# A Distributed Energy-Throughput Efficient Cross-Layer Framework Using Hybrid Optimization Algorithm
## 4 Performance Evaluation
Table 4 demonstrates the average bit rates achieved by both layered systems (DECN, DEAP) and cross-layered systems (DECMN, DECEN, and centralized). The results show that the cross-layer design, including DECMN, outperforms the traditional layered design in terms of bit rate. DECMN, specifically, exhibits superior performance compared with the centralized system across various transmission lengths. DECMN achieves a significantly higher bit rate, particularly over medium communication ranges. This advantage can be attributed to the distributed nature of DECMN, which is not limited by the strict power constraints imposed by two-hop neighbors in a centralized system. DECMN utilizes the MPNMR optimization algorithm to effectively manage the distribution of transmission power among individual sensors, thereby enhancing overall system performance. This distributed approach allows DECMN to overcome the limitations of a centralized system and achieve higher bit rates in WUSNs. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Number of sensors & \(10-50\) \\
3D underground cube volume & \(10\) m \(\times\) \(10\) m \(\times\) \(10\) m \\ Coil radius & \(15\) cm \\ Number of turns & \(5\) \\ Outage delay probability & \(0.8\) \\ Predicted hop latency & \(0.9\) s \\ Packet error rate & \(10^{-4}\) \\ Packet length & \(100\) bytes \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Overall, the results indicate that the proposed DECMN algorithm offers improved performance in terms of bit rate compared to both traditional layered systems and a centralized approach. Indeed, DECMN achieves a comparable energy level to the centralized technique while offering other advantages. One notable advantage is its ability to ensure exceptional connectivity through bandwidth-constrained MI routes. This means that DECMN can effectively utilize the limited bandwidth available in MI communication for reliable and efficient data transmission in WUSNs. \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, \(\theta=0^{\circ}\) & 0.1 & 0.15 & 0.18 & 0.22 & 10.8 & 40 & 600 & 3008 & 15,218 \\ \hline Centralized Cross-layer, \(\theta=63^{\circ}\) & 0.2 & 0.28 & 0.34 & 0.42 & 100 & 290 & 3000 & 10,958 & 15,624 \\ \hline DEAP, \(\theta=0^{\circ}\) & 10.9 & 11.2 & 11.3 & 11.6 & 25.8 & 130.8 & 950 & 5712 & 16,514 \\ \hline DEAP, \(\theta=63^{\circ}\) & 11.2 & 11.4 & 11.7 & 13.1 & 123.2 & 305.3 & 4000 & 17,000 & 60,082 \\ \hline BPSK; No FEC, \(\theta=0^{\circ}\) & 141 & 141 & 141 & 141 & 190 & 540.8 & 3650 & 30,138 & 85,703 \\ \hline BFSK; BCH (63,57,1), \(\theta=0^{\circ}\) & 145 & 145 & 145 & 145 & 200 & 560.8 & 3850 & 34,482 & 99,852 \\ \hline DECN-MI Comm & 10.8 & 11 & 11.1 & 11.3 & 20.8 & 85.3 & 818.5 & 4930 & 14,711 \\ \hline DECN-MI Waveguide & 10.9 & 11.1 & 11.1 & 11.4 & 21.5 & 113.6 & 910.4 & 5512 & 15,894 \\ \hline DECEN-MI Comm & 10.9 & 11 & 11.1 & 11.2 & 20.2 & 84.6 & 811.7 & 4870 & 13,962 \\ \hline DECEN-MI Waveguide & 11 & 11 & 11.1 & 11.3 & 21 & 112.2 & 890.2 & 5372 & 15,154 \\ \hline DECEN-MI WG 3D coils & 11 & 11 & 11.2 & 11.3 & 21.2 & 112.9 & 900.7 & 5473 & 15,521 \\ \hline DECMN-MI Comm & 11 & 11.1 & 11.2 & 11.3 & 20.6 & 85.7 & 815.8 & 4884 & 13,983 \\ \hline DECMN-MI Waveguide & 11 & 11.1 & 11.2 & 11.4 & 21.1 & 113.5 & 894.1 & 5386 & 15,172 \\ \hline DECMN-MI WG 3D coils & 11 & 11.1 & 11.3 & 11.4 & 21.4 & 113.8 & 905.3 & 5491 & 15,538 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison results for transmitted energy (mJ/bit) as a function of distance (m).