# A Distributed Energy-Throughput Efficient Cross-Layer Framework Using Hybrid Optimization Algorithm
## 3 Energy-Throughput Efficient Cross-Layer Solution Using MPNMRA for WUSNs
### DECMN Protocol Using MPNMRA for WUSN  
To address the unique characteristics and challenges of WUSNs, it has been recognized that traditional methodologies for terrestrial WSNs are not suitable. The focus of previous research has primarily been on the physical layer aspects, such as antenna design and signal analysis, with limited attention given to higher-layer protocol design. In order to overcome these limitations and optimize system performance, a distributed cross-layer framework is proposed instead of the traditional layered approach. This approach ensures efficient resource utilization and improves overall system performance, aligning with the principles of the OSI model. Achieving a viable throughput of link transmissions while minimizing energy consumption is a key challenge in WUSNs. The goal is to successfully transmit packets between nodes \(i\) and \(j\) while maximizing the average transmitted packet rate and reducing the average packet energy simultaneously. This can be considered the acceptable link throughput, which refers to the rate at which packets are successfully transmitted over the link. By focusing on optimizing link throughput (\(Q_{ij}\)) and energy consumption \((E_{ij})\), the proposed cross-layer solution aims to address these challenges in WUSNs. This approach considers the specific requirements and constraints of underground environments, enabling efficient and reliable communication while minimizing energy consumption. By striking a balance between throughput and energy efficiency, the system can achieve improved performance and resource utilization in WUSNs. \[Minimize\ E_{ij}=L\left(P_{ij}/R_{ij}(T,\sigma)R_{\text{C}}^{ij}+2E_{dec}^{b}\right)\]  
\[Maximize\ Q_{ij}\]  
\[Subject\ to\ LQ_{ij}<R_{ij}(T,\sigma)R_{\text{C}}^{ij} \tag{9}\]  
The energy component of the objective function represents the energy dissipation per bit for transmitting data from node i to node j, where \(L\) is packet length. It is calculated as \(P_{ij}/R_{ij}(T,\sigma)R_{\text{C}}^{ij}+2E_{dec}^{b}\), where \(P_{ij}/R_{ij}(T,\sigma)R_{\text{C}}^{ij}\) represents the energy consumption as a function of distance, and \(E_{dec}^{b}\) represents the energy dissipation. \(P_{ij}\) is the transmitted power from node \(i\) to node \(j\). \(R_{ij}(T,\sigma)\) is the transmission bit rate, and \(R_{\text{C}}^{ij}\) is the channel coding rate. Here, \(\sigma\) is the medium conductivity expressed in [S/m]. The throughput component of the objective function represents the desired data transfer rate or packet delivery rate between nodes i and j. It can be measured in terms of the achieved link throughput \(Q_{ij}\) expressed in [pkt/s], satisfying the constraint \(LQ_{ij}<R_{ij}(T,\sigma)R_{\text{C}}^{ij}\)[13], or other relevant metrics that reflect the network's throughput performance. The optimization problem, termed energy and throughput (\(EaT\)), in WUSNs can be expressed by combining the objective functions related to energy consumption and throughput into a single objective function using the vector sum method (with weights \(w_{1}>0\), \(w_{2}>0\) and \(w_{1}+w_{2}=1\) for the energy savings and required throughput). The \(EaT\) objective function aims to find an optimal solution that balances both energy efficiency and throughput in the network. The specific form of the \(EaT\) objective function can be represented as follows:  
\[Minimize\ EaT_{ij}(T,\sigma)=w_{1}*L\left(P_{ij}/R_{ij}(T,\sigma)R_{\text{C}} ^{ij}+2E_{dec}^{b}\right)-w_{2}*Q_{ij}\]  
\[Find\ T,\sigma,j\in S_{i}\cap F_{i}^{D},\ m_{ij}\ \in\mathcal{M},c_{ij}\ \in\mathbb{C},\]  
\[P_{ij}\in[0,P_{i}^{max}],\ Q_{ij},\ l_{ij}\in\mathcal{L}\]  
\[Subject\ to\ \text{average delay, link, power, delay, variance constraints.} \tag{10}\]  
The objective function given by Equation (10) focuses on minimizing the link metric \(EaT_{ij}\) (energy and throughput) for each link \(i-j\). This function considers variables such as the power level \(P_{ij}\), the acceptable link throughput \(Q_{ij}\), and the DS-CDMA code length \(l_{ij}\).