Source-linked AI summary
Efficient 3-D Placement of an Aerial Base Station in Next Generation Cellular Networks
R. Irem Bor Yaliniz, Amr El-Keyi, Halim Yanikomeroglu
TL;DR
The paper addresses how to place a rapidly deployable drone-cell when terrestrial infrastructure cannot meet temporary coverage needs. It formulates joint altitude, horizontal location, and coverage-area selection as revenue maximization, then reduces the problem to an efficiently solvable optimization procedure. Numerical studies validate the derivations and show that environment and user clustering affect coverage and revenue.
Problem
Temporary or unexpected cellular demands require aerial assistance, but drone-cell placement must jointly account for horizontal location, altitude, coverage area, and air-to-ground channels.
Method
The paper introduces an altitude-to-coverage variable, uses one-dimensional bisection search, and solves the resulting mixed-integer nonlinear formulation with an interior point optimizer.
Results
Numerical results validate the derivations and show that optimized coverage size and location vary across propagation environments, with high-rise urban conditions reducing coverage and revenue for sparse users.
Takeaways & Limitations
Effective drone-cell deployment must select altitude, coverage size, and horizontal location together while accounting for propagation environment and spatial user clustering.
Abstract
from arXiv · showhide
Agility and resilience requirements of future cellular networks may not be fully satisfied by terrestrial base stations in cases of unexpected or temporary events. A promising solution is assisting the cellular network via low-altitude unmanned aerial vehicles equipped with base stations, i.e., drone-cells. Although drone-cells provide a quick deployment opportunity as aerial base stations, efficient placement becomes one of the key issues. In addition to mobility of the drone-cells in the vertical dimension as well as the horizontal dimension, the differences between the air-to-ground and terrestrial channels cause the placement of the drone-cells to diverge from placement of terrestrial base stations. In this paper, we first highlight the properties of the dronecell placement problem, and formulate it as a 3-D placement problem with the objective of maximizing the revenue of the network. After some mathematical manipulations, we formulate an equivalent quadratically-constrained mixed integer non-linear optimization problem and propose a computationally efficient numerical solution for this problem. We verify our analytical derivations with numerical simulations and enrich them with discussions which could serve as guidelines for researchers, mobile network operators, and policy makers.
I. INTRODUCTION
The paper frames drone-cells as quickly deployable aerial base stations for temporary or unexpected coverage needs, where optimal placement remains challenging. It formulates joint horizontal-and-vertical placement as revenue maximization and develops an efficient numerical solution.
- I. INTRODUCTION: Temporary disruptions, dense demand, and rural connectivity create QoS needs that fixed infrastructure may not economically address.The paper motivates UAV-based assistance because these situations can be unexpected or temporary.
- I. INTRODUCTION: Prior aerial-relay studies often fixed altitude or constrained horizontal placement, while environmental effects on communications were not consistently considered.The cited work spans one-dimensional altitude or two-dimensional horizontal placement and differing channel assumptions.
- I. INTRODUCTION: The paper proposes an efficient 3-D drone-cell placement algorithm that jointly determines the covered area and drone-cell altitude.The formulation also determines the horizontal placement of the drone-cell.
- I. INTRODUCTION: The placement objective is to maximize network revenue, modeled as proportional to the number of users covered by the drone-cell.This connects placement decisions directly to served-user count.
- I. INTRODUCTION: A new altitude-to-coverage variable and one-dimensional bisection search reduce the formulation to a mixed-integer nonlinear problem solved with MOSEK's interior point optimizer.The paper presents numerical results afterward to validate its analytical derivations.
II. SYSTEM MODEL
The system model places a quasi-stationary drone-cell over users not fully served by a terrestrial base station and evaluates service through SNR and air-to-ground pathloss. Because pathloss depends on both altitude and horizontal distance, placement is inherently three-dimensional.
- II. SYSTEM MODEL: User i has known horizontal coordinates (x_i, y_i), while the drone-cell placement variables are altitude h and horizontal location (x_D, y_D).The drone-cell uses fixed transmission power in the modeled assistance scenario.
- II. SYSTEM MODEL: Users are served when received SNR exceeds a common QoS threshold, and maximizing revenue corresponds to offloading the maximum number of users.Placement affects both how many users lie within coverage and the quality of their air-to-ground links.
- II. SYSTEM MODEL: Air-to-ground channels differ from terrestrial channels because aerial links have a higher chance of line-of-sight connectivity and are affected by environmental blockage.The paper discusses Rician, large-scale Rayleigh, free-space, and environment-aware channel models.
- II. SYSTEM MODEL: For user i, the horizontal distance r_i depends on the drone-cell and user coordinates, while line-of-sight probability depends on h and r_i.The environment determines constants a and b in the line-of-sight model.
- II. SYSTEM MODEL: The pathloss model depends on altitude h and horizontal distance r_i, making the drone-cell placement problem three-dimensional.The model includes carrier frequency, speed of light, and environment-dependent LoS and non-LoS losses.
III. EFFICIENT 3-D PLACEMENT OF A UAV
The paper formulates drone-cell deployment as a 3-D placement problem that jointly selects horizontal location, altitude, and coverage region to maximize served users or network revenue. It reduces the formulation to an efficiently solvable MINLP by optimizing an altitude-to-coverage ratio numerically and then solving for placement variables.
- Placement problem: Drone-cell placement jointly determines horizontal location, altitude, and coverage-region size because altitude affects both coverage and the served-user set.Unlike terrestrial cells with known coverage areas, a drone-cell’s coverage region must be identified together with its location and altitude.
- Placement problem: The placement objective identifies the region covering the maximum number of users among users not served by the macrocell.Users are represented with binary service variables, and the QoS condition determines whether each user lies within the drone-cell’s coverage region.
- Problem transformation: The transformed problem is a mixed-integer nonlinear program containing quadratic, exponential, and binary terms, with big-M constraints releasing coverage conditions for unserved users.The formulation uses binary u_i variables and constants M1 and M2 to encode service and coverage conditions.
- Problem transformation: Introducing α as the ratio between altitude h and coverage radius R removes h from the transformed constraint through the function P(α).The coverage condition is expressed with R, while P(α) captures the altitude-dependent propagation relationship after the variable substitution.
- Optimization solution: For the propagation environments considered, Γ(α) has a single maximum α*, whose location is independent of QoS requirement γ and operating frequency f_c.The values of γ and f_c scale Γ(α*) but do not change the maximizing α*; α* is found from the derivative using bisection search.
- Optimization solution: After α* is evaluated, an interior-point optimizer solves the resulting MINLP for drone-cell location, served-user indicators, and coverage radius.The bisection search uses a maximum iteration count and tolerance before MOSEK solves the remaining placement problem.
IV. NUMERICAL RESULTS
Numerical simulations evaluate the proposed placement method across environments, showing that environment parameters affect coverage location, size, and revenue while the method remains consistent across simulations.
- Numerical Results: The bisection search algorithm determines α* before the optimization yields the coverage radius R and drone-cell location.The resulting circular coverage region is illustrated for each environment.
- Numerical Results: The coverage region changes in both size and location across environments, with users often lying on its edge and little area wasted.The altitude is selected so that the coverage boundary reaches users efficiently.
- Numerical Results: The suburban environment produces the largest coverage area, whereas the high-rise urban environment produces the worst coverage.The difference is attributed to reduced blockage in suburban settings compared with high-rise urban settings.
- Numerical Results: Across 100 Monte Carlo simulations with 40 uniformly distributed users, the number of served users varies by at most 1 user.Results include 95% confidence intervals and indicate consistent performance of the proposed method.
- Numerical Results: For sparse user distributions, average revenue in high-rise urban environments is significantly worse than in the other environments.An increase of 13 dB in η_NLoS alone can reduce coverage area by more than 100 times.
V. CONCLUSION
The paper formulates drone-cell assistance as a 3-D placement problem that jointly determines altitude, horizontal location, and coverage size to maximize covered-user revenue. Its equivalent formulation can be solved efficiently, while interference and multiple drone-cells remain future research directions.
- V. CONCLUSION: The air-to-ground channel requires jointly considering drone-cell altitude and horizontal locations of the drone-cell and users.This motivates a 3-D placement formulation rather than separate one- or two-dimensional placement decisions.
- V. CONCLUSION: The objective maximizes revenue, measured as the maximum number of users covered by the drone-cell.The formulation finds the coverage region’s location and size together with the drone-cell altitude.
- V. CONCLUSION: The equivalent optimization problem can be solved efficiently to determine the drone-cell location, coverage-region size, and altitude.
- V. CONCLUSION: Interference and the use of several drone-cells are identified as interesting future research directions.