## 5 Simulation and Analysis  
In this section, we use the NS-3 simulator and MATLAB to simulate the performance of the proposed ACE method. The satellite parameters and the NB-IoT terminal power consumption values refer to 3 GPP's technical report TR 38.821 [25]. To illustrate the effectiveness of the proposed ACE method, we employ the parameters of CE in 3 GPP's technical report TR 36.763 and the Particle Swarm Optimization (PSO) algorithm for terrestrial-based NB-IoT networks as the benchmark problems. The specific parameters of the simulation are shown in Table 2.  
Figure 6 shows that in the feasible solution set within the Pareto front, the random access parameters of the NB-IoT terminal can be configured based on different application requirements. For instance, lower power consumption is crucial to data collection services with a sensitivity towards power consumption. Conversely, for alerting businesses that prioritize high RACH success probability in real time, substantial repetitions are necessary to ensure successful preamble transmission. For this kind of terminal, the parameter configuration should align with the maximum values present within the feasible solution set. Moreover, the parameter configuration of the proposed ACE method is shown in  
For satellites at different altitudes, their parameter configurations can be found in Table 3. This article mainly focuses on the two LEO satellite altitudes recommended by 3 GPP and analyzes the trade-off parameter configuration for the corresponding altitudes and service. For satellites at an altitude of 600 km and with alerting services, the requirement for RACH success probability is above 95%. For this type of NB-IoT terminal, power consumption is not the primary indicator and we need to focus on ensuring RACH success probability.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Transmit power of terminal \(p_{s}\) & 200 mW \\ Receive power of terminal & 90 mW \\ RRC\_Connected power of terminal \(E_{connect}\) & 90 mW \\ Battery capacity & 5 Wh \\ Satellite orbit altitude \(h\) & 600 km, 1200 km \\ Sat Rx max Gain \(G_{0}\) & 24 dBi \\ Sat beam diameter \(R\) & 90 km \\ G/T & \(-4.9\) dB/K \\ Average power of the line-of-sight path \(\Omega_{s}\) & 0.825 \\ Fading severity parameter \(m_{s}\) & 10 \\ Average power of the scattered path \(2b\) & 0.252 \\ Noise density \(\sigma^{2}\) & \(-174\) dBm/Hz \\ Density of active IoT devices \(\lambda\) & 0.1 device/km\({}^{2}\) \\ Number of sub-carriers & 48 \\ Maximum Number of repetitions \(N_{\text{rep}}^{\text{max}}\) & \{4, 12\}, (8, 18) \\ Back-off Window size \(W_{BO}\) & [0, 256-2], j \(\in\) [0, 3] ms \\ Time of RAO \(T_{RAO}\) & 640 ms \\ Packet Size & 125 byte \\ Simulation time & 15 min \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulation parameters.  
Figure 6: NSGA-II Pareto front for different traffic models.  
probability. Therefore, compared to data collection services at the same satellite altitude, the maximum number of retransmissions must reach 12 to achieve the goal of RACH success probability. And it also has a shorter back-off window size to ensure that the terminal retransmits within the beam coverage time. At a satellite altitude of 1200 km, a long delay will increase the probability of repetition failure. Then, a larger maximum number of repetitions needs to be set at this altitude and the back-off time window needs to be increased to 2048 ms to ensure successful repetition after the back-off state.