###### Abstract
Furthermore, the resource allocation procedure will cause additional communication delay, which is unacceptable in satellite communication networks, especially for the networks made up by geosynchronous orbit (GEO) satellites. Some studies on multiple access schemes with distributed energy management policies were presented in References [27; 28; 29]. In this respect, a distributed dynamic optimal policy which maximized the sum throughput by adjusting each EH node's transmission power was introduced in Reference [27]. A decentralized access scheme was designed in Reference [28], where each EH node decided to transmit or discard a packet according to the packet's utility and the energy level independently by a game theoretic analysis method. A distributed scheduling scheme adopting an iterative technique to find the efficient rate and power scheduling for boosting the average throughput was proposed in Reference [29]. The terrestrial RA schemes with energy management policies mentioned above are based on pure S-Aloha, where no contention resolution mechanisms are applied to improve the performance of the networks. The S-Aloha scheme suffers a high collision probability, especially for the heavy traffic load. Without contention resolution mechanisms, colliding frequently requires a large number of retransmissions, which yields very large latencies in the satellite networks. Therefore, those RA schemes based on pure S-Aloha cannot be applied to the satellite scenario directly. In addition, the population of the satellite terminals in the satellite coverage range is much larger than that in the terrestrial cell, which makes the RA schemes with centralized energy management policies unpractical. Thus, the design of RA schemes with efficient energy management policies for the interactive satellite communication networks is urgent. Driven by these requirements, this paper introduces a distributed optimal RA scheme based on the CRDSA protocol for EH-STs in satellite communication networks. Unlike some asynchronous and spread spectrum based RA protocols, such as enhanced spread spectrum Aloha (E-SSA) [30] and minimum mean square error enhanced spread spectrum Aloha (ME-SSA) [31], CRDSA is a non-spread spectrum protocol but requires time slot synchronization. The reason for choosing CRDSA as the basic protocol is its robustness and simplicity of implementation compared with spread spectrum systems [12]. Moreover, CRDSA is a candidate RA protocol for the next generation of interactive satellite systems [6], which is interested in practice. The main contributions of this paper can be summarized as:  
* Propose a distributed optimal RA scheme in satellite communication networks with the consideration of energy management policies by extension of the CRDSA protocol towards an EH scenario. Each EH-ST determines whether to transmit the packet and how many replicas are sent according to its local energy information so as to maximize the average long-term network throughput;
* develop an analytical model of the average long-term throughput with constraints of packet loss ratio and energy. A game theoretic method is adopted to tackle the nonconvex optimization problem. By employing the same access scheme to all EH-STs, the symmetric Nash equilibrium of this game is characterized, and its existence and uniqueness are proved;
* exploit a policy iteration algorithm combined with a bisection method to approximate the optimal solution of the game. The performance of the proposed RA scheme by both numerical analysis and extensive simulations is investigated under different EH rates for different metrics as throughput, packet loss ratio, and data delivery probability. The rest of this paper is organized as follows. Section 2 introduces the system model and performance metrics. Problem descriptions and formulation are presented in Section 3. Section 4 analyzes and solves the optimization problem. Simulation results are shown in Section 5. Finally, Section 6 concludes this paper and indicates future work.