Beyond Path Loss: Altitude-Dependent Spectral Structure Modeling for UAV Measurements

TL;DR

This paper develops an altitude-dependent spectral modeling framework for UAV measurements, capturing complex spectral behavior across multiple frequency bands and altitudes, enabling more accurate spectrum sensing and band selection for UAVs.

Contribution

The paper introduces the ADSSM, a novel model that characterizes altitude-dependent spectral features using differential equations and logistic functions, validated with multi-year outdoor measurements.

Findings

Power transitions occur over narrow low-altitude regions.

Entropy and sparsity evolve over broader altitude ranges.

Model achieves low error and high fit quality across bands and years.

Abstract

This paper presents a measurement-based framework for characterizing altitude-dependent spectral behavior of signals received by a tethered Helikite unmanned aerial vehicle (UAV). Using a multi-year spectrum measurement campaign in an outdoor urban environment, power spectral density snapshots are collected over the 89 MHz--6 GHz range. Three altitude-dependent spectral metrics are extracted: band-average power, spectral entropy, and spectral sparsity. We introduce the Altitude-Dependent Spectral Structure Model (ADSSM) to characterize the spectral power and entropy using first-order altitude-domain differential equations, and spectral sparsity using a logistic function, yielding closed-form expressions with physically consistent asymptotic behavior. The model is fitted to altitude-binned measurements from three annual campaigns at the AERPAW testbed across six licensed and unlicensed sub-6 GHz bands. Across all bands and years, the ADSSM achieves low root-mean-square error and high coefficients of determination. Results indicate that power transitions occur over narrow low-altitude regions, while entropy and sparsity evolve over broader, band-dependent altitude ranges, demonstrating that altitude-dependent spectrum behavior is inherently multidimensional. By explicitly modeling altitude-dependent transitions in spectral structure beyond received power, the proposed framework enables spectrum-aware UAV sensing and band selection decisions that are not achievable with conventional power- or threshold-based occupancy models.