## 1 Introduction
propose a joint beam-hopping and bandwidth allocation strategy based on a multi-agent DRL framework [12]. This scheme achieves improved data throughput performance and latency fairness, while also demonstrating strong generalization capabilities. Despite the extensive research on multi-beam satellite network, the security of wireless transmission between the user equipments and the LEO satellite has not been adequately considered. Due to the broadcast nature of wireless channels, satellite communication systems are susceptible to eavesdropping and malicious jamming. Some electronic reconnaissance satellites with specific functions may eavesdrop on important information transmitted by ground nodes without permission, causing security issues such as sensitive data leakage [13]. In addition, the presence of signals may attract the attention of some active eavesdroppers, who can impose malicious interference to disrupt the transmission. Traditionally, the security of satellite communications has relied primarily on encryption technology and physical layer security (PLS) [14; 15; 16]. Encryption can safeguard data confidentiality and integrity but requires intricate key management, algorithm updates, and remains susceptible to risks like password cracking. Physical layer security (PLS) utilizes modulation techniques and channel characteristics to reduce eavesdropping risks without traditional encryption. However, eavesdroppers with advanced decoding capabilities can overcome its defenses to obtain confidential information successfully [17]. Additionally, both of these measures are also susceptible to interference attacks by active eavesdroppers, causing communication interruptions due to the exposure of signal transmission behaviors. Different from the above traditional methods, covert communication technology aims to ensure privacy and security by hiding wireless signals, thereby avoiding detection by unauthorized eavesdroppers [18; 19]. Motivated by the above discussion, we investigate the design of a multi-dimensional resource allocation strategy to facilitate efficient and covert data transmission within the multi-beam LEO satellite network. Specifically, we jointly optimize satellite beam-hopping scheduling, frequency band allocation, and the transmit power of different user equipments to maximize the rate and covert requirements of different user equipments. By introducing auxiliary binary variables, we convert this optimization problem into a Mixed-Integer Linear Programming (MILP) problem so that machine learning-based techniques can be utilized for efficient solution finding. The main contributions of this paper are as follows:  
* To meet the transmission requirements of various user equipments, we investigate how to utilize a multi-dimensional resource allocation strategy in the multi-beam LEO satellite network. Unlike existing works, we additionally consider the covert transmission requirements and examine their impact on satellite resource allocation. * We derive the uplink covert transmission constraint and formulate the design of the multi-beam LEO satellite resource allocation strategy as an optimization problem. In our formulation, we jointly optimize satellite beam-hopping scheduling, frequency resource allocation, and transmit power of user equipments at different time slots. * To efficiently find a solution, we first employ linearization techniques to transform the optimization problem into a MILP problem. Subsequently, we apply a machine learning-based method, specifically a Tree Markov Decision Process algorithm, to solve this MILP problem. Simulation results demonstrate that our approach is effective.