# Joint Optimization of Data Transmission and Energy Harvesting in Relay Satellite Networks
## 1 Introduction
On the one hand, if the LEO satellite connected to the GEO satellite has insufficient energy to achieve transmission, it will cause a waste of antenna resources. On the other hand, the connected user satellites with a small data buffer will waste scarce bandwidth resources. Therefore, it is of vital importance to develop effective link allocation strategies in dynamic satellite networks. In the literature, there have been some data transmission scheduling schemes for satellite networks [13; 14]. These methods improve the transmission performance to a certain extent, but ignore the impact of insufficient energy supply for satellites in practical applications. Motivated by the actual problems considered in this paper, there are also some works on designing joint energy and resource allocation strategies [15; 16]. However, these works are mainly oriented to predictable data arrival, which cannot be applied to the scheduling of stochastic arrived data directly. The existing works [17; 18] on data transmission with random data arrival has more or less some limitations, such as operating in a finite-horizon or requiring prior statistics on data arrivals. Therefore, an energy-efficiently collaborative transmission method should be carefully designed for random arrived data. To comprehensively consider the characteristics of the relay satellite network, we systematically study an online data transmission optimization method, which can achieve a higher system utility and long-term stability. The main contributions of this paper can be summarized as follows:  
* We design a dynamic stochastic system model considering the RSN features (i.e., dynamics of network topology, limited transmission resources, and unstable energy supply). We present a multi-objective optimization problem to maximize system utility without prior statistics knowledge about the stochastic process. * To solve the joint optimization problem of data transmission and energy management in stochastic satellite networks, we propose an online optimal control algorithm, named DTEM, which can improve transmission performance and energy efficiency. In particular, we construct an optimization framework based on Lyapunov stability theory to decompose the optimization problem into three sub-problems, i.e., data acquisition, energy harvesting, and inter-satellite transmission. Based on this, our proposed method can adaptively optimize the system variables (i.e., data acquisition rate, energy harvesting rate, ISL contact state, and transmission rate) at each time slot. * We analyze the performance of our proposed algorithm in satellite networks comprehensively, including the maximum storage of buffer and the minimum capacity of the battery, which are required to maintain system stability. Furthermore, we compare the time-average system optimal performance with the global system optimal solution. Further, we establish a satellite scenario under dynamic network topology and conduct extensive simulations to demonstrate the efficiency of our method. The remainder of this paper is structured as follows. In Section 2, we introduce the related work about data transmission schemes in satellite networks. In Section 3, we design a dynamic stochastic system model and summarize our optimization formula for maximizing system utility. In Section 4, we elaborate on the solution strategy and propose an efficient online algorithm, and the analysis for system performance is discussed in Section 5. Then, extensive simulations are illustrated in Section 6. Finally, this paper is concluded in Section 7.