## 5 Simulation Results
### Data Delivery Probability  
The trade-off between the average long-term data delivery probability and the network normalized throughput is shown in Figure 7 under different EH rates \(\bar{\beta}\in\{1,2,3\}\). System parameters are the same with the previous simulations. We evaluated the performance of two centralized access protocols, which are time division multiple access (TDMA) and dynamic frame slotted Aloha (DFSA) [20; 21], to compare with that of the proposed distributed RA scheme. TDMA and DFSA are centralized access protocols, while the proposed policy is based on a random access scheme, which is different from the other two protocols in terms of the nature of mechanisms. In fact, the centralized schemes are expected to achieve higher throughput performance than the RA schemes, because packet collisions can be avoided by proper management at the central controller. However, in the energy-constrained networks, the centralized access schemes cannot always achieve such high data delivery probability and throughput due to energy shortage. In the simulations, we compare the performance of these three schemes from the perspective of energy constraint, which seems reasonable. The packet delivery probability of all these three schemes increases with the increase of \(\bar{\beta}\). TDMA always outperforms DFSA and the proposed RA scheme in terms of data delivery probability. Since time slots have been preallocated to each EH-ST, it does not suffer packet collisions. Therefore, the data delivery probability of TDMA is determined by the EH rate. DSFA can adjust the  
Figure 6: Comparison of packet loss ratio of different policies for different network sizes, under different EH rates \(\bar{\beta}\in\{1,2,3\}\), \(e_{max}=10\). For RA schemes, number of time slots in each frame \(N=200\), QPSK modulation, \(E_{s}/N_{0}=10\) dB. length of frame dynamically according to the number of active EH-STs, and it offers retransmission opportunities for the EH-STs. For the lower EH rates, many EH-STs are in a state of energy shortage; thus, the data delivery probability of DSFA is limited by the EH rate. Moreover, a larger frame makes more EH-STs deliver their data to the satellite successfully, but causes lower throughput. Unlike DSFA, the proposed distributed RA scheme balances well for both data delivery probability and throughput. This is because the delivery probability of the proposed scheme is restricted not only by \(\tilde{\beta}\), but also by \(\eta_{PLR_{th}}\). Thanks to the interference cancellation mechanism, the maximum throughput of the proposed RA scheme is higher than that of DFSA. However, transmitting more packet replicas will consume more energy. Compared with TDMA and DFSA (they only transmit one physical packet once), more EH-STs do not have enough energy to deliver the data. That is why the data delivery probability of the proposed RA schemes is only about 0.26 when \(\tilde{\beta}=1\). For the lower EH rates (e.g., \(\tilde{\beta}=1\) and \(\tilde{\beta}=2\)), the EH rate dominates the delivery probability. When EH rates become higher, almost every EH-ST has enough energy to send data. At this time, the proposed policy needs to guarantee the \(PLR\) being not beyond the \(PLR\) threshold; thus, \(\eta_{PLR_{th}}\) determines the delivery probability. Specifically, when \(\tilde{\beta}=3\), the delivery probability of the proposed scheme presents to be flat for the lower and moderate throughput but drops dramatically to control the \(PLR\) for the higher throughput. Notice that both TDMA and DFSA are centralized access protocols, and the central controller will allocate the time slots or adjust the frame length to improve the performance. However, the proposed distributed RA scheme can achieve acceptable throughput under the higher data delivery probability, which even performs better than DFSA.