## 2 Wireless Sensor Network Technology
### LoRa Wireless Sensor Network Technology
The expected communication performance of the LoRa signal transmission technique can be estimated for a single end-device using the following considerations. Following the Friis' transmission equation, the path loss \(g\) can be calculated as a function of distance between sender and receiver \(d\):  
\[g(d)=\frac{\lambda}{\left(4\pi d\right)^{\eta}} \tag{2}\]  
where \(\lambda\) is the carrier frequency wave length, and \(\eta\) is the path loss exponent (\(\eta\geq 2\)), usually taken to be equal to 2.7 in suburban environments. In addition, path loss due to shadowing effects can be approximated with noise variance assuming white Gaussian noise with zero mean:  
\[\sigma^{2}=-174+NF+10 log_{10}(BW) \tag{3}\]  
where NF is the receiver noise and assumed to have a value of 6 dB, and BW is the bandwidth of \(s(t)\), assumed to be 125 kHz in this case. Finally, the coverage probability \(CP\), defined as the probability that the signal-to-noise ratio SNR is equal to or larger than the threshold value \(q_{SF}\), can be obtained as  
\[CP=exp\left(-\frac{\sigma^{2}\cdot q_{SF}}{P\cdot g(d)}\right) \tag{4}\]  
in which \(P\) is the transmitted power, here assumed to be 14 dBm (25.12 mW). Figure 5 presents the coverage probability as a function of distance obtained with values of \(q_{SF}\) from Table 1 and Equation (4). The following conclusions can be drawn from the calculations. In the case of a path loss exponent of 2.5, radio links can cover distances from 6.5 to 23 km, assuming that 90% coverage is sufficient for reliable transmission. When the path loss exponent increases to 2.7, the possible distance of the radio links decreases to 2.7 to 9 km at 90% coverage. This demonstrates the strong sensitivity of the communication distance to the path loss exponent and suggests that this value should be chosen with care. To check the appropriateness of the path loss exponent for a given area, the theoretical results should be compared with transmission performance measurements with mobile LoRa receiver and gateway devices at different distances. Recently, a number of studies have developed and deployed low-cost LoRa-based WSNs for long-distance soil moisture monitoring to test their usability for smart agriculture [49; 50]. In addition, [PERSON] et al. [51] developed and successfully tested a LoRa-based WSN to investigate the control of soil moisture on greenhouse gas emissions in a wetland. The results of the WSN experiment by [PERSON] and [PERSON] [50] showed that LoRa achieves maximum performance when the communication range is below 700 m, with average values of RSSI (received signal strength), SNR (signal-to-noise ratio) and PDR (packet-delivery ratio) of \(-\)120 dBm, 1 dB, and 40%, respectively, for the given conditions in a star fruit plantation. This indicates that local conditions, such as dense vegetation surrounding the LoRa transmitters, can have a strong negative impact on the expected radio link distances of LoRa-based WSNs. \begin{table}
\begin{tabular}{c c c c} \hline
**Spreading Factor** & **Sensitivity (dBm)** & \(q_{\text{SF}}\) (dBm)** & **Bit Rate (bits/s)** \\ \hline
7 & \(-\)123 & \(-\)6 & 5469 \\
8 & \(-\)126 & \(-\)9 & 3125 \\
9 & \(-\)129 & \(-\)12 & 1758 \\
10 & \(-\)132 & \(-\)15 & 977 \\
11 & \(-\)134.5 & \(-\)17.5 & 537 \\
12 & \(-\)137 & \(-\)20 & 293 \\ \hline \end{tabular}
\end{table} 
Table 1: Receiver sensitivities for different spreading factors and the corresponding bit rates. The parameter \(q_{SF}\) indicates the specific noise threshold for a given spreading factor. Values are taken from [PERSON] and [PERSON] [48].