## 2 Network Model and Channel Fading Characteristics
### Influence of Environmental Factors on Channel Fading  
In contrast to above-ground wireless signal transmission, the wireless signal in an underground coal mine is influenced by three factors: (1) the transmission medium, viz., and air quality (e.g., temperature, humidity, dust, and smog); (2) spatial structure (e.g., laneway size, laneway wall roughness and inclination); and (3) moving obstacles [28] (e.g., noise of surrounding electrical equipment, moving people and equipment). References [29; 30; 31] analyze and conclude that the signal fading model of a coal mine face comprises both path loss and additional loss. Equation (1) presents the wireless channel transmission model of a coal mine face:\[ \begin{array}{ll}L_{overall-loss}=L_{Eh}+L_{rc}+L_{tc}+L_{h}+L_{s}\\ \hskip 14.226378 pt=\hskip 14.226378 pt5.13\frac{\epsilon^{2}}{f^{2}}d\left[\frac{ \epsilon_{r}}{a\sqrt{\epsilon_{r}-1}}+\frac{1}{b^{3}\sqrt{\epsilon_{r}-1}} \right]\\ \hskip 14.226378 pt+\hskip 14.226378 pt4.343\pi^{2}\eta^{2}h^{2}\left[\frac{1}{a^{ 4}}+\frac{1}{b^{4}}\right]\frac{\zeta}{f}d\\ \hskip 14.226378 pt+\hskip 14.226378 pt4.343\pi^{2}\theta^{2}\dot{d}f/c\\ \hskip 14.226378 pt+\hskip 14.226378 pt5\times 10^{-3}d^{2}+9\times 10^{-3}d\\ \hskip 14.226378 pt+\hskip 14.226378 pt10\lg(P_{m}n_{1}^{2}/d_{sm}{}^{2})+Y_{c} \end{array}  \tag{1}\]  
In Equation (1), \(L_{Eh}\) refers to the horizontal polarization loss in the electromagnetic wave roadway space, \(L_{rc}\) refers to the fading loss caused by the roadway wall roughness, \(L_{tc}\) refers to the fading loss caused by the roadway wall inclination, \(L_{h}\) is the fading loss of the three machines' metal conductor structure on the electromagnetic wave interference, and \(L_{s}\) is the influence of the mechanical noise of the three machines on the wireless signal's SNR. \(L_{overall-loss}\propto(\epsilon_{r},d,\theta^{2},h^{2},a^{-4},b^{-4},n_{1}{}^{- 2})\). In a practical site environment, when the transmission distance is fixed, the fading loss of a CMFM-WSN system channel is directly influenced by \(\theta\), \(h\), \(a\), \(b\) and \(n_{1}\) through the mining process; however, the variation of \(a\) and \(n_{1}\) is strongest (\(n_{1}\) is the motor speed of the mining machine and \(a\) is the mine face width; \(a\) increases continuously with the mining) and is also affected by shadow fading of moving obstacles. Numerous change factors result in strong channel  
Figure 1: (**a**) Sensor node distribution model on the coal mine face; (**b**) Coal mine face; (**c**) Diagram of the network topology. time-varying characteristics of the CMFM-WSN system. Therefore, nodes have different channel characteristics for a fixed distance at the same position at a different time, which yields different requirements for power regulation and the control of network data transmission. Meanwhile, network topology variations should also adapt to such changes to guarantee network robustness. The channel model of WSN for the coal mine face can be summarized as the superposition of a path loss model and a shadow fading model [32]. Signal transmission loss under a log-normal shadowing channel model can be expressed as follows:  
\[P_{L}(d)=P_{L_{0}}+10\alpha\text{log}_{10}\left(\frac{d}{d_{0}}\right)-X_{ \sigma} \tag{2}\]  
\(X_{\sigma}\) is a Gaussian random variable, and \(X_{\sigma}\sim N(0,\sigma^{2})\). Generally, \(\alpha\) is a path loss index ranging from 2 to 6, and \(\sigma\) is between 1 and 8 dB. Generally, the receiving power for a logarithmic normal distribution model is:  
\[P_{r}(d)=P_{T}-P_{L_{0}}-10\alpha\text{log}_{10}\left(\frac{d}{d_{0}}\right)+X _{\sigma} \tag{3}\]  
Receiving power \(P_{r}\) determines the SNR, which certainly has influence on BER; actually, SNR and BER are closely related to link quality.