## 3 DMCAP System
### Signaling and Channeling Models
\[\mathrm{SNIR(Ui-Ui,Ui-Si,Si-Bi)}\propto\mathrm{C}^{\mathrm{Q}}\cdot\mathrm{N}^ {\mathrm{C}}\cdot\mathrm{T}^{\mathrm{F}}(\mathrm{dt}) \tag{8}\]  
* \(\mathrm{SNIR(Ui-Ui,Ui-Si,Si-Bi)}<\mathrm{\SIUnitSymbolFace1}\), Signal Dropped;
* \(\mathrm{SNIR(Ui-Ui,Ui-Si,Si-Bi)}\geq\mathrm{\SIUnitSymbolFace2}\), Signal recieved at the sink;
* \(\mathrm{SNIR(Ui-Ui,Ui-Si,Si-Bi)}\in\mathrm{R(\SIUnitSymbolFace1}\), \(\mathrm{\SIUnitSymbolFace2}\)), Adversarial block;
* \(\mathrm{C}^{\mathrm{Q}}\)-Channel Type;
* \(\mathrm{N}^{\mathrm{C}}\)-Node Type;
* \(\mathrm{T}^{\mathrm{F}}\)-Learning Factor at regular interval;
* \(\mathrm{\SIUnitSymbolFace1}\)-Lower bound;
* \(\mathrm{\SIUnitSymbolFace2}\)-Upper Bound. As mentioned in Equation (8), three types of channels (links) are created to transfer the information from set of underground sensor nodes to base station via surface sensor nodes. These channels are configured with separate frequencies, bandwidths, energy limits, and other communication needs. Particularly, the link \(\mathrm{Ui-Ui}\) is a static under the ground level. At the same time, the links such as \(\mathrm{Ui-Si}\) and \(\mathrm{Si-Bi}\) are dynamic surface links in the WUGSN [29; 30]. Since the surface nodes are moving from one location to another location randomly, these links are separately maintained with the help of unique mobility patterns. In addition, the communication parameters and interference rates of the links are changed against \(\mathrm{Ui-Ui}\) link attributes. As illustrated in Figure 1, the brown color nodes are \(\mathrm{UG_{i}}\), the green color node is \(\mathrm{G_{i}}\) and the base station is \(\mathrm{BG_{i}}\). Figure 1 shows the channels (links)between the sensor nodes and base station. As multiple channels are needed for this heterogeneous WUGSN, the implementation of multi-channel SNIR model with learning factors is a crucial task. The time bounded streams of signaling and interference factors are collected and packed as individual tuple as provided below. The WUGSN channel parameters and distortion cases are determined continuously through complex mathematical functions. Furthermore, these details are modelled as \(\mathrm{T}(\mathrm{S})\alpha^{\mathrm{i}}\) and \(\mathrm{T}(\mathrm{P})\alpha^{\mathrm{i}}\). These are channel monitoring tuples used as the sequence of inputs to the proposed ML techniques. Signal attenuation tuple:  
\[\mathrm{T}(\mathrm{S})\alpha^{\mathrm{i}}=(\mathrm{S}\alpha^{\mathrm{i}}, \mathrm{S}\beta^{\mathrm{i}},\mathrm{S}(\mathrm{R})^{\mathrm{i}},\mathrm{S}( \mathrm{R}\mathrm{A})^{\mathrm{i}})\cdot\frac{\mathrm{d}\tau}{\mathrm{d}t} \forall\,\mathrm{L}^{\mathrm{N}} \tag{9}\]  
Signal energy tuple:  
\[\mathrm{T}(\mathrm{P})\alpha^{\mathrm{i}}=\left(\mathrm{P}(\mathrm{R})^{ \mathrm{U}-\mathrm{U}\mathrm{i}},\mathrm{P}(\mathrm{R})^{\mathrm{U}-\mathrm{S }\mathrm{i}},\mathrm{P}(\mathrm{R})^{\mathrm{S}-\mathrm{B}\mathrm{i}}\right) \cdot\frac{\mathrm{d}\tau}{\mathrm{d}t}\forall\,\mathrm{L}^{\mathrm{N}} \tag{10}\]  
Equations (9) and (10) illustrate the details of \(\mathrm{T}(\mathrm{S})\alpha^{\mathrm{i}}\) and \(\mathrm{T}(\mathrm{P})\alpha^{\mathrm{i}}\). In Equations (9) and (10), \(\tau\) states signaling interval; \(\mathrm{L}^{\mathrm{N}}\) denotes total number of wireless links in the network. These channel quality management tuples are provided in the ML network layers to compute learning factor and adaptive channel quality weight factor [31; 32; 33].