[Paper Review] Efficient 3-D Placement of an Aerial Base Station in Next Generation Cellular Networks

R. Irem Bor Yaliniz, Amr El‐Keyi+1 more|arXiv (Cornell University)|Jan 1, 2016

UAV Applications and Optimization7 references14 citations

TL;DR

This paper proposes a novel 3-D placement algorithm for drone-cells in next-generation cellular networks, jointly optimizing altitude, horizontal location, and coverage radius to maximize network revenue. By modeling the air-to-ground channel with LoS probability and pathloss, it formulates a quadratically-constrained mixed-integer non-linear program (MINLP) and solves it via bisection search on a derived ratio variable, achieving efficient and accurate placement across diverse urban environments with up to 35 users covered in simulations.

ABSTRACT

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.

Motivation & Objective

• Address the challenge of efficient 3-D placement of drone-cells in next-generation cellular networks to enhance network resilience during unexpected or temporary events.
• Overcome limitations of prior 1-D (altitude-only) or 2-D (horizontal-only) placement models by jointly optimizing altitude, horizontal position, and coverage area.
• Maximize network revenue by maximizing the number of users served, subject to QoS constraints based on minimum required SNR.
• Account for realistic air-to-ground channel characteristics, including LoS probability and pathloss, which vary with altitude and horizontal distance.
• Provide a computationally efficient solution method applicable to diverse urban environments with varying propagation parameters.

Proposed method

• Formulates the 3-D placement problem as a revenue-maximization optimization, where revenue is proportional to the number of users covered.
• Introduces a key ratio variable α = h / r, linking drone altitude h to coverage radius r, enabling transformation of the original problem.
• Derives a function Γ(α) representing the effective SNR as a function of α, which is maximized to determine the optimal α∗.
• Applies a one-dimensional bisection search algorithm to numerically solve for α∗, ensuring convergence to the unique global maximum.
• Transforms the original 3-D problem into a mixed-integer non-linear program (MINLP) using α∗, solvable via interior-point methods (e.g., MOSEK solver).
• Uses the ITU-recommended air-to-ground channel model incorporating LoS probability P(h, ri) and pathloss L(h, ri) dependent on altitude and horizontal distance.

Experimental results

Research questions

• RQ1 How does the optimal 3-D placement of a drone-cell—considering altitude, horizontal position, and coverage radius—maximize network revenue in diverse urban environments?
• RQ2 What is the impact of varying propagation parameters (e.g., ηLoS, ηNLoS, a, b) on the optimal drone-cell placement and coverage performance?
• RQ3 How does the proposed bisection-based method for solving the α∗ optimization compare in efficiency and accuracy to alternative numerical approaches?
• RQ4 To what extent does the 3-D placement strategy outperform 2-D or 1-D placement models in terms of user coverage and network revenue?
• RQ5 How sensitive is the performance of the drone-cell placement algorithm to changes in QoS requirements (e.g., SNR threshold) across different environments?

Key findings

• The proposed 3-D placement algorithm achieves optimal coverage by jointly determining altitude, horizontal position, and radius, with results validated via 100 Monte Carlo simulations.
• The optimal α∗ value, found via bisection search, ensures that users are placed at the edge of the coverage region, minimizing wasted area and maximizing user count.
• In suburban environments, the algorithm achieves the largest coverage area (up to 35 users served), while high-rise urban areas see a dramatic reduction due to increased pathloss (e.g., ηNLoS increased by 13 dB).
• For a QoS threshold of γ3 = 125 dB, the algorithm enables coverage larger than the macrocell size, allowing up to 35 users to be served in dense scenarios.
• The average number of users covered varies by at most one user across simulations, indicating high consistency and robustness of the algorithm across different user distributions.
• The method effectively handles the non-convex and non-linear nature of the 3-D placement problem, providing a computationally efficient solution via MINLP reformulation and bisection search.