## 3 Probe Design and Calibration
Figure 2: Two-antenna method for drone-borne probe calibration: (**a**) off-drone; (**b**) on-drone measurements. Gain measurements need to be performed in a reflection-free environment; since anechoic chambers for HF antennas are quite rare, we opted for an open-area test site (OATS). Reflection and diffraction on massive objects can still occur in that frequency range. The distance-averaging method [33; 34] may reduce the effect of the multipath propagation, even for narrow band antenna measurements. However, for HF antennas it might be unpractical, as the distance variation range between antennas should be in the order of the wavelength so as to provide sufficient variability to the contribution of the indirect wave. Time gating can be applied instead [35; 36], by correlating the gate width with the distance to the nearest massive obstacle in the OATS. Other sources of errors when using the two-antenna method for characterizing HF antennas in an OATS include discrepancies in the individual electric and radiation properties of the antennas, field-zone effect, and ground reflection. The reproducibility of different characteristics for our probe design is very high, as any possible dimensional discrepancy in manufacturing is much smaller than the wavelength. We therefore further investigated the two other sources of errors. It should be emphasized that a one meter-long, folded dipole acts mostly like an electrically small loop near the lowest limit of the HF range, and as an electrically short dipole, near the highest limit. In between, both modes of radiation, i.e., the loop mode and the dipole mode, are present and comparable. The loop mode (Figure 4a) provides omnidirectional radiation in the antenna plane, i.e., YOZ, and a dual polarization, except for the XOY plane, where solely the OZ polarization is present. The dipole mode provides omnidirectional radiation in the XOY plane (Figure 4b), and a linear polarization along the OZ axis. Probe gain was measured by placing the antennas on two 1.25 m high dielectric tripods. The ground-reflected wave magnitude depends on the ground characteristics, e.g., the humidity and soil type, and on the antenna position with respect to the ground. In order to discriminate the contribution of the direct wave regardless of the soil characteristics, the ground reflection effect should be assessed by successively placing the antennas in vertical and horizontal positions, in face-to-face and coplanar configurations (Figure 5). Pattern diagrams have 90 degree-wide radiation lobes (half-power beamwidth) for both the loop and dipole modes; it is therefore worth to place the antennas one away from the other at a distance twice the mast height, in order to have the same weight in the link budget for the loop mode, and a ground-reflected wave both for coplanar and face-to face configurations. Let \(R\) be the ground reflection coefficient; since the distance between the antennas and the mast height are comparable (i.e., in the order of one meter), and both are much shorter than  
Figure 4: Radiation from a short, folded dipole (in red): (**a**) loop mode; (**b**) dipole mode. the wavelengths in the HF range (i.e., tens to one hundred meters), direct and reflected waves are quasi in-phase. For the horizontal coplanar configuration, the electric field contributing to the current on the receiving antenna can be found as follows:  
\[E_{r}^{cpl}=E_{d}+E_{l}-RE_{d}-\frac{R}{\sqrt{2}}E_{l}\, \tag{4}\]  
where \(E_{d}\) and \(E_{l}\) are the contributions of the dipole mode and loop mode, respectively. Similarly, for the horizontal face-to-face configuration one can find the following:  
\[E_{r}^{f2f}=E_{d}-RE_{d}-\frac{R}{\sqrt{2}}E_{l}\, \tag{5}\]  
and  
\[E_{r}^{vert}=E_{d}+\frac{R}{\sqrt{2}}E_{d}-\frac{R}{\sqrt{2}}E_{l}\, \tag{6}\]  
for the vertical face-to-face configuration.