# A Distributed Energy-Throughput Efficient Cross-Layer Framework Using Hybrid Optimization Algorithm
## 4 Performance Evaluation
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Distance [m]** & **1 m** & **2 m** & **3 m** & **4 m** & **5 m** & **6 m** & **9 m** & **12 m** & **15 m** \\ \hline Centralized Cross-layer, \(\theta=0^{\circ}\) & 40 & 40 & 40 & 40 & 40 & 80 & 300 & 4000 & 9000 \\ \hline Centralized Cross-layer, \(\theta=63^{\circ}\) & 40 & 40 & 40 & 40 & 150 & 175 & 2000 & 10,000 & 28,500 \\ \hline DEAP, \(\theta=0^{\circ}\) & 65 & 65 & 65 & 65 & 65 & 170 & 1200 & 9500 & 20,000 \\ \hline DEAP, \(\theta=63^{\circ}\) & 65 & 65 & 65 & 65 & 163.2 & 455.3 & 6500 & 9200 & 27,000 \\ \hline BPSK; No FEC, \(\theta=0^{\circ}\) & 65 & 65 & 65 & 65 & 92 & 220.8 & 1930 & 14,000 & 24,700 \\ \hline BFSK; BCH (63,57,1), \(\theta=0^{\circ}\) & 65 & 65 & 65 & 65 & 92 & 250.8 & 1980 & 14,500 & 28,000 \\ \hline DECN-MI Comm & 50 & 50 & 50 & 50 & 50 & 90 & 340 & 4200 & 9800 \\ \hline DECN-MI Waveguide & 50 & 50 & 50 & 50 & 50 & 100 & 380 & 4500 & 10,800 \\ \hline DECEN-MI Comm & 50 & 50 & 50 & 50 & 50 & 85 & 330 & 4100 & 9600 \\ \hline DECEN-MI Waveguide & 50 & 50 & 50 & 50 & 50 & 90 & 360 & 4350 & 10,200 \\ \hline DECN-MI WG 3D coils & 50 & 50 & 50 & 50 & 50 & 105 & 390 & 4600 & 11,200 \\ \hline DECMN-MI Comm & 50 & 50 & 50 & 50 & 50 & 85 & 325 & 4070 & 9550 \\ \hline DECMN-MI Waveguide & 50 & 50 & 50 & 50 & 50 & 90 & 350 & 4310 & 10,120 \\ \hline DECMN-MI WG 3D coils & 50 & 50 & 50 & 50 & 50 & 105 & 378 & 4570 & 11,110 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison results for transmitted power (Watts) as a function of distance (m). Additionally, DECMN addresses the computational complexity challenges commonly encountered in highly viable WUSNs. By employing a distributed optimization approach, DECMN reduces the computational complexity compared with centralized techniques, making it more practical and feasible for real-world implementation. Overall, DECMN not only achieves energy efficiency comparable to centralized techniques but also provides enhanced connectivity and reduced computational complexity, making it a promising solution for efficient and reliable communication in WUSNs. Tables 5 and 6 demonstrate the benefits of DECMN in terms of normalized energy usage and packet rate for successfully received end-to-end data flow. With an increasing number of sensor nodes, DECMN exhibits lower energy usage and higher throughput, indicating improved performance compared with other simulated procedures. The GEO algorithm, which focuses primarily on geographical progress, performs poorly in terms of system performance. On the other hand, the TPL algorithm reduces the transmitted power in multi-hop scenarios, leading to better energy savings, increased connectivity, and longer routes. In comparison to DEAP and DECN solutions, DECEN and DECMN outperform them by achieving higher throughput gains and greater energy savings. The synergy achieved by optimizing multiple layers' communication features contributes to the overall improvement in system performance. DECMN's suitability for underground conditions is confirmed by its outstanding spectral and energy efficiency, as well as its lower computational complexity. Overall, DECMN presents a novel protocol for efficient and reliable MI communication in WUSNs, accompanied by a cross-layer approach that enhances system performance. Its benefits in terms of energy efficiency, throughput, and suitability for underground environments make it a promising solution for MI-based wireless underground sensor networks. [PERSON]'s rank-sum test and Friedman rank (f-rank) test are both non-parametric statistical tests commonly used to compare the performance of different algorithms or treatments [27]. In this context, these tests are used to assess whether the proposed solution is more efficient than other existing solutions. Table 7 shows the r-rank and f-rank of each algorithm listed in the last column for each algorithm, and it is found that the DECMN protocol ranked higher statistically than the others.