# Evaluating LoRaWAN Connectivity in a Marine Scenario
## 2 Material and Methods  
### LoRa and LoRaWAN  
Among the operational LPWA network technologies, the LoRa solution provides the best technology for the implementation of private IoT networks that can be implemented ad-hoc without the need for using proprietary licenses, with the possibility of using three classes of devices to guarantee efficient energy management depending on the area of application and to allow resilience to interference [28]. LoRa technology uses frequencies of the sub-GHz band (nominally 868 MHz for Europe), minimizing the attenuation due to obstacles, and employs a robust modulation that allows the use of receivers with very low sensitivity (\(Rx_{sens}\)) of the order of \(-140\) dBm. This value represents the known minimum power to obtain a reliable transmission, and it can be calculated through the following equation:  
\[Rx_{sens}=-174\;\mathrm{dBm}+10\cdot\log(BW)+NF+SNR \tag{1}\]  
where \(BW\) is the bandwidth (kHz), \(NF\) is the noise factor (dB), and \(SNR\) is the signal to noise ratio (dB). Under the hypothesis of free space, the simplest model to estimate the power of the LoRa packet received at the gateway is based on the following Friis transmission equation:  
\[P_{rx}=Tx_{power}-Path_{loss}+G_{Tx}+G_{Rx} \tag{2}\]  
where \(Tx_{power}\) is the transmitted power (dB), \(Path_{loss}\) is the free space power loss due to the channel (dB), and \(G_{Tx}\) and \(G_{Rx}\) are the antenna gain in transmission and reception (dBi), respectively. Often, the received power at the gateway is indicated as Received Strength Signal Indicator (\(RSSI\)), also. The simplest model to estimate the \(Path_{loss}\) term in free space is the log-distance path model through the following equation:  
\[Path_{loss}=20\cdot\log_{10}(d)+20\cdot\log_{10}(f)-147.55 \tag{3}\]  
where \(d\) represents the distance between the transmitter and the receiver (meters), and \(f\) is the frequency effectively used for transmission (Hz). A more accurate model that can be applied to the wireless communication system for microwave radio links in the frequency band up to 1500 MHz and for distance up to 100 km is the Hata model [29]. For environments without obstacles the \(Path_{loss}\) can be estimated using the following approximation:\[Path_{loss}=69.55+26.16\cdot\log_{10}\left(f\cdot 10^{-6}\right) \tag{4}\] \[-13.82\cdot\log_{10}\left(h_{B}\right)-C_{H}\] \[+\left(44.9-6.55\cdot\log_{10}h_{B}\right)\cdot\log_{10}\left(d\cdot 1 0^{-3}\right)\] \[-4.78\cdot\left(\log_{10}\left(f\cdot 10^{-6}\right)\right)^{2}+18. 33\cdot\log_{10}\left(f\cdot 10^{-6}\right)-40.94\]  
where \(h_{B}\) is the altitude of the base station antenna (meters) and \(C_{H}\) represents the antenna height correction factor. An approximation of the value of \(C_{H}\) for a semi-urban environment, such as the one in which the experiment was performed, can be expressed by the following equation:  
\[C_{H}=0.8+(1.1\cdot\log_{10}\left(f\cdot 10^{-6}\right)-0.7)\cdot h_{M}-1.56\cdot \log_{10}\left(f\cdot 10^{-6}\right) \tag{5}\]  
where \(h_{M}\) is the altitude of the node antenna (meters). In presence of radio path over semi-urban environment the expression of \(Path_{loss}\) for the Hata model changes as shown in the following equation:  
\[Path_{loss}=69.55+26.16\cdot\log_{10}\left(f\cdot 10^{-6}\right) \tag{6}\] \[-13.82\cdot\log_{10}\left(h_{B}\right)-C_{H}\] \[P_{rx}=Tx_{power}-Path_{loss}+G_{Tx}+G_{Rx} \tag{2}\]0 \[P_{rx}=Tx_{power}-Path_{loss}+G_{Tx}+G_{Rx} \tag{2}\]1  
The European Conference of Postal and Telecommunications through the recommendation ERC-REC-70-3E establishes a maximum transmission power of 25 mW (14 dBm) for uplink message and of 0.5 W (27 dBm) for downlink, and a maximum allowed antenna gain of 2.15 dBi. Furthermore, the proportion of time during which an IoT device can be operated, commonly defined as duty cycle, has to be limited to 0.1% and 1% per day depending on the channel used [30].