# Handover Scheme in LEO Satellite Networks Based on QoE for Streaming Media Services
## 3 Simulation System Design for Handover and Access of Streaming
### Handover Scheme Design Based on Streaming Services
The \(\theta(t)\) obtained in [23] is brought into Equation (6), and then the average channel capacity is calculated as  
\[\overline{C}(P_{i,j})=\frac{1}{t_{\max}-t_{acc}}\int_{t_{acc}}^{t_{\max}}C(t,P _{i,j})dt \tag{7}\]  
To satisfy the first condition, the average channel capacity \(\overline{C}(P_{i,j})\) of the communication link between user \(u_{i}\) and satellite \(S_{i,j}\) must satisfy \(\overline{C}(P_{i,j})\geq R_{v}\). We define \(\overline{C_{Rv1}}\) as the minimum average channel capacity meeting this requirement, where \(\overline{C_{Rv1}}=R_{v}\). However, the functional expression for \(L_{t}(t)\) is so complex that it is not possible to write the original function of \(C(t,P_{i,j})\), and only numerical methods (e.g., [PERSON]'s integral or trapezoidal methods) can be used to calculate the average channel capacity. This also makes it impossible to directly derive the required minimum power \(P_{Rv1}\) with the \(\overline{C_{Rv1}}\) known. In this paper, an indirect mathematical method is used to derive the required power. First, a reference power \(P_{0}\) is preset and substituted into Equation (6). The value of \(P_{0}\) can be arbitrarily selected from common power levels in LEO satellite systems, which does not affect subsequent algorithms. In simulations, we set \(P_{0}=25\) dBW. By combining Equation (6) with Equation (7), the reference average channel capacity \(\overline{C_{0}}\) corresponding to \(P_{0}\) can be calculated:  
\[\overline{C_{0}}=\frac{1}{t_{\max}-t_{acc}}\int_{t_{acc}}^{t_{\max}}B\text{log}_{ 2}(1+\frac{G_{tot}}{N}\cdot\frac{P_{0}}{L_{t}(t)})dt \tag{8}\]  
Using the trapezoidal rule for definite integrals, the definite integral in Equation (8) is rewritten in summation form:  
\[\overline{C_{0}}=\frac{1}{t_{\max}-t_{acc}}\sum_{k=1}^{K}B\text{log}_{2}(1+ \frac{G_{tot}}{N}\cdot\frac{P_{0}}{L_{t}(t_{acc}+(k-1)\Delta t)})\Delta t \tag{9}\]  
After moving the constant term outside the logarithm to the left-hand side, the right-hand side leverages the logarithmic identity by expressing the sum of multiple logarithms as the logarithm of the product of their arguments:  
\[\frac{\overline{C_{0}}\cdot(t_{\max}-t_{acc})}{B\Delta t}=\text{log}_{2}(\prod _{k=1}^{K}(1+\frac{G_{tot}}{N}\cdot\frac{P_{0}}{L_{t}(t_{acc}+(k-1)\Delta t) })) \tag{10}\]  
\[2^{\frac{\overline{C_{0}}\bullet(t_{\max}-t_{acc})}{B\Delta t}}=\prod_{k=1}^ {K}(1+\frac{G_{tot}}{N}\cdot\frac{P_{0}}{L_{t}(t_{acc}+(k-1)\Delta t)}) \tag{11}\]  
\(P_{Rv1}\) and \(\overline{C_{Rv1}}\) also satisfy the relationship in Equation (11), just as \(P_{0}\) and \(C_{0}\) do:  
\[2^{\frac{\overline{C_{Rv1}}\cdot(t_{\max}-t_{acc})}{B\Delta t}}=\prod_{k=1}^ {K}(1+\frac{G_{tot}}{N}\cdot\frac{P_{Rv1}}{L_{t}(t_{acc}+(k-1)\Delta t)}) \tag{12}\]  
Let \(\overline{C_{Rv1}}=d\cdot\overline{C_{0}}\), where \(d\) is the ratio of the minimum channel capacity \(\overline{C_{Rv1}}\) to the reference channel capacity \(\overline{C_{0}}\). We will later discuss the relationship between \(d\), \(P_{Rv1}\), and \(P_{0}\), and we will estimate \(P_{Rv1}\) using \(P_{0}\) and \(d\). Substituting \(\overline{C_{Rv1}}=d\cdot\overline{C_{0}}\) into the left-hand side of Equation (12), we obtain  
\[2^{\frac{\overline{C_{Rv1}}\cdot(t_{\max}-t_{acc})}{B\Delta t}}=2^{\frac{d \overline{C_{0}}\cdot(t_{\max}-t_{acc})}{B\Delta t}}=(2^{\frac{\overline{C_{0 }}\cdot(t_{\max}-t_{acc})}{B\Delta t}})^{d} \tag{13}\]  
Substituting Equation (12) into the left-hand side of Equation (13), and substituting Equation (11) into the right-hand side of Equation (13), we obtain  
\[\prod_{k=1}^{K}(1+\frac{G_{tot}}{N}\cdot\frac{P_{Rv1}}{L_{t}(t_{acc}+(k-1) \Delta t)})=\prod_{k=1}^{K}(1+\frac{G_{tot}}{N}\cdot\frac{P_{0}}{L_{t}(t_{acc} +(k-1)\Delta t)})^{d} \tag{14}\]  
In next-generation LEO satellite communication systems for broadband services, the value of \(G_{tot}\cdot P_{0}/(L_{t}(t_{acc}+(k-1)\Delta t)\cdot N)\) in Equation (13) is positive and often approaches 0.