# Delay-Sensitive NOMA-HARQ for Short Packet Communications
## 4 Numerical Results
### Effect of Power-Sharing Parameters, \(w_{i},\alpha_{i}\), on PER, Throughput, and Delay  
We use \(w_{1}=0.6\) and \(0.51\) (\(w_{2}=1-w_{1}\)) to show performance variation of each user with different power fractions. The parameter \(w_{i}\) indicates the power fraction of NOMA paired users sending packets on the same channel with either S-NOMA-HARQ or D-NOMA-HARQ. In addition to \(w_{i}\), \(\alpha_{i}\) is used to indicate the power fraction of the retransmission packet for D-NOMA-HARQ. First, we present the effect of parameter \(w_{i}\) on the performance of S-NOMA-HARQ in the following. Figure 12 shows the PER of S-NOMA-HARQ and D-NOMA-HARQ with different \(w_{i}\). As shown in this figure, with S-NOMA-HARQ, when the power difference between users is small, i.e., \(w_{1}=0.51\), both users achieve similar PER performance as the SNR increases. More specifically, at SNR \(\approx 3\) dB, both users achieve PER of about \(10^{-6}\) with S-NOMA-HARQ. However, by increasing the power difference between users (\(w_{1}=0.6\)), user 1 achieves much higher  
Figure 11: Throughput performance of D-NOMA-HARQ with CC-HARQ serving maximum 3 users at \(w_{1}=0.43\), \(w_{2}=0.37\), \(w_{3}=0.2\), \(\alpha_{1}=0.8\), \(\alpha_{2}=0.6\), \(\alpha_{3}=0.4\), and \(n=200\). Figure 10: PER performance of D-NOMA-HARQ with CC-HARQ serving maximum 3 users at \(w_{1}=0.43\), \(w_{2}=0.37\), \(w_{3}=0.2\), \(\alpha_{1}=0.8\), \(\alpha_{2}=0.6\), \(\alpha_{3}=0.4\), and \(n=200\). reliability at the cost of a small increase of PER of user 2. When the power difference between users is more considerable (\(w_{1}=0.6\)), the SIC is better, resulting in PER and throughput performance improvement. However, increasing \(w_{i}\) too much leads to PER performance disparity among users, where a user with higher power get much higher reliability, while the PER reliability of other user decreases. More specifically, at \(w_{1}=0.6\), the PER of user 1 is less than \(10^{-8}\) while user 2's PER is slightly higher than \(10^{-6}\). On the other hand, with D-NOMA-HARQ, a larger \(w_{i}\) can be placed between users to improve the SIC decoding, while user performance disparity can be reduced with the adjustment of parameter \(\alpha\). As shown in Figure 12, with D-NOMA-HARQ at \(w_{1}=0.6\) both users achieve similar PER performance. Note that another drawback of S-NOMA-HARQ is that a slight increase in PER of a user results in much lower latency performance. Therefore, increasing \(w_{i}\) too much is also prohibitive. Figure 13 shows the delay performance of each user with S-NOMA-HARQ at SNR 4 dB with their PER performance. Using higher power difference between users, i.e., larger \(w_{1}\), the PER reliability of 1 user increases beyond the need while the other user suffers from slight PER performance degradation. However, the slight PER performance degradation with S-NOMA-HARQ results in significant packet-level latency performance degradation. Next, we present the effect of parameters \(w_{i}\) and \(\alpha_{1}\) on the PER of D-NOMA-HARQ, when \(N_{u}=2\). Figure 14 shows the PER performance of both users with various \(w_{i}\) and \(\alpha_{i}\) settings. Note that the choice of \(w_{i}\) and \(\alpha_{i}\) greatly affect the PER performance of D-NOMA-HARQ. By fixing \(\alpha_{1}\) and \(w_{1}\), \(\alpha_{2}\) is varied to see the performance variation at different settings. As can be seen, at smaller values of \(w_{1}\), e.g., \(0.55\), both users achieve similar PER performance; however, due to the small power difference among users at \(w_{1}=0.55\), SIC is not performing well. By Increasing \(w_{1}\) to 0.6, PER can be reduced further. Furthermore, when \(\alpha_{i}\) is large, e.g., 0.7, excessive power is assigned to conduct retransmission, leaving insufficient power for new arriving packets to be decoded successfully. However, by reducing \(\alpha_{i}\) to 0.6, a further PER reduction is achieved.