# Asynchronous Flipped Grant-Free SCMA for Satellite-Based Internet of Things Communication Networks
## 5 Simulation Results
### Pilot Sequence Detection Performance Assessment  
Pilot sequence detection is crucial to the AF-SCMA decoding procedure, where AF-SCMA can acquire the identification of MTDs and the codebook information. Figure 6 shows the pilot sequence detection assessment results. Since false alarm can be recovered during the procedure of channel estimation [19], we only investigate the probability of missed detection. In the simulation, we adopt ZC sequence as the pilot sequence with the length of \(N_{ZC}\), where \(N_{ZC}\) is an odd and prime number [38]. Each MTD chooses a ZC root index \(u\) randomly to generate its pilot sequence with cyclic shift \(mN_{CS}\), where \(u=0,1,2...,N_{ZC}-1\), \(N_{CS}=floor(N_{ZC}/N_{CS})\) and \(m\) is a positive integer number used to identify different codebooks, \(m\leq N_{CB}\). \(floor(x)\) returns the largest integer number that is less than or equal to \(x\). Please note that the pilot sequences of the two replicas for a specific packet are with the same ZC root index \(u\), but they are with different cyclic shifts to indicate different codebooks. Additionally, carrier frequency offset (CFO) is not taken into consideration in the simulation, since the main frequency error caused in a GEO SAT-IoT networks scenario is due to the satellite oscillator uncertain which can be well estimated within \(\pm 1\) KHz [10]. Thus, by adjusting the subcarrier bandwidth interval properly, the negative impacts of CFO on ZC sequence detection can be ignored.  
Figure 5: AF-SCMA performance comparison for packet size 500 bits, Turbo encoder with \(r=1/3\), \(\left[E_{b}/N_{0}\right]_{D}=13\) dB, \(N_{chunk}=10\), \(N_{iter}=10\), \(N_{CB}=6,12,15\), number of subcarriers \(K=4,6,6\) in the presence of power unbalance with \(\mu=0\) and \(\sigma=0,3\) dB respectively. **(a)** Throughput. **(b)** PLR.  
We compare the missed detection rates for different lengths of ZC sequences. As shown in Figure 6 we can see that pilot signal with longer sequences perform better than the shorter ones. On one hand, longer ZC sequences provide better autocorrelation performance, which makes for easy correlation peak detection. On the other hand, larger \(N_{ZC}\) provides more candidate root indices \(u\), which decreases the probability of different pilot sequences interfering with the same root index. Moreover, the missed detection rate rises with the increase of traffic load. As the traffic load becomes heavier, pilot sequences generated by the same root index collide more frequently, which makes it difficult for the detector to detect the correlation peak. In Figure 6 we notice that the probability of missed detection is below \(10^{-3}\) in the entire traffic load region for both \(N_{ZC}=127\) and \(N_{ZC}=257\), which can satisfy the PLR target of \(10^{-3}\). Although a longer sequence can achieve lower missed detection rate, it will cost too much overhead compared with the useful information in a packet, which is suitable for the larger packet size. Thus, \(N_{ZC}=127\) seems to be a reasonable pilot sequence length.