I. Introduction
For the power limited satellite communication systems, it is important to optimize the efficiency of resource utilization and enhance system capacity by using resource allocation algorithm. Therefore, the research on optimization algorithm is hot issue. There are many studies on how to improve utilization efficiency of resource at present. The paper [1]–[3] set the maximum system capacity as the optimization objective. [1] proposed an optimal power allocation algorithm to satisfy the Qos of users for satellite communication systems. For physical layer security, a joint beam forming and power allocation optimal algorithm that could meet the need of security capacity was raised in [2]. [3] gave a power allocation scheme for fading channel in satellite communication systems. A two-step power allocation algorithm that targets the equilibrium between power and channel capacity was put forward [4]. Taking time delay into account, a joint power and bandwidth allocation algorithm was proposed to ensure the maximum system capacity [5]. Considering the users' needs and channel conditions, [6]–[8] make two order service rejection as the objective. Most of existing research concentrates on the downlink of satellite communication systems, and sets the repeater gain as fixed value ignoring its effects on resource allocation. However, for transparent repeater satellite communication systems, the noise from uplink would be enlarged by repeater and brought into downlink. Hence, the satellite repeater gain makes a big difference on resource allocation for transparent repeater satellite communication systems.