## 3 Methodology
### Packet Delivery Ratio  
Figure 7a presents the PDR of the proposed NBEER protocol, while Figure 7b and Table 9 provide a comparison of NBEER's PDR with that of Co-UWSN and CEER. Notably, NBEER outperforms the other protocols with significantly higher PDR values. This superiority is attributed to neighbor node cooperation and the selection of an NHN for data transfer. By leveraging NHNs, NBEER effectively minimizes packet loss and achieves a remarkable PDR.  
Figure 6: Average values of total energy consumption.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & TEC & TEC & TEC & TEC & TEC & TEC & TEC & TEC & TEC & TEC & TEC & **Avg** \\ \hline
**Protocol** & **after** & **after** & **after** & **after** & **after** & **after** & **after** & **after** & **After** & **After** & **After** & **TEC** \\  & **1000 s** & **2000 s** & **3000 s** & **4000 s** & **5000 s** & **6000 s** & **7000 s** & **8000 s** & **9000 s** & **10,000 s** \\ \hline
**Co-UWSN** & **17.35** & **15.0** & **14.19** & **12.98** & **12.68** & **12.0** & **11.48** & **10.01** & **9.95** & **9.79** & **13.29** \\
**CEER** & **16.93** & **15.62** & **11.26** & **9.54** & **8.31** & **7.113** & **6.56** & **6.145** & **5.93** & **4.93** & **13.15** \\
**NBEER** & **16** & **16.2** & **16.3** & **13** & **12.0** & **11.9** & **10.8** & **9.07** & **8.15** & **8.01** & **12.60** \\ \hline \hline \end{tabular}
\end{table}
Table 8: Total energy consumption after equal intervals of time.  
Furthermore, Figure 8 highlights the average PDR values of the protocols. Co-UWSN demonstrates a PDR of 42.47 and CEER shows a PDR of 53.55, while NBEER excels with an impressive average PDR of 81.1. These results reaffirm the enhanced performance and reliability of NBEER, showcasing its ability to maintain high packet delivery rates in underwater wireless sensor networks.  
The proposed protocol uses the neighboring-based method, in which each node tries to avoid any loss and thus estimate the highest packet delivery ratio. The same procedure is implemented with the proposed NBEER protocol, which shows a greater ratio in comparison with Co-UWSN. In Co-UWSN, only the cooperation scheme has been followed previously. But, in the proposed NBEER protocol, there is cooperation,  
Figure 8: Average values of packet delivery ratio.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & PDR & PDR & PDR & PDR & PDR & PDR & PDR & PDR & PDR & PDR & **Avg** \\ \hline
**Protocol** & **After** & **After** & **After** & **After** & **After** & **After** & **after** & **after** & **After** & **After** & **After** & **PDR** \\
**Co-** & **1000 s** & **2000 s** & **3000 s** & **4000 s** & **5000 s** & **6000 s** & **7000 s** & **8000 s** & **9000 s** & **10,000 s** & \\
**Co-** & **100** & **100** & **98** & **90** & **88** & **80** & **65** & **61** & **57** & **42** & 77.1 \\
**UWSN** & **100** & **100** & **98** & **90** & **88** & **80** & **65** & **61** & **57** & **42** & 77.1 \\
**CEER** & **99.51** & **95.51** & **78.95** & **65.22** & **48.78** & **41.88** & **38.94** & **24.21** & **24.21** & **22.34** & 53.55 \\
**NBEER** & **100** & **100** & **100** & **93** & **91** & **82** & **72** & **58** & **56** & **36** & 78.8 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Packet delivery ratio at equally spaced time intervals.  
Figure 7: (a) Packet Delivery Ratio of NBEER (b) Packet delivery ratio of all protocols vs. time (s).  
and neighboring-based node implementation takes place. This is the key factor allowing the proposed protocol, NBEER, to achieve a greater packet delivery ratio compared to Co-UWSN and the others as well.