## 4 Simulation Results and Discussion
### Simulation Method and Parameter Design  
To facilitate the simulation, while the train is moving, SBSs are deployed within the kernel (\(10\times 10\) square grid with an actual geographic area measuring \(10\sqrt{2}R\times 10\sqrt{2}R\) m\({}^{2}\)) ranges that the OIS generates whenever it does so. It is randomly determined whether an SBS is deployed in a \(1\times 1\) grid. Since the SBS boot preset radius is \(R\), we deployed SBSs in the center of a \(1\times 1\) grid, such that the grids with deployed SBSs are within the signal coverage range. Concurrently, for each kernel range, we also generated the slope \(m\) and constant \(b\) of the track equation that approximates the actual track path. Figure 17 illustrates a track path as well as the deployed SBSs and their statuses within the kernel at \(t_{n}\). When the OIS leaves its current kernel range, the above steps are repeated. A train speed range of 0-603 km/hr is assumed [28] for this study. In order to measure train speed more accurately during our simulations, we used a dashboard to obtain the train's speed at \(t_{n}\) and denoted it as \(v_{\text{GPS}}^{t_{n}}\). Following that, we used the coordinate system conversion framework to obtain the corresponding speed \(v^{t_{n}}\) in the kernel coordinate system. \(v^{t_{n}}\) can be expressed as  
\[v^{t_{n}}=v_{\text{GPS}}^{t_{n}}\times\frac{1000}{3600}\times\frac{1}{\sqrt{2} R}. \tag{32}\]  
To produce more realistic simulations, the random bursts of acceleration were applied based on \(v^{t_{n}}\). Specifically, with the initial train speed 0 km/hr, we designed the train to perform positive variable acceleration (denoted as \(a_{\text{up}}^{t_{n}}\)) from \(v_{\text{GPS}}^{t_{n}}=0\) km/hr to \(v_{\text{GPS}}^{t_{n}}=603\) km/hr; and upon reaching its maximum speed, the train then performed neg  
Figure 17: Diagram showing the track path and the deployed SBSs and their statuses within the kernel at \(t_{n}\); the straight line indicates the track path and “x” indicates the center of an SBS (its coverage range varies depending on its load ratio). ative variable acceleration (denoted as \(a_{\text{down}}^{t_{\text{n}}}\)) from \(v_{\text{GPS}}^{t_{\text{n}}}=603\) km/hr to \(v_{\text{GPS}}^{t_{\text{n}}}=0\) km/hr. \(a_{\text{up}}^{t_{\text{n}}}\) and \(a_{\text{down}}^{t_{\text{n}}}\) were defined as follows:  
\[a_{\text{up}}^{t_{\text{n}}}= \begin{cases}\text{random}(0,0.100),&0\leq v^{t_{ \text{n}}}<0.1964\;(0\leq v_{\text{GPS}}^{t_{\text{n}}}<200)\\ \text{random}(0,0.050),&0.1964\leq v^{t_{\text{n}}}<0.3928\;(200\leq v_{\text{ GPS}}^{t_{\text{n}}}<400)\\ \text{random}(0,0.040),&0.3928\leq v^{t_{\text{n}}}<0.5402\;(400\leq v_{\text{ GPS}}^{t_{\text{n}}}<550)\\ \text{random}(0,0.033),&0.5402\leq v^{t_{\text{n}}}\leq 0.5922\;(550\leq v_{\text{ GPS}}^{t_{\text{n}}}\leq 603)\end{cases} , \tag{33}\]  
\[a_{\text{down}}^{t_{\text{n}}}= \begin{cases}-\text{random}(0,0.100),&0\leq v^{ t_{\text{n}}}<0.1964\;(0\leq v_{\text{GPS}}^{t_{\text{n}}}<200)\\ -\text{random}(0,0.050),&0.1964\leq v^{t_{\text{n}}}<0.3928\;(200\leq v_{\text{ GPS}}^{t_{\text{n}}}<400)\\ -\text{random}(0,0.040),&0.3928\leq v^{t_{\text{n}}}<0.5402\;(400\leq v_{\text{ GPS}}^{t_{\text{n}}}<550)\\ -\text{random}(0,0.033),&0.5402\leq v^{t_{\text{n}}}\leq 0.5922\;(550\leq v_{\text{ GPS}}^{t_{\text{n}}}\leq 603)\end{cases} . \tag{34}\]  
When performing the simulations, we set \(G_{\text{TX}}=100\), \(G_{\text{RX}}=100\), \(\lambda=0.01\) m, and \(L=1\) in RSS formula (22). In addition, we also set \(R=200\) m, which is approximately the preset coverage range of a picocell. Since picocells have been shown to have a \(P_{\text{TX}}\) of 0.26 W when their coverage radius is 400 m [10], RSS \(=-99.8757\) dBm when the OIS is 400 m away from the emission center of a picocell, which also indicates the minimum RSS value allowed when demodulating a signal. The following settings were also used: \(K_{\text{th}}=0.95\), \(k_{\text{hold}}=1/3\), \(k_{\text{RSSmax}}=1/3\), and \(k_{\text{load}}=1/3\).