## 4 Performance Analysis
### Simulations Results Corresponding to BS Motion
#### 4.3.5 Analysis of Handover Decision Errors Due to BS Motion  
As shown in Figure 5a, at the start and end points of the movement of an AUV, the absolute value of \(D_{BA12}\) is large. This result means that there is minimal confusion about whether the AUV should connect to BS1 or BS2, essentially indicating that handover is unnecessary at these times. On the other hand, during the period of passing through the overlapping region, the value of \(D_{BA12}\) approaches \"0\". This implies that the variability caused by BS motion significantly increases the likelihood of handover decision errors. From these results, it can be inferred that considering the handover decision errors based on the AUV-BS distance is justifiable for the cases where the motions of BS1 and BS2 are in the same direction; that is, as shown in Figure 6a, when the value of \(|\Delta D_{BA12}|\) (i.e., variability) is large in the overlapping region, the probability of handover decision errors may also increase.  
We further analyzed \(D_{BA12}\) according to sea state conditions by zooming into the periods when crossing the overlapping area and near the endpoints in Figure 5a. Comparing the overall effect of BS motion on \(\Delta D_{BA12}\) throughout the entire time with its effect during the period of crossing the overlapping region yielded the following: for \(\Delta D_{BA12}\) at SS3, the average variation throughout all points is ~1.18, but it increases to 2.34 during the period of crossing the overlapping region. For \(\Delta D_{BA12}\) at SS6, the average variation throughout all points is ~5.08, but it increases to 8.38 during the period of crossing the overlapping  
Figure 6: \(|\Delta D_{BA12}|\) according to time and BS motion when \(r\) is 100 m: (**a**) When the motion of BS1 and BS2 is in the same direction. (**b**) When the motion of BS1 and BS2 is in opposite directions.  
region. Lastly, for \(\Delta D_{BA12}\) at SS8, the average variation throughout all points is \(\sim\)10.35, but it dramatically increases to 21.61 during the period of crossing the overlapping area. This indicates that the period of crossing the overlapping region, where a handover needs to be performed, is more significantly affected by BS motion.  
Building on the analysis above, we zoomed into Figure 5a, as illustrated in Figure 7, to examine how often handover decision errors occur during the period of highest \(|\Delta D_{BA12}|\) variability, when the motion direction of BS1 and BS2 is the same, specifically in the overlapping region. The squares above the graphs are the points at which errors in distance judgment occur due to BS motion (i.e., when BS1 is judged to be closer, but due to BS motion, BS2 is actually closer, and vice versa). As depicted in Figure 7, handover decision errors occur starting from 75 s in the overlapping region under the given sea state code conditions. This implies that when the motion directions of the two BSs are the same, the AUV may experience periodic handover decision errors upon entering this overlapping region, due to incorrect handover triggering. Moreover, this highlights that as the sea conditions deteriorate, environmental changes such as waves and wind become more severe, thereby exerting a greater influence on communication signals. This causes a mismatch between the expected and actual positions of the BSs, leading to incorrect assessments of the relationship between \(D_{BA1}\) and \(D_{BA2}\).  
The overall results imply that the sea state induces BS motion, which, in turn, increases the variability in AUV-BS distance. It can be observed that when the motions of two BSs are in the same direction, the likelihood of errors in handover decisions increases with the magnitude of BS motion. Specifically, this variability is further amplified in the overlapping region, potentially leading to frequent errors upon determining the timing for handover triggering.