## 4 Performance Analysis
### Parameter Definition  
As mentioned in the Introduction, this study aims to explore the influence of BS motion on handover decisions. For this purpose, we consider the AUV-BS distance as a handover decision criterion, which is denoted as \(D_{BA}\), as depicted in Figure 2. This is because the initial positions of the BSs, as described in Section 2.1, experience changes across the x-, y-, and z-axes, which can be attributed to the dynamics of BS motion. This variation affects the network connectivity of the AUV to the BS and, consequently, induces handover decision errors. In Section 2, we define BS1 and BS2 as the current serving BS and the target BS for handover, respectively. Initially, we derive distance parameters related to the AUV and BS1. For this purpose, we consider the coordinates of the AUV (defined as \((X_{A},Y_{A},Z_{A})\)), \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Description** \\ \hline \(D_{BA1F}\) & The distance between BS1 and an AUV where BS1 is stationary \\ \(D_{BA2F}\) & The distance between BS2 and an AUV where BS2 is stationary \\ \(D_{BA1M}\) & The distance between BS1 and an AUV where BS1 is nonstationary due to BS motion \\ \(D_{BA2M}\) & The distance between BS2 and an AUV where BS2 is nonstationary due to BS motion \\ \(D_{BA1}\) & The distance between BS1 and an AUV (including both two cases) \\ \(D_{BA2}\) & The distance between a BS2 and an AUV (including both cases) \\ \(\Delta D_{BA1}\) & The difference between \(D_{BA1F}\) and \(D_{BA1M}\) (\(=D_{BA1F}-D_{BA1M}\)) \\ \(\Delta D_{BA2}\) & The difference between \(D_{BA2F}\) and \(D_{BA2M}\) (\(=D_{BA2F}-D_{BA2M}\)) \\ \(D_{BA12F}\) & The difference between \(D_{BA1F}\) and \(D_{BA2F}\) (\(=D_{BA1F}-D_{BA2F}\)) \\ \(D_{BA12M}\) & The difference between \(D_{BA1M}\) and \(D_{BA2M}\) (\(=D_{BA1M}-D_{BA2M}\)) \\ \(D_{BA12}\) & The difference between \(D_{BA1}\) and \(D_{BA2}\) (including both cases) \\ \(\Delta D_{BA12}\) & The difference between \(D_{BA12F}\) and \(D_{BA12M}\) (\(=D_{BA12F}-D_{BA12M}\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The definition of parameters related to the AUV–BS distance (the unit for all parameters in Table 2 is meters). Figure 3: Numerical modeling for a buoy (**left**) and a model including a mooring line (**right**) under sea state 8.  
the coordinates of BS1 when stationary (defined as \((X_{F1},Y_{F1},Z_{F1})\)), and the coordinates of BS1 when its position changes due to BS motion (defined as \(((X_{M1},Y_{M1},Z_{M1}))\)). Then, the distance between the AUV and stationary BS1, \(D_{BA1F}\), is expressed as \(\sqrt{\left(X_{F1}-X_{A1}\right)^{2}+\left(Y_{F1}-Y_{A1}\right)^{2}+\left(Z_{F 1}-Z_{A1}\right)^{2}}\). The distance between BS1 and an AUV where BS1 is nonstationary due to BS motion, \(D_{BA1M}\), is also given as \(\sqrt{\left(X_{M1}-X_{A}\right)^{2}+\left(Y_{M1}-Y_{A}\right)^{2}+\left(Z_{M 1}-Z_{A}\right)^{2}}\). In addition, \(D_{BA2F}\), the distance between the AUV stationary BS2, and \(D_{BA2M}\), the distance between the AUV and nonstationary BS2, can be similarly determined. To determine the effect of BS motion, we consider the difference between \(D_{BA1F}\) and \(D_{BA1M}\) for BS1 (defined as \(\Delta D_{BA1}\)) and the difference between \(D_{BA2F}\) and \(D_{BA2M}\) for BS2 (defined as \(\Delta D_{BA2}\)). Additionally, we compare the distances between the AUV and each of the two BSs in order to check the impact of BS motion on handover. To do this, we consider the difference between \(D_{BA1F}\) and \(D_{BA2F}\) for the stationary BS (defined as \(D_{BA12F}\)), as well as the difference between \(D_{BA1M}\) and \(D_{BA2M}\) for the nonstationary BS (defined as \(D_{BA12M}\)). Finally, we also denote the difference between \(D_{BA12F}\) and \(D_{BA12F}\) as \(\Delta D_{BA12}\). Table 2 summarizes the overall parameters related to the AUV-BS distance. Parameters for a stationary BS are marked with an \"F\" subscript (e.g., \(D_{BA1F}\)), whereas those reflecting the BS motion use an \"M\" subscript (e.g., \(D_{BA1M}\)).