## 4 Performance Analysis
### Summary and Handover Considerations  
The analysis of AUV-BS distance considering BS motion was conducted from two aspects: the influence of BS motion and that of network radius, yielding the following expected simulation results:  
* Considering \(D_{BA}\) and \(\Delta D_{BA}\), we analyzed the impact of BS motion in terms of direction and magnitude, as described in Section 4.3.1 and Section 4.3.2 It was found that the distance between the AUV and BS changes remarkably according to the direction of BS motion. In addition, the variability in AUV-BS distance is more significantly influenced by the magnitude of BS motion than its direction, emphasizing the substantial effect of the intensity of BS motion on distance fluctuations. * We analyzed the impact of BS motion on handover by applying \(D_{BA12}\) and \(\Delta D_{BA12}\), as described in Section 4.3.3 and Section 4.3.4. This analysis confirmed that the motion \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Network Radii (m)**} & \multicolumn{2}{c}{\(\Delta\)\(D_{BA12}\) **@SS3 (m)**} & \multicolumn{2}{c}{\(\Delta\)\(D_{BA12}\) **@SS6 (m)**} & \multicolumn{2}{c}{\(\Delta\)\(D_{BA12}\) **@SS8 (m)**} \\ \cline{2-7}  & **Mean** & **STD** & **Mean** & **STD** & **Mean** & **STD** \\ \hline
100 & 1.18 & 0.85 & 5.08 & 3.56 & 10.35 & 7.69 \\
300 & 0.54 & 0.65 & 3.72 & 3.78 & 7.15 & 7.52 \\
500 & 0.46 & 0.55 & 2.44 & 2.90 & 5.66 & 6.36 \\
1000 & 0.33 & 0.49 & 1.57 & 2.22 & 4.21 & 5.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The mean and standard deviation of \(|\Delta D_{BA12}|\) with respect to network radii and sea state. Figure 10: The number of handover decision errors in the overlapping region with respect to network radii when BS1 and BS2 move in the same direction as the AUV. direction of BS1 and BS2 also affects the handover as much as the motion direction between the AUV and the BS. When BS1 and BS2 move in the same direction, the variability spikes in the overlapping region. Conversely, when BS1 and BS2 move in opposite directions, the variability heightens near the start and end points of the path of the AUV. Furthermore, it was found that the symmetry of \(\Delta D_{BA12}\) depends on the direction of BS motion. In particular, the analysis of \(|\Delta D_{BA12}|\) allowed us to identify the timepoints where the impact of BS motion is most significant, and to infer the extent of variability. * From the analysis of AUV-BS distance considering BS motion, we determined \(|\Delta D_{BA12}|\) as an indicator to predict the likelihood of handover decision errors. By assessing how the value of \(|\Delta D_{BA12}|\) increases during the time when handovers are executed, we can predict potential handover decision errors. The pattern of \(|\Delta D_{BA12}|\) changes depending on the direction of BS motion, and the value of \(|\Delta D_{BA12}|\) increases (i.e., variability increases) during the time period when passing through the overlapping region where handovers could occur, especially when the directions of BS motion are the same. Furthermore, it is observed that larger BS motions, which lead to more significant changes in the physical environment (e.g., waves and winds), can have a greater impact on the variability in AUV-BS distance. This suggests that the accuracy of deciding when to execute a handover could decrease, potentially resulting in an increase in handover decision errors. * As described in Section 4.4, through the analysis of AUV-BS distance from the perspective of network radius, we can see that the value of the network radius also impacts \(|\Delta D_{BA12}|\), with larger network radii resulting in a decrease in the statistical magnitude of \(|\Delta D_{BA12}|\), thereby mitigating its influence. * From the simulation results, it was confirmed that both BS motion and network radius are factors affecting the variability in AUV-BS distance in overlapping region. Hence, these parameters can affect handover decision errors.