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

TL;DR

This work tackles the inadequacy of power-only UAV spectrum models by introducing the Altitude-Dependent Spectral Structure Model (ADSSM), which jointly models altitude evolution of band-average power, spectral entropy, and spectral sparsity. By combining first-order differential equations for power and entropy with a logistic function for sparsity, ADSSM delivers closed-form expressions with physically consistent asymptotics and is fitted to multi-year, multi-band measurements from a tethered Helikite in urban settings. The framework is validated across six sub-6 GHz bands, showing high fidelity (low RMSE, high R^2) and revealing that power transitions occur in narrow low-altitude regions while entropy and sparsity evolve over broader altitude ranges, underscoring the multidimensional nature of altitude-dependent spectrum behavior. These results enable spectrum-aware UAV sensing and band selection decisions that go beyond traditional occupancy or threshold-based models, with practical implications for interference management and dynamic spectrum access in shared bands.

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.

Figures (4)

• Figure 1: Spectrum sweep procedure for spectrum data collection using a helikite-mounted portable node.
• Figure 2: Altitude--frequency heatmaps for six representative spectrum allocations: (a) FM broadcast, (b) 5G NR n71 downlink, (c) LTE Band 13 downlink, (d) ISM band, (e) CBRS, and (f) 5G NR C-band. These raw measurements provide the foundational altitude-dependent spectral structure from which subsequent power, entropy, and sparsity metrics are derived.
• Figure 3: Altitude-dependent band-average metrics for six measured allocations: (a) band-average power, (b) normalized spectral entropy, and (c) sparsity. These metrics aggregate the altitude–frequency structure in Fig. \ref{['fig:altfreq_updatedbands']} and quantify each band’s transition from clutter-limited propagation at low altitudes to its high-altitude asymptotic regime.
• Figure 4: Transition-region characterization for six measured bands based on the ADSSM power, normalized entropy, and sparsity models: (a) FM broadcast, (b) 5G NR n71 downlink, (c) LTE Band 13 downlink, (d) ISM, (e) CBRS, and (f) 5G NR C-band. Each panel displays model fits, measurements, the 10--90% transition region, and the midpoint height $h_{50}$.