## 3 DMCAP System
### Signaling and Channeling Models  
The proposed system formulates complex signaling parameters and channel distortion factors as provided below. The multi-channel signal models and noise models are provided in the following equations. Signal Attenuation factor:  
\[\mathrm{S}\alpha^{\mathrm{i}}=\omega\sqrt{\frac{\mathrm{me}}{2}}\Bigg{(}\sqrt {1+\Big{(}\frac{\mathrm{e_{\prime}}}{\mathrm{e}}\Big{)}^{2}}-1\Bigg{)} \tag{1}\]  
Equations (1) and (2) state \(\omega\) as signal wavelength. m and e are electromagnetic permeability and real permittivity factor respectively. e, indicates imaginary portion of dielectric permittivity factor. Signal Phase shifting factor:  
\[\mathrm{S}\beta^{\mathrm{i}}=\omega\sqrt{\frac{\mathrm{me}}{2}}\Bigg{(}\sqrt {1+\Big{(}\frac{\mathrm{e_{\prime}}}{\mathrm{e}}\Big{)}^{2}}+1\Bigg{)} \tag{2}\]  
signal reflection factor:  
\[\mathrm{S}(\mathrm{R})^{\mathrm{i}}=\frac{1-\sqrt{\mathrm{e_{\prime}}}}{1+ \sqrt{\mathrm{e_{\prime}}}} \tag{3}\] \begin{table}
\begin{tabular}{l l} \hline \hline
**Previous Techniques** & **Motivations of Proposed Work** \\ \hline Homogeneous wireless channel assessment techniques are proposed. & Multi-channel (heterogeneous) assessment techniques are required. \\ Linear and moderate channel models are created for implementing the networks. & WUGSNs are expected to be considered with more realistic network parameters. \\ Uncertain conditions are not produced in the network model effectively. & More uncertain conditions must be imposed on underground and open medium of WUGSN. \\ Energy optimization is not taken crucially for WUGSN with differentiated channel qualities. & Energy optimization must be taken crucially for WUGSN with differentiated channel qualities. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Previous works and motivation of proposed work. attenuation due to reflection:  
\[\mathrm{S(RA)}^{\mathrm{i}}=10\log\frac{2\cdot\mathrm{S(R)}^{\mathrm{i}}}{1+ \mathrm{S(R)}^{\mathrm{i}}} \tag{4}\]  
Equations (3) and (4) illustrate reflection models. Similarly, the underground particles such as soil contents, water contents and other particles create signal attenuation between all sensor nodes. The underground sensor signals are affected due to reflection, absorption, refraction, and scattering of electromagnetic signals. The receiving power at different links are derived as provided in Equations (5)-(7). Receiving power at \(\mathrm{UG_{N}}\) link,  
\[\mathrm{P(R)}^{\mathrm{Ui-Ui}}=\mathrm{P}^{\mathrm{tr}}+\mathrm{G}^{\mathrm{tr }}+\mathrm{G}^{\mathrm{rx}}-\mathrm{Loss}^{\mathrm{UG}} \tag{5}\]  
* \(\mathrm{P}^{\mathrm{tr}}\)-Sensor Node\({}^{\prime}\)s Transmission Power;
* \(\mathrm{G}^{\mathrm{tr}}\)-Transmission Gain;
* \(\mathrm{G}^{\mathrm{rx}}\)-Receiving Gain;
* \(\mathrm{Loss}^{\mathrm{UG}}\)-Underground Signal Loss. Receiving power at \(\mathrm{G_{s}}\) and \(\mathrm{UG_{N}}\) link: \[\mathrm{P(R)}^{\mathrm{Ui-Si}}=\mathrm{P}^{\mathrm{tr}}+\mathrm{G}^{\mathrm{tr }}+\mathrm{G}^{\mathrm{rx}}-\left[\mathrm{Loss}^{\mathrm{UG}}+\mathrm{Loss}^{ \mathrm{A}}\right]\] (6)
* \(\mathrm{Loss}^{\mathrm{0}}\)-Free space loss;
* \(\mathrm{Loss}^{\mathrm{A}}\)-Loss due to adversarial events. Receiving power at \(\mathrm{G_{s}}\) and \(\mathrm{BG_{s}}\) link: \[\mathrm{P(R)}^{\mathrm{Si-Bi}}=\mathrm{P}^{\mathrm{tr}}+\mathrm{G}^{\mathrm{tr }}+\mathrm{G}^{\mathrm{rx}}-\left[\mathrm{Loss}^{\mathrm{0}}+\mathrm{Loss}^{ \mathrm{A}}\right]\] (7)  
Over these signaling models, Signal to Noise Interference Ratio (SNIR) is determined for uncertain and lossy conditions under different channels and links. In the determination phase, set SNIR threshold range between \(\mathrm{\SIUnitSymbolFace1}\) and \(\mathrm{\SIUnitSymbolFace2}\). In this work, SNIR is adjusted for different channels (Equation (8)). The SNIR is tuned based on novel training algorithm.