# Joint Optimization of Data Transmission and Energy Harvesting in Relay Satellite Networks
## 6 Simulation Evaluation
### System Utility  
We evaluate the effects of weights \(V\) on system utility as shown in Figure 3. As we can see, with the increase in \(V\), the system utility follows an upward trend. It verifies the theory that a larger \(V\) can increase the system utility as Theorem 4. It can be further noted that the system utility increases rapidly at the initial stage. Since system utility \(\mathcal{H}(t)\) is a concave function, it can be observed that the growth rate of \(\mathcal{H}(t)\) decreases when \(V>2\times 10^{5}\).  
To test the performance of the proposed DTEM algorithm in improving system utility, four benchmark algorithms are taken for comparison. We evaluate the effectiveness of different optimization modules (i.e., data transmission and energy management) separately. In terms of the data transmission performance, we compare the DTEM algorithm with a fair contact plan (FCP) scheme proposed in [40], which allocates ISL connections with maximum cumulative disable connection opportunities. We also set a Random Link Matching Scheme (RLMS) via the idea of ISL allocation in [18] for comparison. In terms of the energy management performance, we consider two reference schemes, a greedy algorithm [41] with maximum remaining energy (GMR) for ISL contacts and an energy harvesting for the randomness scheme (EHRS) [23]. Specifically, FCP and RLMS have a similar control strategy for energy harvesting and data acquisition as DTEM, but without a data transfer optimization module. Correspondingly, GMR and EHRS do not consider energy management optimization compared to DTEM.  
Figure 3: System utility versus \(V\).  
The system utility of DTEM and benchmark algorithms are compared under different weights \(V\) in Figure 4, where we can observe that DTEM has the highest system utility among the three algorithms. As mentioned in Section 4, the optimal solution for the DACO problem indicates that a smaller size of the data queue or a larger size of the energy queue will result in a higher data acquisition rate (i.e., system utility). Since the DTEM schema jointly optimizes the performance of data transmission and energy harvesting, DTEM is superior to the other four schemes in improving system utility. It can be observed that the system utility increases with the weight \(V\) at the beginning and converge afterwards in Figure 4. The reason is that \(V\) is a weight to tradeoff the system utility and stability. According to (14), a larger \(V\) brings a larger system utility. Furthermore, since \(U(t)\) is a logarithm, the increase in system utility slows down after \(V>2\times 10^{5}\).  
To further test the performance of DTEM, the system utility of all five algorithms has been evaluated under different numbers of antennas on relay satellites (i.e., \(K\)) and different maximum data acquisition rates \(\varphi_{\max}\), respectively. We can observe that DTEM can achieve higher system utility compared with benchmark algorithms under different \(K\) in Figure 5. Furthermore, the system utility increases with the increase in antenna number, which enables more data transmission to relay satellites. Then, the system utility trends stable level due to the bottleneck of limited energy harvested by user satellites. Figure 6 depicts the system utility of DTEM and benchmark algorithms under different \(\varphi_{\max}\). It can be shown that DTEM has better performance gain in system utility than the other four schemes. Moreover, the increase in \(\varphi_{\max}\) can bring higher system utility. However, when the maximum data acquisition rate rises to some value, the system utility is improved very slowly. This is due to the limited transmission channels and energy resources. In terms of the maximum system utility, DTEM has a performance improvement of 4.8%, 9.6%, 10.6%, and 20.3% compared to FCP, CGLM, GME, and EHRS, respectively, when the maximum data acquisition rate \(\varphi_{\max}=100\) Mbps. This is attributed to the joint optimization of data transmission scheduling and energy management.