Inter-Year Transfer of Altitude-Dependent Spectrum Activity Models Using Minimal Calibration
Amir Hossein Fahim Raouf, İsmail Güvenc
TL;DR
This work addresses whether an altitude-dependent mean-field interference model can be transferred across years using aerial spectrum measurements. It develops a physics-informed mean-only stochastic geometry framework in which altitude effects enter through a logistic LoS transition $p_L(H)=\frac{1}{1+\exp[-\beta(H-H_0)]}$ and a frequency-normalized activity index $\tilde{C}$, with the mean received power given by $\mu(H)=2\pi\lambda C_{\mathrm{eff}} \int_{r_0}^{\infty}(r^2+H^2)^{-\alpha(H)/2} r\,dr$ and $\alpha(H)=\alpha_N-(\alpha_N-\alpha_L)p_L(H)$. A minimal two-point calibration is proposed to test inter-year transfer by fixing $H_0$ from a reference year and estimating $\beta$ and $C_{\mathrm{eff}}$ from two altitude bins, enabling cross-year predictions with limited data. Empirical results across DL, UL, and CBRS bands show that DL and CBRS maintain a persistent altitude structure and transfer well (RMSE$_{\mathrm{dB}}<4$ and positive $R^2_{\mathrm{dB}}$) when $H_0$ is fixed, while UL bands exhibit weak altitude dependence and poor transfer, highlighting the need for traffic-aware modeling for UL. Overall, inter-year reuse of these mean-field models is feasible in stable environments for geometry-dominated interference, offering a path to low-cost, scalable spectrum-sharing analyses. $p_L(H)$, $\alpha(H)$, $\mu(H)$, and $\tilde{C}$ remain central quantities linking physics and calibration across years.
Abstract
This paper studies the transferability of altitude-dependent spectrum activity models and measurements across years. We introduce a physics-informed, mean-only stochastic-geometry model of aggregate interference to altitude-binned received power, yielding three interpretable parameters for a given band and campaign: 1) line-of-sight transition slope, 2) transition altitude, and 3) effective activity constant. Analysis of aerial spectrum measurements collected from 2023 to 2025 across multiple sub-6 GHz bands reveals that downlink (DL) and shared-access bands preserve a persistent geometry-driven altitude structure that is stable across years. In contrast, uplink (UL) bands exhibit weak altitude dependence with no identifiable transition, indicating that interference is dominated by activity dynamics rather than propagation geometry. To quantify the practical limits of model reuse, we evaluate a minimal-calibration method in which the transition altitude is fixed from a reference year and the remaining parameters are estimated from only two altitude bins in the target year. The results further indicate that the proposed approach provides accurate predictions for DL and CBRS bands, suggesting the feasibility of low-cost model transfer in stable environments, while highlighting the reduced applicability of mean-field models for UL scenarios.