# Overcoming Limitations of LoRa Physical Layer in Image Transmission
## 5 Results
### Effects of Fresnel Zone  
Although the results of this experiment demonstrate that by adopting the proposed encryption scheme image data can be transferred over the LoRa physical layer, they do not indicate the full capabilities of LoRa communication based on the nine trials which ended in failure. We posit that the reason for these failures was the dense growth of coconut trees around the mangrove area, which worked as obstacles preventing signals from traveling between the transmitter and receiver nodes. These trees lie in the so-called 'Fresnel zone', defined in point-to-point networks by a cylindrical ellipse drawn between the transmitter and the receiver nodes, as illustrated in Figure 11. It is known that this zone should be at least 60% free of obstructions, such as buildings, mountains, or trees, failing which, signal energy loss is incurred. This, reduce the performance of the wireless link, as was the case with our experiment. Hence, it is important to have a clear 'line of sight (LOS)' between the transmitter and the receiver, as much as possible [25]. In our experiments, the transmitter node was fixed on a Skylift at a height of 40 m. The height of the receiver node, which was installed on the back of a four-wheel drive vehicle did not exceed 5 m. On average, coconut trees are approximately 12 m tall. This height can sometimes approach 25 m in isolated incidences [26]. Consequently, these trees fall in \begin{table}
\begin{tabular}{c c c c c} \hline _SF_ & **Distance (km)** & _MSE_ & _PSNR (dB)_ & **SSIM** \\ \hline
7 & 2 & 0 & INF & 1 \\
7 & 3 & 0 & INF & 1 \\
7 & 4 & 98.7301 & 28.1863 & 0.9321 \\
8 & 4 & 9.4572 & 38.3732 & 0.9953 \\
9 & 4 & 8.9987 & 38.5890 & 0.9968 \\
10 & 4 & 0 & INF & 1 \\
11 & 4 & 0 & INF & 1 \\
11 & 5 & 189.3394 & 25.3584 & 0.9437 \\
12 & 4 & 0 & INF & 1 \\
12 & 5 & 62.4792 & 30.1734 & 0.9625 \\
12 & 6 & 234.5309 & 24.4288 & 0.9528 \\ \hline \end{tabular} INF refers to infinity. We obtained this when the value of a divisor was small, such that the result of the subsequent MATLAB calculation was numerically undefined.  
\end{table} 
Table 6: Summary of image quality metrics (_MSE_, _PSNR_, and SSIM) calculated using MATLAB. \begin{table}
\begin{tabular}{c c c c c} \hline _SF_ & **Distance (km)** & _MSE_ & _PSNR (dB)_ & **SSIM** \\ \hline
7 & 1 to 3 & 0 & INF & 1 \\
10 & 4 & 0 & INF & 1 \\
11 & 4 & 0 & INF & 1 \\
12 & 4 & 0 & INF & 1 \\ \hline \end{tabular}
\end{table} 
Table 7: LoRa physical _SF_ setting which has identical image quality metrics. the first order Fresnel zone, based on the geometry of the measurement environment, as illustrated in Figure 12. This has a negative effect on the transmission of the LoRa signals. To figure out whether or not the trees are acting as an obstacle of signal performance between the sender and the receiver, the Fresnel zone radius and diameter can be calculated using the following formulas:  
\[r=8.656\times\sqrt{\frac{D}{F}} \tag{5}\]  
where  
\(r\) = The radius of the Fresnel zone  
\(D\) = The distance between Rx and Tx (km)  
\(F\) = Frequency used in the transmission process which is 921.9 MHz  
\[\text{Fzone Diameter}=r\times 2 \tag{6}\]  
The Fresnel zone midpoint calculated using the following  
\[\text{Fzone midpoint height}=\frac{40+5}{2}=22.5\;\text{m} \tag{7}\]  
Figure 11: Illustration of line-of-sight point-to-point wireless communication. Image 3 shows how the trees act as obstacles that can affect signal performance. Figure 12: Dense growth of Coconut trees around the mangrove forest, which fall in the first order Fresnel zone. where the 40 m and the 5 m are the height of the transmission and the receiver node from the ground respectively.