###### Abstract  
This paper considers satellite communication networks where each satellite terminal is equipped with energy harvesting (EH) devices to supply energy continuously, and randomly transmits bursty packets to a geostationary satellite over a shared wireless channel. Packet replicas combined with a successive iteration cancellation scheme can reduce the negative impact of packet collisions but consume more energy. Hence, appropriate energy management policies are required to mitigate the adverse effect of energy outages. Although centralized access schemes can provide better performance on the networks' throughput, they expend extra signallings to allocate the resources, which leads to non-negligible communication latencies, especially for the satellite communication networks. In order to reduce the communication overhead and delay, a distributed random access (RA) scheme considering the energy constraints is studied. Each EH satellite terminal (EH-ST) decides whether to transmit the packet and how many replicas are transmitted according to its local energy and EH rates to maximize the average long-term network throughput. Owing to the nonconvexity of this problem, we adopted a game theoretic method to approximate the optimal solution. By forcing all the EH-STs to employ the same policy, we characterized and proved the existence and uniqueness of the symmetric Nash equilibrium (NE) of the game. Moreover, an efficient algorithm is proposed to calculate the symmetric NE by combining a policy iteration algorithm and the bisection method. The performance of the proposed RA scheme was investigated via numerous simulations. Simulation results showed that the proposed RA scheme is applicable to the EH devices in the future low-cost interactive satellite communication system. s 2019 19 99 10.3390/s19010099 10.  
networks, because they are insensitive to the network size and traffic characteristics, as well as easy to be implemented for satellite terminals. Specifically, RA is a kind of distributed uplink access scheme. Terminals upload their data packets directly via a shared wireless channel, and they do not need to request resources. For bursty traffic, it is inefficient for massive terminals to request resources frequently, especially for the network made up by a geosynchronous orbit (GEO) satellite. Moreover, centralized resource allocation and scheduling for massive terminals are really complicated and impractical, and the extra communication delay brought by resource allocation is intolerant. Thus, RA can be well applicable to the large network size and bursty traffic. Aloha and slotted Aloha (S-Aloha) are the classical RA protocols, and they are widely applied in satellite communication networks [2]. However, their performance in terms of network throughput is really poor due to packet collisions. Satellite communication networks suffer from large propagation delay, especially for the geostationary satellite. Packet collisions decrease the throughput of the network and further enlarge the access delay caused by packet retransmission, which is intolerant to interactive applications. Therefore, the research for more efficient satellite RA schemes is triggered by this issue. Thanks to the evolution and implementation of a physical layer forward error correction (FEC) coding scheme and iterative signal processing [3] at the gateway station, the performance of random access is improved greatly, which is more practical for interactive satellite networks. Contention resolution diversity slotted Aloha (CRDSA) [4; 5] as a candidate RA scheme for the next generation of interactive satellite systems [6] adopted the concept of time diversity and successive interference cancellation (SIC) to enhance the performance of RA, where the maximum throughput could reach up to 0.55 packets/slot. More specifically, a packet is transmitted two or more times within a frame, and each packet contains the location information of the replicas in the packet header, which is used to resolve the collisions.