# Enhanced LoRaWAN Adaptive Data Rate for Mobile Internet of Things Devices
## 4 Experimental Results and Analysis
### Convergence Period Analysis
#### 4.3.1 Static EDs scenario  
The convergence period and \(PSR\) of static EDs during a simulation period of 4 days is shown in Figure 8. All of the schemes begin transmission with SF = 12 and TP = 14 dBm, as indicated in Figure 8a.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Scheme** & **ADR** & **ADR+** & **G-ADR** & **G-ADR (I-SFA)** & **EMA-ADR** & **EMA-ADR (I-SFA)** \\ \hline SF 7 & 25.8\% & 14\% & 25.4\% & 24\% & 25.8\% & 25.2\% \\ SF 8 & 8.4\% & 6.2\% & 6.4\% & 10\% & 10.8\% & 6.6\% \\ SF 9 & 11\% & 7\% & 12.2\% & 13  
Figure 8a,b show the amount of time for the EDs to reach a steady SF and \(PSR\) (i.e., convergence period), whereas both typical ADR and ADR+ require 20 h in converging to a stable state. The primary reason for this high convergence period is that the frequency of a typical ADR (NS-managed ADR) is entirely arbitrary, which is activated after \(M\) UL packets. The changes in the ED-managed ADR occur in time in steps of \(ADR\_ACK\_DELAY\times uplink\_period\)[18]. This is a time-consuming process and, thus, yields a high convergence period. In general, an ED-managed ADR is intended to maximize DL traffic flexibility, restricted by the duty cycle limitations that are imposed by LoRaWAN. This helps the EDs to reestablish reliable communication links by steadily increasing the SF (\(SF<12\)). This flexibility increases the convergence period in the worst case. For example, an ED is presently employing a lower SF than needed to deliver a packet to the nearest GW successfully.  
By contrast, G-ADR follows a similar trend with a convergence period of 14 h along with a better \(PSR\) when compared to both a typical ADR and ADR+. Moreover, EMA-ADR outperforms the other schemes in terms of both the convergence period (i.e., 3 h) and \(PSR\). As the reason for the quick convergence, the EMA filter resists against the rapid changes in the SNR of \(M\) packets and acts as a local averaging function. Thus, the proposed EMA-ADR scheme attains a higher \(PSR\) that is related to typical ADR and ADR+, as shown in Figure 8a. Figure 8b presents another scenario in which G-ADR  
Figure 7: Final network topology in the case of static EDs with N = 500 and starting SF = 12: **(a)** typical ADR; **(b)** ADR+; **(c)** G-ADR, and **(d)** EMA-ADR.  
and EMA-ADR are employed while using the I-SFA scheme. There is no convergence period when I-SFA is jointly utilized with both G-ADR and EMA-ADR. This is because I-SFA assigns a suitable SF to the EDs based on \(P_{r}\). Table 4 highlights the detailed convergence periods of different EDs in hours for static EDs.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**N** & **ADR** & **ADR+** & **G-ADR** & **G-ADR (I-SFA)** & **EMA-ADR** & **EMA-ADR (I-SFA)** \\ \hline
200 & 20 & 18 & 15 & 0 & 3 & 0 \\
400 & 21 & 19 & 15 & 0 & 3 & 0 \\
500 & 20 & 20 & 14 & 0 & 5 & 0 \\
600 & 18 & 20 & 16 & 0 & 6 & 0 \\
800 & 28 & 28 & 26 & 0 & 11 & 0 \\
1000 & 40 & 39 & 37 & 0 & 19 & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Convergence period in hours for static EDs (with starting SF = 12, uplink period = 24 packets/day, and total simulation time = 4 days).  
Figure 8: Convergence period and PSR of static EDs with N = 500: (**a**) initial allocation of SF with 12, and (**b**) initial allocation of SF with 12 (for ADR and ADR+) and initial SF allocation with I-SFA (for G-ADR and EMA-ADR).