## 4 Performance Analysis
### Simulations Results Corresponding to BS Motion
#### 4.3.3 Analysis of \(D_{ba12}\)  
When deciding to execute a handover based on the AUV-BS distance, it is necessary to compare the values of \(D_{BA1}\) and \(D_{BA2}\); this is relative to the AUV to determine which BS is closer. Accordingly, this analysis involves examining \(D_{BA12}\), which enables comparison between \(D_{BA1}\) and \(D_{BA2}\).  
As shown in all panels in Figure 5, \(D_{BA12}\) commonly starts with a negative value, progresses to zero, and subsequently shifts to a positive value as time passes. This consistent behavior occurs irrespective of the direction or magnitude of BS motion, attributed to the scenario wherein the AUV steadily transitions from the coverage area of BS1 to that of BS2.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**BS Motion**}} & \multicolumn{8}{c}{\(\Delta D_{BA1}\) **(m)**} & \multicolumn{8}{c}{\(\Delta D_{BA2}\) **(m)**} \\ \cline{2-13}  & \multicolumn{3}{c}{**SS3**} & \multicolumn{3}{c}{**SS6**} & \multicolumn{3}{c}{**SS8**} & \multicolumn{3}{c}{**SS3**} & \multicolumn{3}{c}{**SS6**} & \multicolumn{3}{c}{**SS8**} \\ \hline
**BS1** & **BS2** & **Mean** & **STD** & **Mean** & **STD** & **Mean** & **STD** & **Mean** & **STD** & **Mean** & **STD** & **Mean** & **STD** \\ \hline F & F & 0.44 & 0.98 & 1.53 & 4.87 & 2.79 & 10.07 & \(-\)0.73 & 0.91 & \(-\)3.55 & 4.63 & \(-\)7.56 & 9.13 \\ F & R & 0.44 & 0.98 & 1.53 & 4.87 & 2.79 & 10.07 & 0.73 & 0.91 & 3.42 & 4.71 & 7.04 & 9  
However, the variability pattern of \(D_{BA12}\) shifts based on the BS motion direction. When BS1 and BS2 move in the same direction, the variability spikes in the overlapping region, meaning that the gap between \(D_{BA12F}\) and \(D_{BA12M}\) widens, as shown in Figure 5a,d. Conversely, when BS1 and BS2 move in opposite directions, the variability heightens near the start and end points of the path of the AUV, as depicted in Figure 5b,c. This demonstrates that, in scenarios where the AUV transitions from the periphery of BS1 to BS2, the instances of increased or decreased variability are influenced by BS motion direction.  
As the magnitude of BS motion increases, the variability in \(D_{BA12}\) also intensifies. In scenarios where the motion directions of BS1 and BS2 are the same, the difference between \(D_{BA12F}\) and \(D_{BA12M}\) grows as the BS motion magnitude increases, especially during the time at which the AUV passes through the overlapping region, as illustrated in Figure 5a,d. Conversely, when the motion directions of BS1 and BS2 are opposite, the variability in \(D_{BA12}\) increases near the start and end points of the movement of the AUV as the sea state code rises, demonstrating a notable impact of BS motion magnitude in these scenarios, as shown in Figure 5b,c.  
Figure 5: \(D_{BA12}\) with respect to time and BS motion when \(r\) is 100 m: (**a**) BS1 and BS2 move in the same direction as the AUV. (**b**) BS1 moves in the same direction as the AUV, while BS2 moves in the opposite direction. (**c**) BS1 moves in the opposite direction to the AUV, while BS2 moves in the same direction. (**d**) BS1 and BS2 move in the opposite direction to the AUV.