A Geometric Method to Complete Closed-Form Solutions for UAV-Assisted 3D Coverage

IEEE Communications Letters, vol. 30, pp. 2183–2187

Abstract

This letter investigates a UAV-assisted wireless communication coverage network, where a UAV equipped with a directional antenna is dispatched to provide communication coverage service to two ground nodes. To improve communication quality under a fairness consideration, we aim to minimize the maximum UAV-to-node distance (i.e., a min–max fairness objective) while ensuring both nodes lie within the antenna beamwidth cone through jointly optimizing the 3D position and the antenna orientation of UAV. To tackle the formulated highly complicated non-convex problem, we propose a novel geometric approach which rigorously maps the original 3D position design problem to an equivalent 2D position design problem through leveraging the axis-symmetric structure of the problem and applying a bijection-based transformation. Then, via characterizing the monotonicity of the objective function, the closed form expression for the optimal solution is derived which can be equivalently covered to the optimal UAV 3D position of the original problem by inverse mapping. Afterwards, the corresponding optimal antenna orientation is obtained by analyzing the coverage constraints of the original 3D problem. Finally, simulation results demonstrate that our method provides the complete set of globally optimal closed-form solutions compared with benchmark.

Authors 6

1. Xuan Wen

   Wuhan University

   Affiliation as printed

   Electronic Information School, Wuhan University, Hubei, Wuhan, China

2. Peng Wu

   Wuhan University

   Affiliation as printed

   Electronic Information School, Wuhan University, Hubei, Wuhan, China

3. Yunfei Gao

   Wuhan University

   Affiliation as printed

   Electronic Information School, Wuhan University, Hubei, Wuhan, China

4. Xiaopeng Yuan Aachen Chair of Information Theory and Data Analytics

   RWTH Aachen University

   Affiliation as printed

   Chair of Information Theory and Data Analytics, RWTH Aachen University, Aachen, Germany

5. Y Z Zhu

   Wuhan University

   Affiliation as printed

   Electronic Information School, Wuhan University, Hubei, Wuhan, China

6. Yulin Hu

   Wuhan University

   Affiliation as printed

   Electronic Information School, Wuhan University, Hubei, Wuhan, China