## 3 Proposed Model and Experiment Setup
### Mathematical Calculation  
This subsection aims to highlight the mathematical calculations for conducting the experiment from the space segment, which represents the drone, to the ground segment, which represents the GCC. This includes the Hata-Davidson empirical model [48; 49], which is a radio propagation model used to predict path loss in fifth-generation multiple-input multiple-output (5G MIMO) antennae transmissions between drones and ground control stations (GCS). This is followed by the equations of the proposed optimization techniques for tunning the propagation model, called the \"least squares tuning algorithm\". Additionally, more mathematical details are presented to calculate the related link budget parameters, such as: RSS, signal-to-interference-noise-ratio (SINR), and throughput (T). Additional to geolocation information using a GPS sensor that is used to identify the locations of casualties or lost people, and then notify authorities as to the target's exact GPS coordinates. The Hata-Davidson empirical propagation model can be calculated as per (1) to (5) [48; 49]:  
\[\mathrm{P_{L}HD}=\mathrm{P_{L}Hata}+\mathrm{A}\ (\mathrm{h_{t}},\mathrm{d})- \mathrm{S_{1}}(\mathrm{d})-\mathrm{S_{2}}(\mathrm{h_{t}},\mathrm{d})-\mathrm{S_ {3}}(\mathrm{f})-\mathrm{S_{4}}(\mathrm{f},\mathrm{d}) \tag{1}\]  
\[\mathrm{d}\ [\mathrm{km}]=2\ \mathrm{E_{r}}[\cos^{-1}(\frac{\mathrm{E_{r}}}{ \mathrm{E_{r}}+\mathrm{h_{t}}}*\cos(\theta))-\theta] \tag{2}\]  
Figure 4: Flowchart of the proposed model and experiment setup. For urban areas:  
\[a(h_{r})=(3.2[\log\left(11.75\times h_{r})]^{2}\right)-4.9 \tag{3}\]  
For suburban, or rural areas:  
\[a\ (h_{r})=(1.1\log(f)-0.7)(h_{r})-(1.56\ \log\ (f)-0.8) \tag{4}\]  
\[P_{L}Hata=69.55+26.16\log\ (f)-13.82\ \log\ (h_{t})-a(h_{r})+[44.9-6.55\log\ (h_{t})] log\ (d) \tag{5}\]  
where \(P_{L}HD\) denotes the path loss of Hata-Davidson, \(h_{t}\) denotes the transmitter antenna altitude, \(h_{r}\) denotes the receiver antenna altitude, \(a(h_{r})\) denotes the correction factor for the mobile antenna height, \(f\) denotes the carrier frequency, \(E_{r}\) denotes the Earth radius, \(P_{L}Hata\) denotes the path loss of Hata, \(d\) denotes the distance at which the propagation model's range is computed based on the elevation angle (\(\theta\)), \(A\) and \(S_{1}\) represent factors that extend the distance to 300 km, \(S_{2}\) denotes the correction factor for the height \(h_{t}\) of the base station antenna extending the value of \(h_{t}\) to 2.5 km, and \(S_{3}\) and \(S_{4}\) represent the correction factors for the Hata-Davidson model that extend the frequency to 1.5 GHz [46; 47]. To reach an optimum communication link with different environment characteristics, the least squares tuning algorithm is considered where tuning is necessary to adjust the Hata-Davidson propagation model's parameters to the measured data. Mathematical equations for the least squares tuning algorithm are presented as per Equations (6) to (8). \[E=\sum_{i=1}^{n}\left(Y_{i}-PLHD_{i}\right)^{2} \tag{6}\]  
where the tuning algorithm is exemplified by the concept of minimizing the sum of the squares of the differences \(E\) between the measured data \(Y_{i}\) and the predicted data \(PLHD_{i}\); \(n\) denotes the total number of used data. In the Hata-Davidson propagation model, we used two main tuning terms, as per Equations (7) and (8). These two terms reportedly affect propagation models, which are related to distance (d), and frequency (f). \[K_{1}=A\ (h_{t},d) \tag{7}\]  
\[K_{2}=\log\ (f) \tag{8}\]  
where \(K_{1}\) and \(K_{2}\) denote the Hata-Davidson propagation model coefficients for the tuning and optimization process.