## 2 System Model
### MAC Protocol Operation and Performance Metrics  
(1) MAC Protocol Operation: The adopted MAC protocol is based on the idea of CRDSA and its frame structure is shown in Figure 2[4]. Time is slotted, and each RA frame consists of \(N\) time slots. The duration of each time slot is assumed to be equal to the packet transmission time, which is denoted as \(T_{s}\). Once the EH-STs have registered in the network, they will keep time synchronization via the procedures described in Reference [33] or in Reference [34]. An EH-ST can transmit only one MAC packet per RA frame. In fact, the EH-ST will transmit \(l\) replicas of the same MAC packet physically, where \(l\in\mathbb{Z}^{+}\) and \(l\leq N\). These replicas carry the same preamble and payload information and are randomly put in \(l\) slots of an RA frame. For a specific replica, the payload should contain the location  
Figure 1: Satellite communication networks with energy harvesting terminals. information of other replicas within the frame. Once a packet is detected successfully at the gateway station (e.g., the first packet of user 3 in Figure 2), it will use the location information to cancel the interference caused by other replicas on other slots (e.g., the second packet of user 3 in Figure 2). Most of the packets that are collided initially can be recovered by iterating the above approach. For packets decoded at the gateway station, it is assumed that channel information is always available, which can be acquired by the methods mentioned in References [4; 10]. For every frame, the EH-STs will always have a packet to send, and all packets are with equal importance. Each EH-ST decides whether to transmit the packet independently following the policy \(\omega\), which is only related to its current energy level and EH rate. Specifically, \(\omega\) indicates two parts. One is the number of packet replicas to send, which is denoted as \(l\), and the other one is the probability of transmitting these replicas, which is denoted as \(\eta\). For simplicity, this paper only considers stationary policies independent of each frame, and \(\mathbf{\omega}=(\omega_{1},\omega_{2},\ldots,\omega_{l})\) denotes as the joint transmission policy of the network. If the packet is not transmitted at the current frame, or it fails to be transmitted successfully, it will be transmitted in the next frame. (2) Performance Metrics: The performance of the RA scheme is measured by the packet loss ratio (\(PLR\)), the throughput \(T\) of the system, and data delivery probability \(p_{d}\), where \(PLR\) and \(T\) are related to the normalized traffic load \(L\), number of packet replicas \(l\), and number of time slots in a frame \(N\)[4]. Similar to the definition of throughput in Reference [10], for given \(l\) and \(N\), which are usually predefined in the network, the relationship between \(PLR\) and \(T\) is defined as:  
\[T\left(L,l,N\right)=\left(1-PLR\left(L,l,N\right)\right)L, \tag{1}\]  
where \(L=M/N\), and \(M\) is the number of the co-transmitted EH-STs within the duration of one frame (\(M\in\mathbb{Z}^{+}\)). Moreover, \(PLR\) is supposed to be a continuous increasing function with respect to (w.r.t) the traffic load \(L\)[4], and the traffic load increases with the increase of packet transmission probability. The data delivery probability is the probability of the data of any EH-ST \(u\) to be successfully delivered and correctly received by the satellite during the \(k\)th frame when there are new packets ready to be reported at the start of the frame \(k\). This metric, denoted as \(p_{d}\), measures the ability of the RA scheme to successfully transmit the packets from EH-STs to the satellite in every frame, without depleting their energy.