## 1 Introduction
To extend the supported satellite beam size, the authors in [10] design a new preamble format for the NB-IoT RA procedure. The work in [11] presents a simulation tool which is conceived as a new module for the open-source 5G-air-simulator, deriving the performance of NB-IoT in LEO satellite-based networks. The authors in [12] make a comparison of the RACH success probability and the access time for different combinations of the configurable random access parameters which are given by the 3 GPP standard [13]. Although the studies mentioned above have proposed some solutions to the problems that may arise in the NB-IoT RA procedure, the impact of the NB-IoT unique coverage enhancement (CE) mechanism in LEO satellite-based networks has not been taken into consideration. In the NB-IoT RA procedure, 3 GPP mandated a special link adaptation technology named the CE mechanism to achieve the objective of the 20 dB enhanced coverage of NB-IoT for wide-area outdoor coverage [14]. However, the NB-IoT terminal distributed in the center and edge of the LEO satellite beam has a large difference in the Signal-to-Interference-plus-Noise Ratio (SINR) due to the wide coverage of LEO satellite beams. Therefore, it is crucial to ensure lower power consumption and diverse business RACH success probability requirements in an NTN scenario [15]. The CE mechanism plays a key role in meeting these demands. If we directly employ the CE parameter configuration of terrestrial-based networks in LEO satellite-based IoT networks, it will result in lower RACH success probability and higher power consumption because of the long propagation delay between LEO satellites and NB-IoT terminals. By addressing the above challenges, the major contributions in this paper are summarized as follows:  
* To address the problem of CE parameter configurations in LEO satellite-based IoT networks, we propose an Adaptive Coverage Enhancement (ACE) method to optimize RACH success probability and the power consumption of the terminal for diverse LEO satellite-based IoT applications. * Based on stochastic geometry theory, we present a mathematical framework for analyzing RACH success probability in the LEO satellite-based IoT networks and derive a closed-form expression of RACH success probability for NB-IoT terminals. * To meet the different requirements of diverse applications in LEO satellite-based IoT networks, we formulate an optimization problem, that considers the trade-off between RACH access success probability and power consumption, to optimize the number of maximum repetitions and back-off window size. This is essentially a multi-objective optimization problem. To solve this optimization problem, we employ the Non-dominated Sorting Genetic Algorithms-II (NSGA-II) method to obtain the Pareto front for different applications. On this basis, we also present a parameter configuration method to achieve the RACH parameter settings of the NB-IoT terminal. * In order to evaluate the performance of proposed ACE method by system-level simulation, we use the NS-3 simulator to simulate the system throughput and support NB-IoT's technical application in LEO satellite-based IoT networks. The rest of this paper is organized as follows. Section 2 describes the system model and the principle of CE. In Section 3, we derive the RACH success probability and establish a power consumption model for NB-IoT in a LEO satellite channel. In Section 4, we formulate the optimization problem and solve it to obtain RA parameters for diverse applications. Simulation results are presented in Section 5. Finally, we conclude this paper in Section 6.