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Efficient UAV Coverage in Large Convex Quadrilateral Areas with Elliptical Footprints

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

TL;DR

The paper tackles efficient wireless coverage of a large convex quadrilateral using multiple UAVs that generate elliptical footprints through tilted directional antennas. It introduces a deterministic approach that packs equal circles in a unit square and employs a homography to map the configuration onto the target quadrilateral, producing non-overlapping ellipses with controllable geometry. UAV altitude is optimized per footprint using aLoS/NLoS path loss model to minimize the maximum loss at the coverage boundary, with ellipse axes derived from the transformed circle packing. Case studies show that four and nine UAV configurations achieve substantial coverage (around 75–79%) in a representative area across suburban, urban, and dense urban scenarios, demonstrating scalability and practical deployment potential, while outlining future work on more complex terrains and dynamic interference.

Abstract

Unmanned Aerial Vehicles (UAVs) have gained significant attention for improving wireless communication, especially in emergencies or as a complement to existing cellular infrastructure. This letter addresses the problem of efficiently covering a large convex quadrilateral using multiple UAVs, where each UAV generates elliptical coverage footprints based on its altitude and antenna tilt. The challenge is approached using circle-packing techniques within a unit square to arrange UAVs in an optimal configuration. Subsequently, a homography transformation is applied to map the unit square onto the quadrilateral area, ensuring that the UAVs' elliptical footprints cover the entire region. Numerical simulations demonstrate the effectiveness of the proposed method, providing insight into coverage density and optimal altitude configurations for different placement scenarios. The results highlight the scalability and potential for improving UAV-based communication systems, focusing on maximizing coverage efficiency in large areas with irregular shapes.

Efficient UAV Coverage in Large Convex Quadrilateral Areas with Elliptical Footprints

TL;DR

The paper tackles efficient wireless coverage of a large convex quadrilateral using multiple UAVs that generate elliptical footprints through tilted directional antennas. It introduces a deterministic approach that packs equal circles in a unit square and employs a homography to map the configuration onto the target quadrilateral, producing non-overlapping ellipses with controllable geometry. UAV altitude is optimized per footprint using aLoS/NLoS path loss model to minimize the maximum loss at the coverage boundary, with ellipse axes derived from the transformed circle packing. Case studies show that four and nine UAV configurations achieve substantial coverage (around 75–79%) in a representative area across suburban, urban, and dense urban scenarios, demonstrating scalability and practical deployment potential, while outlining future work on more complex terrains and dynamic interference.

Abstract

Unmanned Aerial Vehicles (UAVs) have gained significant attention for improving wireless communication, especially in emergencies or as a complement to existing cellular infrastructure. This letter addresses the problem of efficiently covering a large convex quadrilateral using multiple UAVs, where each UAV generates elliptical coverage footprints based on its altitude and antenna tilt. The challenge is approached using circle-packing techniques within a unit square to arrange UAVs in an optimal configuration. Subsequently, a homography transformation is applied to map the unit square onto the quadrilateral area, ensuring that the UAVs' elliptical footprints cover the entire region. Numerical simulations demonstrate the effectiveness of the proposed method, providing insight into coverage density and optimal altitude configurations for different placement scenarios. The results highlight the scalability and potential for improving UAV-based communication systems, focusing on maximizing coverage efficiency in large areas with irregular shapes.

Paper Structure

This paper contains 5 sections, 6 theorems, 17 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Homography Transformation
  3. UAV Placement
  4. Case Study
  5. Conclusions and Further Research

Key Result

Theorem 1

The family of horizontal lines $y = y_0$ and vertical lines $x = x_0$, with $x_0$ and $y_0$ as arbitrary constants, intersect under the homography transformation $\mathbf{H}$ at the points $\left( \frac{h_{11}}{h_{31}}, \frac{h_{21}}{h_{31}} \right)$ and $\left( \frac{h_{12}}{h_{32}}, \frac{h_{22}}{

Figures (5)

  • Figure 1: Homography transformation on $Q$.
  • Figure 2: Circle packing in $Q$ vs. ellipse packing in $Q'$.
  • Figure 3: $H_{\mathrm{OPT}}$ and $PL_{\mathrm{max}}$ for four UAVs (indices on the horizontal axes).
  • Figure 4: $H_{\mathrm{OPT}}$ and $PL_{\mathrm{max}}$ for nine UAVs (indices on the horizontal axes).
  • Figure 5: Four and nine UAV placements in the suburban environment.

Theorems & Definitions (12)

  • Theorem 1
  • proof
  • proposition 1
  • proof
  • Theorem 2
  • proof
  • corollary 1
  • proof
  • corollary 2
  • proof
  • ...and 2 more