# 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
\(C_{0}(t)\) is then taken into the left half of the inequality in Equation (18), and the total data volume in time \([t_{acc},t_{R0}]\) is calculated by numerical integration. \[C(t,P_{i,j})=B\text{log}_{2}(1+\frac{G_{tot}}{N}\cdot\frac{P_{i,j}}{L_{t}(t)}), \tag{6}\]7  
Without loss of generality, we assume the preset power \(P_{0}\) is sufficiently small, resulting in a reduction of \(\Delta H_{0}\) in buffer data compared to \(H_{rem}\) within the interval \([t_{acc},t_{R0}]\), as shown in Equation (19). This configuration fails to satisfy the condition in Equation (18). Consequently, we employ an estimation scheme analogous to the approach in Equation (17) to calculate the power \(P_{1}=d\cdot P_{0}\) (\(d>1\)) that meets the second condition, as demonstrated in Equation (20):  
\[C(t,P_{i,j})=B\text{log}_{2}(1+\frac{G_{tot}}{N}\cdot\frac{P_{i,j}}{L_{t}(t)}), \tag{6}\]8  
\[C(t,P_{i,j})=B\text{log}_{2}(1+\frac{G_{tot}}{N}\cdot\frac{P_{i,j}}{L_{t}(t)}), \tag{6}\]9 Graph of input and output rate functions for user buffers. Substituting \(P_{1}=d\cdot P_{0}\) and Equation (20) into the left-hand side of Equation (19), we derive the following process:  
\[\overline{C}(P_{i,j})=\frac{1}{t_{\max}-t_{acc}}\int_{t_{acc}}^{t_{\max}}C(t,P _{i,j})dt \tag{7}\]0  
In Equation (21), the relation \(C(t,P_{1})=d\cdot C(t,P_{0})\) in the first step is derived from Equation (17). While Equation (21) appears to satisfy the second condition (i.e., Equation (18)), the inequality \(C(t_{R0},P_{1})=d\cdot C(t_{0},P_{0})>C(t_{1},P_{0})=R_{v}\) implies that when power increases to \(P_{1}\), \(t_{R0}\) no longer represents the time when the user's channel capacity \(C(t_{R0},P_{1})\) equals the streaming bit rate \(R_{v}\). Let \(t_{R1}\) denote the new time satisfying \(C(t_{R1},P_{1})=R_{v}\), which differs from \(t_{R0}\). Thus, substituting \(t_{R1}\) into the left-hand side of Equation (21) invalidates the equality, indicating that \(P_{1}\) is not the minimum power satisfying Equation (18). To apply the previous iterative approach, we must further analyze whether updating \(P_{0}=P_{1}\) in Equation (19) brings \(\Delta H_{0}\) closer to 0. Given that \(C(t,P)\) increases with time \(t\), we assume \(C(t_{R1},P_{1})=R_{v}\) (\(t_{acc}<t_{R1}<t_{R0}\)) and substitute it into the left-hand side of the inequality in Equation (18)):  
\[\overline{C}(P_{i,j})=\frac{1}{t_{\max}-t_{acc}}\int_{t_{acc}}^{t_{\max}}C(t,P _{i,j})dt \tag{7}\]1  
For \(\Delta H_{0}\) and \(\Delta H_{1}\):  
\[ \begin{array}{l}\Delta H_{0}=\int_{t_{acc}}^{t_{R0}}C(t,P_{1})dt{-}\int_{t_ {acc}}^{t_{R0}}C(t,P_{0})dt\\ =(d-1)\cdot\int_{t_{R0}}^{t_{R0}}C(t,P_{0})dt\\ >(d-1)\cdot\int_{t_{R1}}^{t_{R0}}C(t,P_{0})dt\\ =\int_{t_{R1}}^{t_{R0}}C(t,P_{1})dt{-}\int_{t_{R1}}^{t_{R0}}C(t,P_{0})dt\\ >\int_{t_{R1}}^{t_{R0}}C(t,P_{1})dt{-}R_{v}(t_{R0}-t_{R1})\\ =\Delta H_{1}\end{array}  \tag{23}\]  
From Equation (23), we observe \(\Delta H_{0}>\Delta H_{1}\), indicating that using Equation (20) to compute \(P_{1}=d\cdot P_{0}\) brings the updated power \(P_{1}\) closer to the true minimum power satisfying Equation (18). This scheme can be iterated several times to estimate the minimum power. Let \(P_{Rv2}\) denote the minimum power fulfilling Equation (18). Analogous to the iterative scheme for the first condition, we first preset a reference power \(P_{0}\), compute \(t_{R0}\), substitute it into Equation (20), and finally derive the adjusted power \(P_{1}=d\cdot P_{0}\). By iteratively updating \(P_{0}\) with \(P_{1}\) and repeating the process, the computed power converges toward the target \(P_{Rv2}\). The algorithm flowchart for \(P_{Rv2}\) is shown in Figure 6.  
Finally, the problem is formulated  
\[ \begin{array}{l}CHO_{i,j}\big{(}P_{i,j},S_{i,j}\big{)}=-\alpha_{1}\gamma_{ Pow}-\alpha_{2}\gamma_{Ch}\\ \left\{\begin{array}{l}\gamma_{Pow}=\frac{P_{i,j}+P\alpha_{i,j}}{P_{tot}}, \gamma_{Pow}\leq 1\\ \gamma_{Ch}=\frac{1+Chc_{i,j}}{C_{Htot}},\gamma_{Ch}\leq 1\\ P_{i,j}\geq\max(P_{Rv1},P_{Rv2})\end{array}\right.,\end{array}