# Experimental Study of LoRa Transmission over Seawater
## 3 Materials, Experimental Setup and Methods
### RSSI Correction Factors and SNR Measurement Chain Linearity  
LoRa ICs are equipped with RSS indicators and SNR measurement capabilities. Measured values are stored in the corresponding registers and can be read via the SPI bus by the host processor. For the proper interpretation of the experimental results, it is necessary to assess RSSI accuracy and determine the saturation threshold for the SNR measurement chain. However, until now, there is no work which fully addresses this issue. For example, [PERSON] et al. [27] found the SNR measurement chain saturation threshold for the transceiver used in their experiments, but without finding RSSI correction factors. RSSI correction factors imply correlation of actual received power at the IC's RF pin and the value available in the corresponding transceiver's register. The measurement offset may be a consequence of the transceiver's RF front end attenuation and/or the inherent IC production tolerances. To find RSSI correction factors and investigate SNR measurement chain linearity, we arranged the setup shown in Figure 6.  
An ODT was used as a transmitter set to 5 dBm of output power. The output was connected through a coaxial cable and a variable attenuator to the channel power meter (Keysight FieldFox N9915A handheld microwave analyzer). We performed channel power measurements on LoRa signals at different attenuations and for both frequencies of interests. The results are presented in Figure 7a,b in magenta color for both 868 MHz and 434 MHz. In that way, we obtained reference RSS values for both frequencies. We then repeated the same measurements replacing the channel power meter with each of the LoRa transceivers used in the field experiments, recording RSS and SNR for both frequencies of interest. The results are presented in the same plots. Figure 6: Measurement setup for RSSI correction factors and SNR measurement chain linearity. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**LoRa Parameters** & **Packet Air Time** & **Equiv. Bit Rate** & **Theoretical Sensitivity** & **Experiment Duration** \\ \hline \(SF7\), \(BW125\,\mathrm{kHz}\), \(CR4/6\) & \(51.46\,\mathrm{ms}\) & \(4557\,\mathrm{bps}\) & \(-123\,\mathrm{dBm}\) & \(84\,\mathrm{min}\) \\ \(SF10\), \(BW125\,\mathrm{kHz}\), \(CR4/6\) & \(313.34\,\mathrm{ms}\) & \(813\,\mathrm{bps}\) & \(-132\,\mathrm{dBm}\) & \(171\,\mathrm{min}\) \\ \(SF12\), \(BW125\,\mathrm{kHz}\), \(CR4/6\) & \(1056.77\,\mathrm{ms}\) & \(214\,\mathrm{bps}\) & \(-137\,\mathrm{dBm}\) & \(419\,\mathrm{min}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experiments’ technical details. Applying a least squares error polynomial fit through the measured points we obtained the following equations:  
\[Reference_{43\mathrm{MHz}}=-0.9948\times att+4.556 \tag{1}\]  
\[Reference_{868\mathrm{MHz}}=-0.9938\times att+4.628 \tag{2}\]  
\[ODT_{43\mathrm{MHz}}=-0.9626\times att-2.205 \tag{3}\]  
\[ODT_{868\mathrm{MHz}}=-0.9743\times att-4.194 \tag{4}\]  
\[Uputronics_{868\mathrm{MHz}}=-0.9007\times att-11.41 \tag{5}\]  
\[Libelium_{868\mathrm{MHz}}=-0.8962\times att-10.22 \tag{6}\]  
The obtained equations were used to correct the values reported by corresponding transceivers. As can be seen in Figure 7a,b, RSS reported by the transceivers is linear in a wide range, although there is a constant offset between the power measured with the power meter and the corresponding values read in the devices' registers. The difference is about 6.7 dB at 434 MHz and about 8.8 dB at 868 MHz for ODT. The commercial devices exhibit different offsets due to different RF front-end attenuations: 16 dB for the Uptronics and 14.8 dB for the Libelium. It can be inferred that the devices are self-coherent but the absolute values reported by the transceivers significantly differ from absolute values measured with the power meter. The linearity of the SNR reported by the transceivers is also experimentally verified for all transceivers used in the experiments.