Frenet–Serret Frame Aided Beam Tracking for High-Mobility UAV mmWave Communications: A Geometric Approach

Abstract

Narrow millimeter-wave (mmWave) beams are highly susceptible to misalignment during aggressive maneuvers of high-mobility uncrewed aerial vehicles (UAVs). To address this challenge, this letter proposes a lightweight beam tracking method leveraging the Frenet-Serret (F-S) frame, a fundamental construct of differential geometry that encodes the intrinsic geometric characteristics of the UAV’s trajectory. The key innovation lies in utilizing the F-S frame as a motion-adaptive, real-time coordinate system, enabling direct mapping of instantaneous kinematic states (e.g., velocity and acceleration) to the optimal beam direction for post-initialization tracking, without relying on explicit channel estimation or historical data. Simulations demonstrate that our method outperforms LSTM-based and EKF-based approaches in typical high-mobility trajectories, reducing the beam misalignment error by over 73% on average. The method also maintains millisecond-level computational delay with less than 1% spectral efficiency loss. This work validates the proposed geometric approach as an accurate and efficient solution for beam tracking in high-mobility mmWave systems.