# The SF12 Well in LoRaWAN: Problem and End-Device-Based Solutions
## 5 End-Device-Based Solutions
### Evaluation
Only a significant SF value distribution difference exists for a very low EDL, but even in this case, the probability of using the most likely SF value (i.e., SF7) is below 41% for all numbers of the CEDs considered (see Figure 18b). The more even distribution of SF values achieved by SFM2 (see Figure 18h) exploits the orthogonality of different SF values and leads to less collisions than the rest of the considered SFMs, especially for a high load (see Figure 15). However, the number of losses due to duty cycle restrictions of SFM2 is greater than the one obtained for SFM1 (at both the CEDs and the gateway), and, for high EDL and a high number of CEDs, it is also greater than the SFM3 one, regarding losses at the gateway (see Figures 16b and 17b, respectively). Such behavior of SFM2 is due to its tendency to lead to greater frame ToA, because of its greater probability of using greater SF values than those of SFM1 and SFM3 (regarding the latter, one exception is the high EDL and the high number of CEDs). Nevertheless, SFM2 yields a PDR increase, compared with SFM0 (Figure 10), by a factor of up to 4.7 for the range of scenarios considered. Figure 16: Packet losses due to duty cycle restrictions at the EDs vs. EDL for (**a**) SFM1, (**b**) SFM2, and (**c**) SFM3. Figure 15: Frame collisions at the gateway vs. EDL for (**a**) SFM1, (**b**) SFM2, and (**c**) SFM3. On the other hand, comparing losses due to duty cycle restrictions at the gateway for SFM0, SFM2, and SFM3 schemes (Figures 13c and 17b,c), we can appreciate an increase in those losses for the mentioned alternative SFMs. For SFM0, the lower number of packet (ACK) drops at the gateway is due to a lower PDR (which is due to a greater number of packet losses due to collisions, and the duty cycle restrictions at the EDs) and thus a lower number of ACKs to be sent. For the alternative SF management schemes, the PDR is greater than for SFM0, which increases the ACK traffic, and the number of packet drops at the gateway. Therefore, the gateway becomes a limitation for the alternative SF management techniques. Figure 17: Packet losses due to duty cycle at the gateway vs. EDL for (**a**) SFM1, (**b**) SFM2, and (**c**) SFM3. Figure 18: _Cont._  
From the above analysis, it can be highlighted that any of the considered alternative SF management techniques allow the avoidance of the SF12 Well and improve the network PDR. SFM1 offers the best performance in terms of the PDR and packet losses due to duty cycle restrictions, although, as aforementioned, this SF management technique is only included in the evaluation as a benchmark. Both SFM2 and SFM3 outperform SFM0 but offer different trade-offs. In terms of collisions at the gateway, SFM2 is the best option because it presents a more even SF value distribution. However, for low loads, SFM3 offers a lower number of duty-cycle-induced packet drops, due to a higher fraction of devices using low SF values. In consequence, SFM2 tends to offer a greater PDR than SFM3 for high EDL and a high number of CEDs, whereas SFM3 yields a higher PDR than SFM2 for a low EDL and a low number of CEDs.