Source-linked AI summary
Efficient Deployment of Multiple Unmanned Aerial Vehicles for Optimal Wireless Coverage
Mohammad Mozaffari, Walid Saad, Mehdi Bennis, Merouane Debbah
TL;DR
The paper studies how to deploy multiple directional-antenna UAV base stations to cover a target ground area while managing power, interference, and coverage lifetime. It derives coverage probability and applies circle packing to determine three-dimensional placements. Results show that altitude must be adjusted with UAV count and antenna beamwidth, and that the required UAV count depends on the target area and coverage threshold.
Problem
Deploying multiple UAV base stations requires jointly managing 3D placement, coverage, energy use, and interference for a specified geographical area.
Method
The paper derives downlink coverage probability under probabilistic LoS/NLoS propagation and uses circle packing to optimize non-overlapping UAV coverage with minimum transmit power.
Results
Doubling the UAV count from 3 to 6 reduces the optimal altitude from 2000 m to 1300 m, while higher antenna beamwidths require lower optimal altitude.
Takeaways & Limitations
Altitude and UAV locations can be adjusted according to UAV count, antenna gain or beamwidth, area size, and coverage requirements.
Abstract
from arXiv · showhide
In this paper, the efficient deployment of multiple unmanned aerial vehicles (UAVs) with directional antennas acting as wireless base stations that provide coverage for ground users is analyzed. First, the downlink coverage probability for UAVs as a function of the altitude and the antenna gain is derived. Next, using circle packing theory, the three-dimensional locations of the UAVs is determined in a way that the total coverage area is maximized while maximizing the coverage lifetime of the UAVs. Our results show that, in order to mitigate interference, the altitude of the UAVs must be properly adjusted based on the beamwidth of the directional antenna as well as coverage requirements. Furthermore, the minimum number of UAVs needed to guarantee a target coverage probability for a given geographical area is determined. Numerical results evaluate the various tradeoffs involved in various UAV deployment scenarios.
I. INTRODUCTION
The paper addresses how to deploy multiple UAV base stations in three dimensions while balancing wireless coverage, energy use, and interference. It derives a coverage-based deployment framework using directional antennas and circle packing.
- Motivation: UAVs can serve as flexible aerial base stations for enhanced coverage, rate performance, and rapid on-demand communications.Their higher altitude improves the chance of line-of-sight links, while mobility and directional antennas support flexible deployment and beamforming.
- Challenges: The deployment problem must jointly address optimal 3D placement, energy limitations, interference management, and path planning.Deployment strongly affects both UAV energy consumption and the interference generated by UAVs.
- Research gap: Prior work has only limitedly examined the interplay between UAV deployment and wireless performance.Related studies considered relay connectivity, covered area, or disaster-relief placement, but used differing deployment assumptions.
- Approach: The paper derives coverage probability as a function of altitude and antenna gain, then uses circle packing to maximize non-overlapping coverage with minimum transmit power.The framework determines UAV locations for a target area, coverage requirement, and available number of directional-antenna UAVs.
- Scope: The framework determines altitude, locations, and the minimum UAV count needed to satisfy target coverage for a given geographical area.The paper also evaluates how antenna gain or beamwidth, area size, and UAV availability affect deployment choices.
II. SYSTEM MODEL
The system models M symmetric, stationary low-altitude UAVs covering a circular area with directional antennas. Air-to-ground links use probabilistic LoS/NLoS propagation, path loss, and shadow fading.
- Deployment assumptions: The model deploys M symmetric UAVs with equal transmit power and altitude inside a circular area of radius Rc.Ground users are located within the target area, and the UAVs use directional antennas with half beamwidth θB.
- Antenna model: The directional antenna is characterized by its half beamwidth θB and a main-lobe gain, with additional gain outside the main lobe.The antenna gain depends on the directional-beam configuration.
- Channel model: Air-to-ground propagation separately models LoS and NLoS links, whose occurrence probabilities depend on elevation angle, environment, and relative UAV-user location.NLoS links have higher shadowing and blockage loss than LoS links.
- Received power: Received signal power combines UAV transmit power, antenna gain, path loss, and LoS- or NLoS-specific shadowing loss.The path-loss model depends on carrier frequency, propagation distance, and path-loss exponent n ≥2.
- Fading assumptions: Shadow fading is modeled with normal distributions for LoS and NLoS links, with parameters that depend on elevation angle and environment.The elevation angle is θj = sin^-1(h/dj).
III. OPTIMAL MULTI-UAV DEPLOYMENT
The deployment analysis first determines each UAV’s coverage radius under interference, then optimizes multiple UAV locations to maximize coverage without overlap. The coverage probability is constrained by directional-antenna range and interference conditions.
- Deployment procedure: The method derives a single-UAV coverage radius before optimizing the deployment of M UAVs.The resulting strategy aims to maximize total coverage and coverage lifetime.
- Coverage condition: A ground user can be covered only within r ≤ h·tan(θB/2), the directional antenna’s coverage range.This condition links feasible ground distance to UAV altitude and antenna beamwidth.
- Coverage probability: The coverage probability accounts for the desired UAV’s LoS/NLoS received power and interference from the nearest UAV.The analysis uses mean interference as a tractable approximation and evaluates Gaussian shadowing through the Q function.
10 PNLoS,k
The paper formulates multi-UAV coverage as a non-overlapping circle-packing problem, linking coverage probability, altitude, antenna beamwidth, interference, and coverage lifetime. It uses equal-radius deployments and packing geometry to select UAV locations and constrain altitude for maximizing coverage within a circular area.
- Coverage model: Increasing altitude raises path loss, LoS probability, and feasible coverage radius, while interference may require higher transmit power to meet coverage requirements.The feasible directional-antenna range is constrained by r ≤ h.tan(θB/2).
- Coverage model: Coverage radius ru is the maximum range where coverage probability exceeds threshold ε, depending on transmit power, beamwidth, UAV count, and locations.The coverage condition is defined by Pcov(r, Pt, θB) ≥ ε.
- Deployment formulation: The deployment maximizes total coverage without overlap while using equal transmit power and coverage radius to maximize coverage lifetime.The optimization constrains UAV separation to at least 2ru and keeps each coverage region inside the desired area.
- Circle-packing deployment: Circle packing converts the nonlinear deployment problem into arranging M equal circles inside a larger circle with maximum packing density.Each small circle represents one UAV coverage region, and the resulting packing determines coverage radii and two-dimensional UAV locations.
- Circle-packing deployment: For M = 3, placing the circle centers at the vertices of an equilateral triangle gives the optimal mutually tangent arrangement.This geometry provides the illustrative three-UAV packing used to derive the associated spacing relationship.
- Altitude constraint: Proposition 2 gives a necessary altitude condition for avoiding overlapping coverage, while altitude must be adjusted according to UAV count and antenna beamwidth.The corresponding upper-bound construction is parameterized by the desired-area radius and the number of UAVs.
IV. SIMULATION RESULTS AND ANALYSIS
The simulations show tradeoffs among UAV count, altitude, coverage, coverage lifetime, and geographical area. Optimal deployment depends on coverage requirements, antenna beamwidth, and target-area size.
- Coverage and lifetime: Increasing the number of UAVs increases coverage lifetime because each UAV requires less transmit power.For Rc = 5000 m and θB = 80o, a single UAV provides maximum coverage but minimum lifetime.
- Altitude adjustment: The optimal altitude decreases as the number of UAVs increases to prevent overlapping coverage regions.Reducing height decreases each UAV’s coverage radius according to h = ru tan(θB/2).
- Altitude adjustment: Doubling the UAV count from 3 to 6 reduces optimal altitude from 2000 m to 1300 m.Optimal altitude is also lower for higher antenna beamwidths.
- Required UAV count: For at least 0.7 coverage, either one UAV or more than 6 UAVs are required under the stated simulation conditions.With 1 < M < 7, the 0.7 coverage target cannot be achieved; larger target areas generally require more UAVs.
- Required UAV count: For Rc < 5400 m, one UAV can satisfy a 0.6 coverage threshold, whereas larger areas require additional UAVs.The result uses Pt = 35 dBm, θB = 80o, and optimal altitudes subject to h < 5000 m.
V. CONCLUSIONS
The paper studies directional-antenna UAV deployment using coverage analysis and circle packing. It determines UAV locations and altitudes from UAV count and antenna characteristics while maximizing coverage with minimum transmit power.
- The paper derives downlink coverage probability using probabilistic LoS/NLoS links and shadow fading.
- A circle-packing deployment approach maximizes coverage while each UAV uses minimum transmit power.
- Optimal UAV altitude and location depend on the number of available UAVs and directional-antenna gain or beamwidth.