## 2 System Model
### The Random Access Procedure and Coverage Enhancement  
Figure 2 shows the RA procedure between the terminal and LEO satellite. For LEO satellite-based IoT networks, a two-step random access procedure can reduce half of the access delay at the expense of receiver complexity compared with four-step random access [17]. Without a loss of generality, we analyzed the RACH success probability on the basis of the four-step random access procedure, because four-step random access is the 3 GPP recommended standard [18] in NTN networks. Furthermore, we focus on repetitions of the preamble for achieving the CE mechanism in MSG1 and the random access response (RAR) in MSG2 on the condition that MSG3 and MSG4 are in ideal states and always successful. It is important to note that the most critical part of the RA procedure is the repetition of the preamble in the MSG1 because the terminal has not synchronized with the networks [19]. Therefore, we assume that if the MSG1 and MSG2 processes are successful in transmission, then the entire random access procedure is considered successful in this paper. The two key factors affecting the RACH success probability are as follows: (1) whether the SINR of the preamble received by the LEO satellite is above the demodulation threshold; (2) whether multiple NB-IoT terminals select the same preamble in the same time slot. Combining the probabilities of these two key factors, we derive the RACH success probability in Section 3. Figure 3 illustrates the schematic diagram of the NB-IoT CE mechanism in LEO satellite-based IoT networks. From the figure, it can be seen that the CE mechanism is mainly realized by the repetition of the preamble. NB-IoT terminals measure the value of RSRP to determine its initial coverage class. In this way, NB-IoT terminals select appropriate random access parameters to match the coverage class. When a terminal fails to receive the RAR sent by the LEO satellite, it enters a back-off state and restarts the RA procedure again in the next time slot. Although repetitions increase the transmission delay, it can enhance the processing gain of the receiver and extend the coverage of the LEO satellite. Consequently, the CE mechanism is a crucial function for NB-IoT to achieve wide-area coverage in LEO satellite-based IoT networks. Figure 2: Random access procedure: (**a**) four-step random access procedure; (**b**) two-step random access procedure. Table 1 shows the NB-IoT repetition parameter configuration in the terrestrial networks. Because the distance between ground base stations and NB-IoT terminals is generally within a few thousand meters, the delay caused by repetitions to the terrestrial networks can be ignored. Conversely, the transmission delay must be considered in the RA procedure due to the fact that the value ranges from 2 ms to 5 ms during the overhead period of a LEO satellite with 600 km height. Moreover, the transmission delay exhibits significant differences when the NB-IoT terminal is distributed at the center and edge of the LEO satellite beam. In summary, if we use the random access parameters of the terrestrial networks, the repetition of the preamble will cause the NB-IoT terminal to be always in the state of transmitting MSG1 due to the existence of a long delay and the high dynamics of the LEO satellite. This situation not only fails to establish a connection with the LEO satellite but also results in a lot of power consumption. Furthermore, the choice of an excessively long back-off window size is similarly unfavorable to the RA procedure in LEO satellite-based IoT networks. A long back-off window size means that the terminal has to be in the RRC Connected state for a long time which will increase power consumption. It can also lead to a channel state of outdated information when the RA procedure restarts in the next time slot. The outdated CSI will cause a loss of synchronization and result in access failure.