# Experiencing LoRa Network Establishment on a Smart Energy Campus Testbed
## 5 Experiments for LoRa MAC
### Impact of Back-Off Algorithm on LoRa
These findings imply that the back-off algorithm does not influence performance at higher SF nodes, but rather that it is primarily affected by other factors, such as the data period and payload length. With respect to the ToA CW algorithm, the two graphs on the right in the figures are the same because \(CW_{max}\) does not change. The graph reveals that the PDR at SF 7 nodes becomes stable after reaching a sensing count of 5 and is greater than that at SF 8 and 9 nodes. Moreover, the PDR is lower than that at SF 8 nodes. The huge number of SF 7 nodes and the short \(CW_{max}\) (66 ms) explain these results: severe contention occurs among many SF 7 nodes, and thus, it takes time to detect an empty channel (i.e., more trials of sensing are needed). In the case of SF 8, contention is avoided after two consecutive sensing counts since there are fewer nodes (250 nodes). A similar pattern appears for SF9 nodes (300 nodes) but with a worse PDR performance. The difference is mainly attributed to the relationship between the data period and their \(CW_{max}\). Nodes at SF 9 send data every 60 s but must wait two times longer (226 ms at max) than the duration with SF 8 nodes. This increases the possibility of contention. Regarding the fixed CW algorithm with a \(CW_{max}\) of 10 ms, PDR performance at low SF nodes (7-9) varies within a 10% range for all the sensing counts except for 0 (see the left graph in Figure 18). A short  
Figure 19: Doubling \(CW_{max}\) ultimately affects PDR performance. Please note that the ToA algorithm sets \(CW_{max}\) values differently, and thus, the PDR does not change. Figure 18: We record PDR performance with an increasing number of sensing counts after setting \(CW_{max}\) to 10 ms. The left, middle, and right graphs represent the case of fixed, exponential, and ToA algorithms, respectively. and fixed \(CW_{max}\) value explains this pattern. Each node retries data transmission after waiting for a very short back-off time, and these retransmission attempts quickly saturate the network capacity. Moreover, since \(CW_{max}\) is fixed, the intensity of contention does not lessen, even though the sensing count increases. When doubling \(CW_{max}\) to 20 ms, PDR performance rises with the increasing sensing count, as shown in the left graph in Figure 19. In particular, PDR performance at SF 7 nodes continuously increases. This indicates that a longer back-off time can lessen the network contention that occurs when a node keeps trying to transmit data. It is noted that with a sensing count of 10, PDR performance (85%) becomes as good as the maximum performance at SF 7 nodes with the ToA algorithm (see the right graph of the same figure). Recall that SF 7 nodes in two algorithms use fixed \(CW_{max}\) values: 66 ms and 20 ms. When using 66 ms, PDR saturates at a sensing count of 5 as compared with saturating at a sensing count of 10 when using a 20 ms back-off time. This indicates that the maximum performance of 85% in the fixed algorithm is a saturated value. The exponential algorithm changes \(CW_{max}\) dynamically, unlike the other two. Figure 19 allows us to compare its performance at low SF nodes to the performance of the other two algorithms more accurately. In particular, the PDR at SF 7 nodes outperforms the others. Having a huge number of SF 7 nodes implies severe contention that can be alleviated by increasing \(CW_{max}\) gradually. Please note that the PDR exceeds 90% with a sensing count of more than 8. With nodes at SF 8 and 9, the exponential algorithm shows similar performance to that of the other fixed algorithms. Notably, when comparing performance at SF 8 nodes in the exponential and ToA algorithms, the former achieves a 90% PDR with a sensing count of 2 while the latter does so with a sensing count of 4. The difference is mainly attributed to the back-off time. \(CW_{max}\) is set to 123 ms in the ToA algorithm, in which a back-off time longer than 123 ms is reached after 4 sensing trials.