## 4 Statistical Testing of ENMRA Algorithm
### Distributed Cross-Layer Energy-Throughput-Efficient Protocol Using ENMRA for WUSNs  
Because of the significant differences in communication media (for example, between the air and the soil), it was discovered that the methodologies for terrestrial WSNs were not appropriate to WUSNs. In addition, the majority of the study centered around the physical layer, such as receiving signal analysis and antenna design. As a result, a wholly distributed cross-layer solution was proposed rather than the traditional layered protocol approach, resulting in well-organized resource usage and high system performance (the OSI model). In WUSNs, viable throughput of link transmissions and energy consumption were the main challenges to be addressed. To obtain the packet successfully for link \(i-j\), the objective was to reduce average packet energy and make the most of the average transmitted packet rate, characterized by the acceptable link throughput, given by:  
\[ \begin{array}{c}\textbf{{Minimize}}\ E_{ij}=L(P_{ij}/R_{ij}(T,\sigma)R_{C} ^{ij}+2E_{elec}^{b})\\ \textbf{{Maximize}}\ Q_{ij}\end{array}  \tag{15}\]  
The energy dissipation per bit for transfer data from the node \(i\) to \(j\) is expressed as \(P_{ij}/R_{ij}(T,\sigma)R_{C}^{ij}+2E_{elec}^{b}\). \(P_{ij}/R_{ij}(T,\sigma)R_{C}^{ij}\) is the energy consumption as a function of distance. \(E_{elec}^{b}=E_{elec}^{trans}=E_{elec}^{rec}\ [|/bit|]\) represents the energy dissipation independent of transmitter-receiver separation. \(E_{elec}^{trans}\) and \(E_{elec}^{rec}\) denote the energy consumed per bit by the transmitter and receiver circuit, respectively. The above objective functions were transformed to a single one using the vector sum method, and the optimization problem (i.e., energy and throughput \((EaT)\)) is expressed as:  
\[ \begin{array}{c}\textbf{{Minimize}}\ EaT_{ij}(T,\sigma)=w_{1}*L(P_{ij}/R_{ ij}(T,\sigma)R_{C}^{ij}+2E_{elec}^{b})-w_{2}*Q_{ij}\\ \textbf{{Find}}\ T,\sigma,j\in S_{i}\cap\ F_{i}^{D},\ m_{ij}\in\mathcal{M},\ c_{ij}\in\mathbb{C},\\ P_{ij}\in\left[0,P_{i}^{max}\right],\ Q_{ij},\ l_{ij}\in\mathcal{L}\\ \textbf{{Subject to}}\ \text{power,}\ \text{link, average delay, delay variance constraints}\end{array}  \tag{16}\]  
The decision variables for node \(i\) are the allowed link throughput, DS-CDMA code length, operating temperature, modulation scheme, forwarder, soil conductivity, power level, and channel coding scheme. For the best support in actual applications of WUSNs, cross-layer frameworks should have environmentally aware and distributive properties. DECEN's main concerns were that: (i) it calculate the relationship between link throughput and chaotic code, (ii) it achieve sensing and information exchange, (iii) it measure two environment-dependent parameters (electrical conductivity and temperature), (iv) it employ a two-phase decision strategy, and (v) it implement a loss-tolerance random-access scheme. DECEN was intended to solve the initial cross-layer design's application-driven objective optimization problem. DECEN employed non-cooperative game theory to solve a near-far dilemma in DS-CDMA and examined the relationship between link throughput and chaotic code length using distributed power management. The goal was to determine the relationship between DS-CDMA code lengths and link throughput. A two-phase technique was used to determine which geographic routes can be favored by low signaling overhead and their scalability, which is ideal for oil reservoirs. As a result, we presented a distributed two-stage framework with a cross-layer design. The sender divided the cross-layer optimization into two sequentially solved subproblems, taking inspiration from the geographical routing algorithm as follows:  
1. Minimize link metric \(EqT_{ij}\) using ENMRA, concerning power level \(P_{ij}\), acceptable link throughput \(Q_{ij}\), DS-CDMA code length \(l_{ij}\), and possible modulation function and channel coding combinations, i.e., \(j,~{}m_{ij}\), and \(c_{ij}\), and each of its possible next-hop neighbors. 2.