Geography-aware Optimal UAV 3D Placement for LOS Relaying: A Geometry Approach

TL;DR

This work tackles the problem of geographically aware UAV placement to guarantee LOS relays to two ground terminals in dense urban environments. It develops a geometry-driven optimization framework that exploits upward invariance and colinear invariance to bound the search to a bounded 2D region, enabling a fast trajectory-based search on the middle-perpendicular plane with guaranteed global optimality. Building on this, it introduces a dynamic, multi-stage algorithm that achieves $\epsilon$-optimal 3D placements with complexity $O(1/\epsilon)$ by operating over bounded 2D regions and leveraging closed-form solutions for simple LOS patterns. Across real city-map tests, the methods deliver near-100% optimality with significantly reduced search lengths, enabling reliable UAV relaying and wireless power transfer in urban scenarios.

Abstract

Many emerging technologies for the next generation wireless network prefer line-of-sight (LOS) propagation conditions to fully release their performance advantages. This paper studies 3D unmanned aerial vehicle (UAV) placement to establish LOS links for two ground terminals in deep shadow in a dense urban environment. The challenge is that the LOS region for the feasible UAV positions can be arbitrary due to the complicated structure of the environment. While most existing works rely on simplified stochastic LOS models and problem relaxations, this paper focuses on establishing theoretical guarantees for the optimal UAV placement to ensure LOS conditions for two ground users in an actual propagation environment. It is found that it suffices to search a bounded 2D area for the globally optimal 3D UAV position. Thus, this paper develops an exploration-exploitation algorithm with a linear trajectory length and achieves above 99% global optimality over several real city environments being tested in our experiments. To further enhance the search capability in an ultra-dense environment, a dynamic multi-stage algorithm is developed and theoretically shown to find an $ε$-optimal UAV position with a search length $O(1/ε)$. Significant performance advantages are demonstrated in several numerical experiments for wireless communication relaying and wireless power transfer.

Figures (12)

• Figure 1: Double-LOS regions sliced at the altitude $H_{\text{min}}$ under building topologies in extreme cases from a top view, where the building height is close to the minimum altitude $H_{\min}$. (a) $\tilde{\mathcal{D}}_{0}$ appears off the middle-perpendicular plane between the two users. (b) $\tilde{\mathcal{D}}_{0}$ appears at the top-left in the region, i.e., could be far away from both users.
• Figure 2: Search trajectory on the middle perpendicular plane from the perspective of $\mathbf{u}_{2}$: flying straight down and along the circle makes $r(\mathbf{p})$ gradually decrease, and correspondingly, the objective value $F(\mathbf{p})$ increases.
• Figure 3: Region $\mathcal{B}(\mathbf{p}_{0})$: The status to $\mathbf{u}_{1}$ of a point $\mathbf{p}\in\mathcal{B}(\mathbf{p}_{0})$ can be determined by that of $\mathbf{p}_{1}\in\mathcal{S}$ or $\mathbf{p}_{1}'\in\mathcal{H}$.
• Figure 4: (a) double-ray LOS pattern; (b) double-stripe LOS pattern
• Figure 5: An example of search trajectory on $\mathcal{B}(\mathbf{p}_{0})\cap\mathcal{S}$: The bold solid line represents the critical trajectory. The thin dashed lines with arrows indicate a search trajectory to connect the critical trajectories at different stages ($m=1,2,3$). The light green and light blue shaded areas portray the NLOS patterns to user 1 and user 2, respectively. The overlapping region of the two NLOS patterns is NLOS to both users.

Theorems & Definitions (14)

• Lemma 1: Double-LOS structure on $\mathcal{S}$
• proof
• Lemma 2: Optimality with minimum radius
• proof
• Theorem 1: Global optimality in 2D
• proof
• Proposition 1: Maximum trajectory length
• proof
• Proposition 2: Double-ray LOS Pattern
• proof