Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Optimizing Coverage in Convex Quadrilateral Regions with a Single UAV

Alexander Vavoulas, Nicholas Vaiopoulos, Konstantinos K. Delibasis, Harilaos G. Sandalidis

TL;DR

This work addresses the problem of optimally deploying a single UAV to cover an arbitrary convex quadrilateral using a tiltable directional antenna that yields an elliptical ground footprint. It develops two coverage scenarios—the largest inscribed ellipse and the smallest circumscribed ellipse—by employing affine and similarity transforms to compute the ellipse parameters, and it formulates an altitude-optimization framework that jointly considers path loss, SNR, and energy consumption. Key contributions include explicit procedures for generating the inscribed and circumscribed ellipses, deriving altitude-optimal conditions via numerical solutions for $PL_{max}$, $\gamma_{min}$, and $E_C$, and a case study demonstrating trade-offs under diverse environments and antenna directivities. The results provide actionable guidance for energy-efficient UAV-based coverage of irregular regions and lay the groundwork for dynamic altitude control and multi-UAV coordination in realistic scenarios.

Abstract

The integration of unmanned aerial vehicles (UAVs) into next-generation wireless networks is a promising solution for providing flexible, efficient coverage. This paper explores the optimal deployment of a single UAV to cover an arbitrary convex quadrilateral region, utilizing a directional antenna with a tiltable beam that produces an elliptical coverage footprint. We examine two distinct coverage scenarios: (i) the largest inscribed ellipse, which maximizes coverage within the quadrilateral while excluding the boundary, and (ii) the smallest circumscribed ellipse, ensuring complete coverage of the entire area. The study formulates an optimization framework that accounts for path loss, signal-to-noise ratio (SNR), and energy consumption to determine the optimal altitude of the UAV. By employing a simplified path loss model, we derive the altitude that minimizes maximum path loss, while also analyzing the impact of antenna directivity on maximizing the minimum SNR at the coverage boundary. Additionally, the UAV's energy consumption is evaluated, considering the power demands during hovering, forward flight, and vertical takeoff. Numerical simulations are presented to illustrate the trade-offs between coverage effectiveness, communication performance, and energy efficiency across various environmental conditions and antenna configurations.

Optimizing Coverage in Convex Quadrilateral Regions with a Single UAV

TL;DR

This work addresses the problem of optimally deploying a single UAV to cover an arbitrary convex quadrilateral using a tiltable directional antenna that yields an elliptical ground footprint. It develops two coverage scenarios—the largest inscribed ellipse and the smallest circumscribed ellipse—by employing affine and similarity transforms to compute the ellipse parameters, and it formulates an altitude-optimization framework that jointly considers path loss, SNR, and energy consumption. Key contributions include explicit procedures for generating the inscribed and circumscribed ellipses, deriving altitude-optimal conditions via numerical solutions for , , and , and a case study demonstrating trade-offs under diverse environments and antenna directivities. The results provide actionable guidance for energy-efficient UAV-based coverage of irregular regions and lay the groundwork for dynamic altitude control and multi-UAV coordination in realistic scenarios.

Abstract

The integration of unmanned aerial vehicles (UAVs) into next-generation wireless networks is a promising solution for providing flexible, efficient coverage. This paper explores the optimal deployment of a single UAV to cover an arbitrary convex quadrilateral region, utilizing a directional antenna with a tiltable beam that produces an elliptical coverage footprint. We examine two distinct coverage scenarios: (i) the largest inscribed ellipse, which maximizes coverage within the quadrilateral while excluding the boundary, and (ii) the smallest circumscribed ellipse, ensuring complete coverage of the entire area. The study formulates an optimization framework that accounts for path loss, signal-to-noise ratio (SNR), and energy consumption to determine the optimal altitude of the UAV. By employing a simplified path loss model, we derive the altitude that minimizes maximum path loss, while also analyzing the impact of antenna directivity on maximizing the minimum SNR at the coverage boundary. Additionally, the UAV's energy consumption is evaluated, considering the power demands during hovering, forward flight, and vertical takeoff. Numerical simulations are presented to illustrate the trade-offs between coverage effectiveness, communication performance, and energy efficiency across various environmental conditions and antenna configurations.

Paper Structure

This paper contains 20 sections, 30 equations, 8 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Related work
  4. Motivation
  5. Contribution
  6. Organization
  7. Elliptical Cell Generation
  8. Setup configuration
  9. Inscribed ellipse with largest area
  10. Circumscribed ellipse with smallest area
  11. Geometric relationships
  12. UAV Placement and Altitude Optimization
  13. Optimal altitude vs. path loss
  14. Optimal altitude vs. SNR
  15. Optimal altitude vs. energy consumption
  16. ...and 5 more sections

Figures (8)

  • Figure 1: System configurations
  • Figure 2: Geometric transformations for determining the inscribed and circumscribed ellipse.
  • Figure 3: Antenna gain vs. incidence angle for various values of $m$.
  • Figure 4: Maximum path loss vs. altitude, with $H_{\text{OPT}}$ values highlighted for the inscribed (dashed lines) and the circumscribed (solid lines) ellipse.
  • Figure 5: Setup for covering the inscribed ellipse in an urban environment.
  • ...and 3 more figures