin, M.; Champagne, B.; Zhu, W.-P. Secrecy-Energy Efficient Hybrid Beamforming for Satellite-Terrestrial Integrated Networks. IEEE Trans. Commun.
**2021**, 69, 6345–6360. [Google Scholar] [CrossRef] - Lin, Z.; An, K.; Niu, H.; Hu, Y.; Chatzinotas, S.; Zheng, G.; Wang, J. SLNR-Based Secure Energy Efficient Beamforming in Multibeam Satellite Systems. IEEE Trans. Aerosp. Electron. Syst.
**2023**, 59, 2085–2088. [Google Scholar] [CrossRef]

**Figure 5.**PMF of the percentage of users receiving performance improvement when user positions were generated as Poisson cluster process.

**Figure 6.**PMF of the percentage of users receiving performance improvement when user positions were generated as Poisson point process.

Parameter | Value |
---|---|

a | 4.88 |

b | 0.49 |

ηLoS | 0.1 dB |

ηNLoS | 21 dB |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Rahman, S.U.; Khan, A.; Usman, M.; Bilal, M.; Cho, Y.-Z.; El-Sayed, H.
Dynamic Repositioning of Aerial Base Stations for Enhanced User Experience in 5G and Beyond. *Sensors* **2023**, *23*, 7098.
https://doi.org/10.3390/s23167098

**AMA Style**

Rahman SU, Khan A, Usman M, Bilal M, Cho Y-Z, El-Sayed H.
Dynamic Repositioning of Aerial Base Stations for Enhanced User Experience in 5G and Beyond. *Sensors*. 2023; 23(16):7098.
https://doi.org/10.3390/s23167098

**Chicago/Turabian Style**

Rahman, Shams Ur, Ajmal Khan, Muhammad Usman, Muhammad Bilal, You-Ze Cho, and Hesham El-Sayed.
2023. "Dynamic Repositioning of Aerial Base Stations for Enhanced User Experience in 5G and Beyond" *Sensors* 23, no. 16: 7098.
https://doi.org/10.3390/s23167098