# Asynchronous Flipped Grant-Free SCMA for Satellite-Based Internet of Things Communication Networks
## 5 Simulation Results
### AF-SCMA MAC Performance Results  
We first investigate the performance of AF-SCMA in terms of PLR and throughput for both simulation and analytical model (refer to Section 4) with and without power unbalance. The results are shown in Figure 3. The codebooks of SCMA adopted in the simulation are referred to [36], which is a 150% overloading system. Specifically, the number of subcarriers \(K=4\), codebook size \(M=4\), number of non-zero entities \(N=2\), and the number of codebooks \(N_{CB}=6\). Thus, we use SCMA (\(K\), \(N_{CB}\)) to reflect the relationship between resources and codebooks. As we can see in Figure 3, the throughput of AF-SCMA increases linearly with the increase of traffic load first, and then it drops due to the severe packet collisions. In addition, we notice that AF-SCMA can benefit from the power unbalance. For a target \(PLR-10^{-3}\), the maximum throughput increases from 1.9 bits/symbol/carrier for the case of \(\sigma=0\) dB to 2.4 bits/symbol/carrier for the case of \(\sigma=3\) dB. Please note that, for the system of SCMA(4, 6), the theoretical maximum throughput is 3 bits/symbol/carrier. However, without request-grant procedure and time synchronization, the proposed AF-SCMA can achieve a relatively high throughput (2.4 bits/symbol/carrier) with low PLR flexible to power unbalance, which is remarkable. By comparing the simulation results with the analytical results, we notice that in the higher traffic load region (G = 2.5-3) there are some differences between the curves, especially for \(\sigma=2\) and \(\sigma=3\). This is probably because we adopt AWGN to approximate the behavior of MAI. Moreover, by introducing the empirical compensation factor \(\beta\)[9] and different codebooks interfering factor \(\alpha\) in the analytical model will also loose the accuracy of the analytical model, especially for the severe collisions scenario. However, these differences occur in a high traffic load region which corresponds to really large PLR (beyond the practical target PLR). Therefore, this simple but effective analytical model can well match with the simulation results. In addition, we notice an interesting phenomenon in Figure 3b that for the large \(\sigma\) some packet cannot be received correctly although the traffic load is not very high. This phenomenon is dubbed as floor effect which is discussed in [10]. This is because in the presence of power unbalance, the received power of some packets cannot reach the decoding threshold, especially for large standard deviation. Therefore, these packets cannot be decoded although the IC procedure is assumed to be perfect. Figure 3: AF-SCMA analytical and simulation results comparisons for packet size 500 bits, Turbo encoder with \(r=1/3\), SCMA (4, 6), \(\left[E_{b}/N_{0}\right]_{D}=13\) dB, \(N_{chunk}=10\), \(N_{iter}=10\), in the presence of power unbalance with \(\mu=0\) and \(\sigma=0,1,2,3\) dB respectively. (**a**) Throughput. (**b**) PLR. This phenomenon can be mitigated by increasing the transmission power or enlarging the packet size [10]. We also compare the performance of AF-SCMA with asynchronous SCMA (A-SCMA) and slotted SCMA (S-SCMA) with and without power unbalance under the scenario of the grant-free system. As a baseline, IC technique is applied to both A-SCMA and S-SCMA. Specifically, if a packet is decoded correctly, it can be subtracted from the overlapping signal and the IC procedure is assumed to be error-free. Noted that, two packets are transmitted simultaneously in AF-SCMA, which means the transmission power is twice as high as the schemes with transmitting only one packet (A-SCMA and S-SCMA). For the sake of fairness, we double the desired receive power for A-SCMA and S-SCMA schemes in the simulation to compare with the performance of AF-SCMA with \(\left[E_{b}/N_{0}\right]_{D}=13\) dB, and the simulation results are illustrated in Figure 4. For the higher \(\left[E_{b}/N_{0}\right]_{D}\) (i.e., \(\left[E_{b}/N_{0}\right]_{D}=13\) dB), we can see that the performance of AF-SCMA outperforms the other schemes in any case.