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Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
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Updated: Sep 16, 2025

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A homotopy estimation based temporal-spatial spectrum prediction for UAV communications with arbitrary flight paths.

Shan Luo1, Wenjun Zhou2, Lifan Wu2

  • 1School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu, 611731, China. luoshan@uestc.edu.cn.

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|July 11, 2025
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Summary

Unmanned aerial vehicles (UAVs) need spectrum prediction for efficient sharing. A new method uses homotopy theory (HT) to estimate historical data, enabling accurate spectrum prediction for UAVs during arbitrary flights.

Keywords:
Hidden Markov modelHomotopySpectrum predictionUnmanned aerial vehicles

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Area of Science:

  • Electrical Engineering
  • Computer Science
  • Aerospace Engineering

Background:

  • Rapid growth of Unmanned Aerial Vehicles (UAVs) leads to spectrum scarcity.
  • Existing spectrum prediction methods struggle with real-time data limitations for moving UAVs.
  • Need for advanced prediction models that can handle dynamic environments and limited historical data.

Purpose of the Study:

  • To introduce a novel temporal-spatial spectrum prediction approach for UAVs during arbitrary flights.
  • To address the challenge of estimating historical spectrum data at future locations.
  • To develop a method that overcomes non-stationarity and correlation issues in spectrum data.

Main Methods:

  • Extension of homotopy theory (HT) from two to multiple objects.
  • Estimation of historical data using homotopy mapping derived from HT boundary conditions and model parameters.
  • Spectrum prediction via a hidden Markov model (HMM) utilizing HT-estimated data, termed Multiple Objects HT-HMM (MOHT-HMM).

Main Results:

  • The MOHT-HMM method effectively estimates historical spectrum data for dynamic UAV trajectories.
  • The approach successfully predicts spectrum states at the next location without prior historical data.
  • Experimental validation using real civil aviation data demonstrates high prediction accuracy.

Conclusions:

  • The MOHT-HMM provides an effective solution for real-time UAV spectrum prediction in arbitrary flight scenarios.
  • Homotopy theory is a viable tool for estimating missing or future data in dynamic systems.
  • The proposed method enhances spectrum sharing capabilities for the growing UAV ecosystem.