Active Search for Low-altitude UAV Sensing and Communication for Users at Unknown Locations

TL;DR

This paper develops an LOS discovery trajectory on the equipotential surface while the closed-form search directions are determined using perturbation theory and proposes a channel model for each user in the LOS regime utilizing polynomial regression without depending on user locations or propagation distance.

Abstract

This paper studies optimal unmanned aerial vehicle (UAV) placement to ensure line-of-sight (LOS) communication and sensing for a cluster of ground users possibly in deep shadow, while the UAV maintains backhaul connectivity with a base station (BS). The key challenges include unknown user locations, uncertain channel model parameters, and unavailable urban structure. Addressing these challenges, this paper focuses on developing an efficient online search strategy which jointly estimates channels, guides UAV positioning, and optimizes resource allocation. Analytically exploiting the geometric properties of the equipotential surface, this paper develops an LOS discovery trajectory on the equipotential surface while the closed-form search directions are determined using perturbation theory. Since the explicit expression of the equipotential surface is not available, this paper proposes to locally construct a channel model for each user in the LOS regime utilizing polynomial regression without depending on user locations or propagation distance. A class of spiral trajectories to simultaneously construct the LOS channels and search on the equipotential surface is developed. An optimal radius of the spiral and an optimal measurement pattern for channel gain estimation are derived to minimize the mean squared error (MSE) of the locally constructed channel. Numerical results on real 3D city maps demonstrate that the proposed scheme achieves over 94% of the performance of a 3D exhaustive search scheme with just a 3-kilometer search.

Figures (11)

• Figure 1: Illustration of a system where a provides sensing and/or communication services for a cluster of sensing targets and/or communication users without knowing their locations, channel models, and the city topology while establishing an backhaul link to a .
• Figure 2: (a) An alternating spiral trajectory (orange dots) that satisfies conditions (i)--(iii) in Theorem \ref{['thm:variance-minimization']}. (b) A spiral trajectory that satisfies conditions (i) and (iii) in Theorem \ref{['thm:variance-minimization']} and it is smooth.
• Figure 3: (a) LOS discovery trajectory on the equipotential surface. (b) Search directions in Phase $1$ and $2$.
• Figure 4: Map A (left) is a sparse commercial area, and map B (right) is a dense residential area in Beijing, China.
• Figure 5: Normalized estimation error of channel gain $g(\mathbf{x})$ versus measurement range $r_{1}$.

Theorems & Definitions (14)

• Proposition 1: Existence condition in a specified balancing problem
• proof
• Proposition 2: A spherical equipotential surface
• proof
• Theorem 1: Minimum variance
• proof
• Theorem 2: MSE of the estimated channel gain
• proof
• Proposition 3: Upper bound of trajectory length
• proof