## 5 Simulation Results  
This section provides some simulation results to evaluate the proposed random access policy. It is assumed that the number of time slots in a frame \(N\) is 200 and each packet occupies one time slot. The length of each packet is 100 bits and the data are modulated by QPSK. The received energy per symbol noise power spectral density ratio \(E_{s}/N_{0}\) of each packet is assumed to be equal with 10 dB. Additive white Gaussian noise (AWGN) is added before CRDSA demodulating, and the maximum decoding iteration is to set \(N_{iter}^{max}=15\). For CRDSA, a packet is either clear (not collided with other packets) or interfered with other packets entirely [4]. For the clear packets, they can be decoded easily even without FEC, since \(E_{s}/N_{0}\) is large enough to decode the packets correctly. For the entirely collided packets, they can hardly be decoded correctly even with FEC, since the power of the overlapped packets is nearly the same [11]. Thus, we do not consider FEC in this paper. Actually, a power unbalance scenario and proper transmission power selection schemes combined with FEC can further boost the performance of the CRDSA [40], but the analytical model needs to be redesigned, which is out of the scope of this paper. This paper aims to provide a common but effective train of thought of designing a distributed RA policy for energy harvesting devices in satellite communication networks. Thus, the application of FEC is left for future research together with the power unbalance scenario and some variant CRDSA protocols. The main simulation parameters in this section are listed in Table 1.  
Since CRDSA adopts the scheme of successive interference cancellation, the value of \(PLR\) is obtained by an iteration method for a specific traffic load [4; 10]. Therefore, the expression of \(PLR(L)\) cannot be obtained directly. This paper uses the method of curve fitting to approximate the \(PLR\) function. In order to guarantee the \(PLR(L)\) increasing and \(g(\eta)\) concave in the range \((0,1)\), we adopt a Gaussian model with 8 terms to fit the curve, and the simulation results are shown in Figure 3. \(PLR\) value of CRDSA is computed by the method mentioned in Reference [10]. The traffic load is normalized by \(M/N\), where \(M\) is the number of concurrent terminals. Figure 3 shows the fitted curves are well matched with CRDSA \(PLR\) curves for both 2 and 3 replicas.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Settings** \\ \hline Number of time slots in a frame & \(N=200\) \\ Length of each packet & 100 bits \\ Modulation scheme & QPSK \\ Energy per symbol noise power spectral density ratio & \(E_{s}/N_{0}=10\) dB \\ Maximum decoding iteration & \(N_{iter}^{max}=15\) \\ Number of EH-STs & \(U=[0\):\(20\):\(200]\) \\ Number of replicas in CRDSA & \(l\leq 3\) \\ Energy harvesting rates & \(\beta\in\{1,2,3\}\) \\ Battery capacity & \(e_{max}=10\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation parameters. EH-ST: Energy harvesting satellite terminal.  
Figure 3: Packet loss ratio \(PLR\) curves comparison of the fitted curves and CRDSA with 2 and 3 replicas, number of time slots \(N=200\), QPSK modulation, \(E_{s}/N_{0}=10\) dB.