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3D Placement of an Unmanned Aerial Vehicle Base Station for Maximum Coverage of Users with Different QoS Requirements
Mohamed Alzenad, Amr El-Keyi, Halim Yanikomeroglu
TL;DR
The paper addresses 3D UAV-BS placement for maximizing coverage among users with different QoS requirements. It models coverage as multiple circles, uses exhaustive altitude search for an optimal method, and proposes MWA as a lower-complexity alternative. Simulations report performance very close to ES with significant complexity reduction.
Problem
The paper studies where to deploy a UAV-BS so it maximizes coverage of users with different QoS requirements under limited transmit power.
Method
The placement is modeled as a multiple-circles problem, solved optimally by exhaustive search over altitude and approximately by the low-complexity MWA algorithm.
Results
MWA performs very close to ES, while ES has the worst execution time and a significant gap relative to MWA and LQ.
Takeaways & Limitations
MWA provides a low-complexity placement solution with coverage performance close to the exhaustive-search benchmark.
Abstract
from arXiv · showhide
The need for a rapid-to-deploy solution for providing wireless cellular services can be realized by unmanned aerial vehicle base stations (UAV-BSs). To the best of our knowledge, this letter is the first in literature that studies a novel 3D UAV-BS placement that maximizes the number of covered users with different Quality-of-Service requirements. We model the placement problem as a multiple circles placement problem and propose an optimal placement algorithm that utilizes an exhaustive search (ES) over a one-dimensional parameter in a closed region. We also propose a low-complexity algorithm, namely, maximal weighted area (MWA) algorithm to tackle the placement problem. Numerical simulations are presented showing that the MWA algorithm performs very close to the ES algorithm with a significant complexity reduction.
I. INTRODUCTION
UAV-BSs offer rapid wireless-service deployment, but placing one is a challenging 3D optimization problem when users have different QoS requirements and limited transmit power. The paper formulates this setting and proposes ES and MWA solutions.
- UAV-BSs can rapidly provide wireless services during terrestrial-BS malfunctions or congestion.
- A2G path loss depends on both user and UAV-BS locations, making placement inherently three-dimensional.
- Limited onboard energy can prevent full serving-area coverage, so partial coverage may be unavoidable.
- The paper maximizes covered users with different QoS requirements through a multiple-circles placement model.
- MWA performs very close to exhaustive search in simulations while substantially reducing complexity.
II. SYSTEM MODEL
The system models stationary or low-mobility users grouped by SNR-based QoS requirements and evaluates UAV-BS coverage through probabilistic mean path loss. Each QoS group produces a height-dependent circular coverage region.
- Users are stationary or low-mobility and partitioned into K QoS groups with requirements defined by SNR.
- The UAV-BS path-loss model combines LoS and NLoS links with environment-dependent occurrence probabilities and additional losses.
- Coverage is declared when a user's probabilistic mean SNR exceeds its predefined QoS threshold.
- For a fixed altitude and QoS requirement, the coverage region is a circular disc whose radius depends on altitude.
- With multiple QoS requirements, the overall coverage region becomes a set of concentric circular discs with radii determined by their thresholds.
III. PROBLEM FORMULATION AND ALGORITHMS
The placement formulation uses shared-center coverage discs and binary user-coverage variables, producing a MINLP because altitude and horizontal location are coupled through the radii. The algorithms decouple these dimensions by searching altitude over a guaranteed closed region.
- All QoS-specific coverage discs share the UAV-BS horizontal center, and a user is covered when it lies within its group's radius.
- Binary variables indicate whether users lie inside their corresponding coverage discs, while big-M constraints encode the placement conditions.
- The resulting placement problem is a MINLP because altitude and horizontal location are coupled through the height-dependent coverage radii.
- The proposed decoupling searches altitude over a closed region guaranteed to contain an optimal solution, then solves the horizontal placement problem.
- Coverage radii are concave in altitude with one maximum, and enlarging a radius cannot decrease the placement objective.
A. Exhaustive search (ES):
The ES algorithm exhaustively searches the UAV-BS altitude over a closed interval, computes the associated coverage radii, and solves the resulting horizontal placement problem at each candidate altitude.
- ES searches exhaustively for the optimal altitude over the closed interval [h*_1, h*_K].
- For each searched altitude, ES computes all QoS-specific coverage radii numerically.
- ES then solves the horizontal UAV-BS location problem for the computed radii.
- The horizontal subproblem is a MISOCP with worst-case complexity O(2^n n^3.5 log(ε^-1)).
B. Maximal weighted area (MWA)
The MWA algorithm selects an altitude by maximizing the average number of covered users under uniform user distributions, then solves the placement problem at that altitude.
- For uniformly distributed users with density λ_k, Navg(h) denotes the average number of covered users at UAV-BS altitude h.
- Maximizing Navg(h) depends only on the UAV-BS altitude.
- The optimal altitude h*_M is found numerically by searching an implicit equation with a solution in [h*_1, h*_K], which may not be unique.
- MWA deploys the UAV-BS at h*_M and then reduces the placement problem to the stated optimization problem.
- The resulting formulation is a MISOCP.
IV. SIMULATION RESULTS
Simulations compare UAV-BS placement algorithms in a 3 km × 3 km urban area with two uniformly distributed user classes and fixed total density. ES and MWA achieve similar coverage, while MWA avoids ES’s execution-time cost and both outperform LQ as density imbalance grows.
- Simulation setup: The simulation uses a square 3 km × 3 km urban area, two user classes, and fixed total density λ = 11 users/km2.The users are uniformly distributed with densities λ1 and λ2.
- Simulation setup: The LQ baseline assumes a common QoS requirement γ_th = 50 dB and deploys the UAV-BS at h*_LQ = 646.5 m.This produces a maximal coverage radius R* = 707 m.
- Simulation setup: The ES altitude search covers [646.5, 913] m using a nine-point grid with discretization step Δh = 29.6 m.
- Coverage and execution time: For ρ = 1, ES and MWA have very close covered-user performance and both outperform LQ.The comparison uses the CDF of the number of covered users.
- Coverage and execution time: For ρ = 1, ES has the worst execution time, with a significant gap relative to MWA and LQ.
- Density-ratio comparison: As ρ increases, the coverage gap between MWA or ES and LQ increases because LQ does not consider the density of users in U2.
V. CONCLUSION
The paper formulates 3D UAV-BS placement for users with different QoS requirements as a multiple circles placement problem and proposes ES and MWA algorithms. Simulations show that MWA closely matches ES with significantly lower complexity.
- The study addresses 3D UAV-BS placement to maximize covered users with different QoS requirements.
- The placement problem is modeled as a multiple circles placement problem.
- An optimal placement algorithm uses exhaustive search over a one-dimensional parameter in a closed region.
- The low-complexity MWA algorithm solves the placement problem.
- Simulations show that MWA performs very close to ES with a significant reduction in complexity.