# Multi-Connectivity-Based Adaptive Fractional Packet Duplication in Cellular Networks
## 5 Simulation Results
### Fade-Threshold-Based Packet Duplication  
As discussed earlier, the fade duration outage probability (FDOP) defines a time over which a communication will fail if a fade persists too long. As per Figures 5 and 6, the average SINR with a smaller sample size of 50 shows very drastic changes over a very small interval of time. If the SINR falls below a certain minimum acceptable value, any packets transmitted over that time interval could be either corrupt or completely lost. This fading of the signal below a certain threshold value is used to decide whether or not the packets will be duplicated. Figures 15 and 16 show the packet duplication operation for the different fade threshold values used in our simulation for an average SINR sample size of 500. Figures 17 and 18 represent the very same information for an average SINR sample size of 50.  
\begin{table}
\begin{tabular}{c c c} \hline
**SINR Difference (dB)** & **500 Samples** & **50 Samples** \\ \hline
5 & \(-5.48\%\) & \(-5.56\%\) \\
10 & \(-0.34\%\) & \(-3.22\%\) \\
15 & \(6.83\%\) & \(2.71\%\) \\
20 & \(5.64\%\) & \(5.76\%\) \\
25 & \(8.03\%\) & \(8.19\%\) \\
50 & \(11.82\%\) & \(13.52\%\) \\ \hline \end{tabular}
\end{table}
Table 1: Relative decrease in the % corrupt packets vs. % increase in Packet Duplication.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Average** & **Original Scenario** & **Second Scenario** & **Third Scenario** & **Fourth Scenario** \\ \hline
6.73\% & 5.45\% & 7.19\% & 6.03\% & 8.23\% \\
10.23\% & 11.21\% & 8.03\% & 9.04\% & 12.65\% \\ \hline \end{tabular}
\end{table}
Table 2: Average of the multiple scenarios using Adaptive-Fractional Packet Duplication and hard handover for a 10 dB SINR difference.  
Figure 19 shows, for the fade threshold on the \(x\)-axis, how much reduction in corrupt packets can be achieved with PD. We also show how much of the actual packet duplication is required to reach this number. For example, 52.52% packet duplication is required to have 4.05% of corrupt packets in the overall communication. This amount of PD increases in order to achieve the minimum corrupt packets. This also means more radio resource utilization. In contrast to the average SINR with a sample size of 500, we simulate the environment using the average SINR with a sample size of 50, and the chart is shown in Figure 20. The average SINR with a sample size of 50 has more fluctuations than the average SINR with a sample size of 500, and PD switching happens many more times.  
Figure 16: Packet Duplication with an average (500 sample size) fade threshold of 30 dB.  
Figure 15: Packet Duplication with an average (500 sample size) fade threshold of 15 dB.  
Figure 21 shows the number of times that packet duplication was triggered for the average SINR with sample sizes of 500 and 50 for the two base stations. As shown in Table 3, for every fade threshold in dB, we have columns for 500 and 50 samples. Each of these values are the difference of the 10-times relative decrease in corrupt packets and the percentage increase in packet duplication. For example, from 20 to 25 dB for a 500 sample size, a 1.33% decrease in corrupt packets was observed for 20.12% additional packet duplication. This gives us 6.82%, which is the difference of 20.12% and 13.30%. Similarly, we calculated values for all others to determine the pattern where this difference then becomes positive.  
Figure 17: Packet Duplication with an average (50 sample size) fade threshold of 15 dB.  
Figure 18: Packet Duplication with an average (50 sample size) fade threshold of 30 dB.  
Figure 21: Actual number of times that Packet Duplication is triggered.  
Figure 19: Fade-threshold-based (500 sample size) Packet Duplication.  
Figure 20: Fade-threshold-based (50 sample size) Packet Duplication.