# The SF12 Well in LoRaWAN: Problem and End-Device-Based Solutions
## 5 End-Device-Based Solutions
### Evaluation  
In this subsection, we evaluate the performance of the presented alternative SF management techniques (i.e., SFM1, SFM2, and SFM3) in the same conditions considered for SFM0 in Section 4. We focus on the network PDR as the main performance metric (Figure 14). However, in order to better understand the network performance and behavior, we also study the number of collisions (Figure 15), the number of losses due to duty cycle restrictions at both  
Figure 13: (**a**) Collision ratio at the gateway. (**b**) Packet drop ratio at EDs due to duty cycle restrictions. (**c**) Packet drop ratio at the gateway due to duty cycle restrictions. the ED (Figure 16) and the gateway (Figure 17), and the distribution of the SF values used for each mode, and for each considered number of CEDs (Figure 18). Figure 14 illustrates the total PDR for traffic including confirmed and not-confirmed transmission modes, as a function of the EDL. SFM1 (see Figure 14a) yields the highest PDR among the considered SF management modes, even in high load conditions. For SFM1, the PDR is always above 80% in the considered scenarios. SFM1 also offers the best behavior in terms of losses due to duty cycle restrictions (see Figures 16a and 17a). This best performance under congestion is due to the fact that SF7 leads to the minimum ToA, which minimizes channel utilization and the impact of the duty-cycle limitation on network performance. This occurs despite the fact that the collision ratio of SFM1 is not the best among the considered SF management techniques, except for a very low packet load (see Figure 15). The observed collision ratio is a consequence of the approach in SFM1 based on always using the same SF value (i.e., SF7), which precludes exploiting the orthogonality that stems from using different SF values. It is interesting to compare the high PDR achieved by using SFM1 (Figure 14a), with the low PDR obtained by the CEDs when using SFM0 (Figure 11) for the same range of EDL values and number of CEDs. The low PDR of SFM0 is mainly due to the use of high SF values (equal to SF12 for all CEDs after the WFT), which lead to high ToA values and produce a high number of collisions at the gateway (Figure 13a) and packet drops at the EDs (Figure 13b). The gateway is also unable to transmit all the ACKs to the corresponding CEDs due to duty cycle restrictions (Figure 13c), leading to unnecessary retries by those CEDs which increase the offered load and contribute to the decrease of the PDR. In contrast, in SFM1 all nodes use SF7, which minimizes the ToA and yields a high PDR. However, we hypothesize that there exists a higher number of CEDs and/or traffic load that will create a low PDR problem equivalent to the one found for SFM0, regardless of the SF values used by the EDs. In contrast with the SFM1 behavior, SFM3 leads to a quick PDR decrease as the offered load increases, especially for a high number of CEDs (Figure 14c). This is due to an increase in the number of CEDs that use SF12 or an SF value close to this one (see Figure 18i), leading to greater ToA values and contributing to higher collision probability (see Figure 15c), which results in low PDR values. On the other hand, for a low number of CEDs, the PDR obtained with SFM3 tends to be the highest among all of the considered SF management modes. This is, again, related to the distribution of the SF values used by the CEDs: they mainly use SF7 for a low number of CEDs, even for high EDL (see Figure 18i). This SF value distribution leads to a low collision ratio (see Figure 15c and a very low number of losses due to duty cycle restrictions, at both the EDs (see Figure 16c)  
Figure 14: PDR vs. EDL for (**a**) SFM1, (**b**) SFM2, and (**c**) SFM3. and the gateway (see Figure 17c). Finally, SFM3 offers a higher PDR compared with SFM0 by a factor of up to 2.44, within the study conditions. SFM2 leads to intermediate PDR results (see Figure 14b) because it produces a distribution of SF values used by the CEDs that is rather uniform (see Figure 18b,e,h).