## 4 Characterization Using the Frequency Domain Measurement Data  
The measurement results of the welder robot are shown in Figure 4. As shown in Figure 4a, the received signals contained electromagnetic noise, background noise, and operating mobile communication signals, such as 2G (Global System for Mobile Communications, GSM) and 4G  
Figure 3: A simple envelope model. (Long Term Evolution, LTE) signals. Table 3 shows the spectrum occupancy rate of existing communication signals, in which the operating mobile communication signals were mainly between 900 MHz and 1800 MHz. In Figure 4a, we can see that mobile communication signals had wideband spectrums and high power levels. However, the power of electromagnetic noise was small, mainly below 1 GHz. Figure 4b shows that the results measured by horizontal and vertical polarization of the antenna were similar. Low power wireless sensors are often used in industrial scenarios. The noise power has a great impact on the wireless links of sensors. Low power wireless sensors usually work in five frequency bands, i.e., 315 MHz, 433 MHz, 779 MHz, 868 MHz, and 916 MHz, and the bandwidth is usually from 10 kHz to 200 kHz. Therefore, we focused our measurements on the spectral bands near the above five bands. Figure 5 shows the spectrum near the above frequency bands. Note that there were mobile communication signals in the frequency bands above 870 MHz and below 915 MHz. We extracted the average power levels of five bands of noise, as shown in Table 4. According to the extracted results, we could see that the power of the electromagnetic noise was decreased with the increase of the frequency. Figure 4: Spectrums of the noise measured near welder robot. (**a**) Amplitude spectrum of noise; (**b**) Power spectrum of noise. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Frequency (MHz)** & **Signal Type** & **Frequency (MHz)** & **Signal Type** \\ \hline
478–486 & & 825–835 & CDMA UL \\
518–526 & & 870–880 & CDMA DL \\
526–534 & & 890–915 & GSM800 UL \\
614–622 & & 935–960 & GSM800 DL \\
654–662 & & 1710–1755 & GSM1800 UL \\
662–670 & Radio and TV Signals & 1755–1785 & FDD-LTE UL \\
670–678 & & 1805–1840 & GSM1800 DL \\
702–710 & & 1840–1875 & FDD-LTE DL \\
718–726 & & 1885–1915 & TD-LTE \\
758–766 & & 2130–2145 & WCDMA DL \\
766–774 & & 2401–2481 & WIFI \\
790–798 & & 2575–2595 & TD-LTE \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Frequency spectrums occupancy of communication signals. However, according to the principle of the transmission theory, the path loss increases with the increase of frequency. The frequency selection of the IIoT needs to consider not only noise but also path loss. Therefore, we needed to calculate the path loss in different frequency bands. Thus, we could judge which frequency band is most suitable for IIoT. The expression of path loss in free space is:  
\[L(d)=32.45+20\lg(f)+20\lg(d) \tag{5}\]  
where \(f\) is the frequency in MHz and \(d\) is the distance between the transmitter and the receiver. The unit is kilometers. We assumed that \(d\) was equal to 0.1 km. We calculated the path loss according to Equation (5) and the results are shown in Table 5.  
Taking 315 MHz as a reference, let its gain be 0. We defined the gain equal to the reduction of the average power of the noise minus the increase of the transmission loss. Taking 868 MHz as an example, the average noise power was reduced by 8.3 dB (\((-111\) dBm\()-(-119.3 dBm)\)) compared to 315 MHz, and the path loss was increased by 8.8 dB (\(71.2\) dB \(-62.4\) dB). Therefore, the gain of 916 MHz was \(-0.5\) dB (\(8.3\) dB \(-8.8\) dB). Similarly, we calculated the gain of other frequency bands. The specific results are listed in Table 6. According to the results in Table 6, the best choice of frequency of IIoT was 916 MHz, and the others were 315 MHz, 433 MHz, 868 MHz, and 779 MHz.