## 3 Probe Design and Calibration
Three maximum-gain figures can then be defined: the dipole mode gain (corresponding to the 'face-to-face' orientation),  
\[G_{\text{probe off drone}}=\sqrt{\left(\frac{4\pi r}{\lambda}\right)^{2}\frac{R_ {0}}{R_{a2\text{ off drone}}(f)}\frac{\left|S_{21\text{ off drone}}\right|^{2}}{ \left|1-S_{22\text{ off drone}}\right|^{2}\left(1-\left|S_{11}\right|^{2} \right)}}\, \tag{1}\]9  
the loop mode gain,  
\[G_{\text{probe on drone}}=\frac{1}{G_{\text{probe off drone}}}\bigg{(}\frac{4\pi r }{\lambda}\bigg{)}^{2}\frac{R_{0}}{R_{a2\text{ on drone}}(f)}\frac{\left|S_{21 \text{ on drone}}\right|^{2}}{\left|1-S_{22\text{ on drone}}\right|^{2}\left(1- \left|S_{11}\right|^{2}\right)}. \tag{2}\]0  
and the total gain (corresponding to the 'coplanar' orientation),  
\[G_{\text{probe on drone}}=\frac{1}{G_{\text{probe off drone}}}\bigg{(}\frac{4\pi r }{\lambda}\bigg{)}^{2}\frac{R_{0}}{R_{a2\text{ on drone}}(f)}\frac{\left|S_{21 \text{ on drone}}\right|^{2}}{\left|1-S_{22\text{ on drone}}\right|^{2}\left(1- \left|S_{11}\right|^{2}\right)}. \tag{2}\]1  
As the antenna length and the distance between antennas fall in the same order and both are much shorter than the wavelength, measurements are performed in the near-field zone. The most important effect compared to a far-field measurement setup comes from the variability of the longitudinal component of the electric field generated by the transmitting antenna along the receiving antenna (Figure 6). Let \(V_{0}\) be the output voltage at the receiving antenna. One can define a normalized, received voltage by compensating for the effects of propagation in terms of magnitude and phase. By taking into consideration the radiation field in the expression of the mutual impedance for two straight dipoles [37], the normalized received voltage can be written as follows:  
\[G_{\text{probe on drone}}=\frac{1}{G_{\text{probe off drone}}}\bigg{(}\frac{4\pi r }{\lambda}\bigg{)}^{2}\frac{R_{0}}{R_{a2\text{ on drone}}(f)}\frac{\left|S_{21 \text{ on drone}}\right|^{2}}{\left|1-S_{22\text{ on drone}}\right|^{2}\left(1- \left|S_{11}\right|^{2}\right)}. \tag{2}\]2  
\[G_{\text{probe on drone}}=\frac{1}{G_{\text{probe off drone}}}\bigg{(}\frac{4\pi r }{\lambda}\bigg{)}^{2}\frac{R_{0}}{R_{a2\text{ on drone}}(f)}\frac{\left|S_{21 \text{ on drone}}\right|^{2}}{\left|1-S_{22\text{ on drone}}\right|^{2}\left(1- \left|S_{11}\right|^{2}\right)}. \tag{2}\]3 Near-field transmission between electrically short dipoles. Current distributions are assumed to be quasi-constant. Moreover, since \(r\) and \(d\) are much smaller than the wavelength the phase of the integrand, they can be neglected. Given that \(\sin\theta=d/r\),  
\[G_{\text{probe on drone}}=\frac{1}{G_{\text{probe off drone}}}\bigg{(}\frac{4\pi r }{\lambda}\bigg{)}^{2}\frac{R_{0}}{R_{a2\text{ on drone}}(f)}\frac{\left|S_{21 \text{ on drone}}\right|^{2}}{\left|1-S_{22\text{ on drone}}\right|^{2}\left(1- \left|S_{11}\right|^{2}\right)}. \tag{2}\]4  
The far-field received voltage can be found by making \(d\)\(\rightarrow\)\(\infty\),  
\[G_{\text{probe on drone}}=\frac{1}{G_{\text{probe off drone}}}\bigg{(}\frac{4\pi r }{\lambda}\bigg{)}^{2}\frac{R_{0}}{R_{a2\text{ on drone}}(f)}\frac{\left|S_{21 \text{ on drone}}\right|^{2}}{\left|1-S_{22\text{ on drone}}\right|^{2}\left(1- \left|S_{11}\right|^{2}\right)}. \tag{2}\]5  
A simple correction factor for close-distance transmission between two identical, electrically short dipoles can be found [38] as follows:  
\[G_{\text{probe on drone}}=\frac{1}{G_{\text{probe off drone}}}\bigg{(}\frac{4\pi r }{\lambda}\bigg{)}^{2}\frac{R_{0}}{R_{a2\text{ on drone}}(f)}\frac{\left|S_{21 \text{ on drone}}\right|^{2}}{\left|1-S_{22\text{ on drone}}\right|^{2}\left(1- \left|S_{11}\right|^{2}\right)}. \tag{2}\]6  
Gain measurements in the near-field zone would yield \(\frac{G}{F^{2}(d)}\) instead of \(G\).