Low earth orbit (LEO) satellites are a key technology to enable connectivity for rural and remote users. Communication satellites in LEO can provide coverage to much larger areas than terrestrial or aerial systems, while offering improved data rates when compared with geostationary systems. However, a major challenge with LEO satellite communications is the high mobility of the satellite, which results in a rapidly changing communication channel. Due to this, it is challenging to fairly allocate communication resources to multiple users in the system. This work proposes an Adaptive Power Allocation and Scheduling Scheme (APASS) to ensure user fairness in the downlink of a LEO satellite system serving mobile ground users. First, a novel channel and transmission model is introduced to capture the variability in channel statistics due to the satellite's trajectory. Then, a non-convex optimization problem is formulated to maximize the minimum rate across all ground users over a fixed set of time slots. To solve this problem, the proposed APASS dynamically allocates power and schedules transmissions based on predicted future channel gains. Numerical results show that APASS achieves strong performance even with substantial prediction errors, faring close to an upper bound that assumes perfect future channel knowledge. Furthermore, it improves the minimum user rate by a factor of 2.98 compared to equal-power allocation and maintains user fairness with a Jain's fairness index of well above 0.99.

翻译：低地球轨道（LEO）卫星是实现偏远及乡村地区连接的关键技术。与地面或空中系统相比，LEO通信卫星可覆盖更大范围，同时相较于地球静止轨道系统能提供更优的数据速率。然而，LEO卫星通信的主要挑战在于卫星的高移动性导致通信信道快速变化。这给系统中多用户通信资源的公平分配带来了困难。本文提出一种自适应功率分配与调度方案（APASS），以确保为移动地面用户服务的LEO卫星系统下行链路的用户公平性。首先，引入一种新型信道与传输模型以捕捉卫星轨迹造成的信道统计特性变化。随后，建立了一个非凸优化问题，旨在固定时隙集合内最大化所有地面用户的最小速率。为解决该问题，所提出的APASS方案基于预测的未来信道增益动态分配功率并调度传输。数值结果表明，即便存在显著预测误差，APASS仍能实现强健性能，其表现接近假设完美未来信道知识的上界。此外，与等功率分配相比，该方案将用户最小速率提升了2.98倍，并以远高于0.99的Jain公平指数维持了用户公平性。