## 4 Statistical Testing of ENMRA Algorithm
### Performance Evaluation  
This section examines DECEN's performance in comparison to other algorithms. The DECEN algorithm was modeled in MATLAB version R2020a with the same system and resource characteristics. DECEN's performance (for MI communication, MI waveguide, and MI waveguide with 3D coil) was compared to DEAP and DECN [55], two traditional layered protocol systems. The population size (\(NP=20\)), number of iterations (\(t_{max}=100\)), and problem dimension (\(D=2\)) were the simulation parameters employed by DECEN and DECN algorithms. The simulation results revealed that DECEN saved substantial energy while also providing higher throughput, ideal for use in WUSNs. Figures 6 and 7 illustrate the results for a successfully decoded payload bit on the receiver. Because centrally regulated power gives more network information, it uses less energy and power than the proposed distributed method. Such assumptions can only be reached theoretically with a massive interchange of control signals, untenable in real-world settings, such as WUSNs. DECEN enabled the MAI power level, and the received noise at the receivers became the transmitter's only required information. It allowed for practically centralized energy usage and even achieved efficiency over extended transmission distances. The effect of the coil angle inaccuracy on the DECEN was not considered, and actual applications did not permit the use of multilayer arrangements. In this setting, DECEN and the central design required about the same amount of energy even over small transmission distances. Huge antenna size, dynamic channel conditions, and small communication range were addressed by MI-based WUSNs using MI waveguide and 3D MI coils, making them better for underground communication. Cross-layered architecture proved superior to traditional layered protocol architecture in terms of energy savings and link reliability. Figure 6: Comparison graph for transmitted energy as a function of distance. Figure 8 depicts the average bit rates of layered and cross-layered systems (i.e., DECEN, DECN, DEAP, and centralized). Cross-layer design is preferable over layered design because of its higher bit rate. On the other hand, the proposed DECEN outperformed the centralized system for almost all transmission lengths and allowed for a much greater bit rate, especially over medium communication ranges. This was because our distributed method was not constrained by the severe power limits of two-hop neighbors, like a centralized system, which is always the worst-case situation. Instead, DECEN employed the ENMRA optimization algorithm to manage each sensor's transmission power distribution better and increase its performance. DECEN achieved an energy level that was nearly identical to that of the centralized technique. It also enabled exceptional connectivity via bandwidth-constrained MI routes and significantly reduced the computational complexity of highly viable WUSNs. Figures 9 and 10 depict the normalized energy usage and packet rate for the successfully received end-to-end data flow, respectively. As the number of sensor nodes grew,  
Figure 8: Comparison graph for average bit rate as a function of distance. Figure 7: Comparison graph for transmitted power as a function of distance. better routes became available, and a wider variety of cooperatives emerged. In all of the simulated procedures, these benefits were demonstrated by lower energy usage and higher throughput. Without interchanging data between the multiple layer functionalities and employing a layered strategy, GEO precisely picked the set of nodes that advance successively closest to their target, principally in terms of geographical progress and the poorest performance. TPL reduced the amount of transmitted power required in multihop scenarios, resulting in improved energy savings, more connections, and longer routes. Our solutions delivered the best energy and performance by overcoming GEO, TPL, DEAP, and DECN solutions with higher throughput gain and more energy savings.