# Performance Comparison of NB-Fi, Sigfox, and LoRaWAN
## 5 Numerical Results
As was explained in Section 3.3, for downlink transmissions, the server calculates the central frequency  
Figure 13: The average delay in (**a**) the unreliable transmission of short packets scenario; (**b**) the unreliable transmission of long packets scenario (\(T_{start}=$10\,\mathrm{m}\mathrm{s}$\), \(T_{end}=$100\times T_{frame}$\)); (**c**) the unreliable transmission of long packets scenario (\(T_{start}=$T_{end}=$10\,\mathrm{m}\mathrm{s}$\)). as a function of bitrate and Modem_ID, which means a higher probability that the server chooses the same central frequencies for multiple sensors at higher rates. Thus, ACK transmission is delayed and if this delay exceeds the timeout duration (\(T_{L}\) in Table 3) the ACK is not transmitted. On the other hand, in Sigfox networks, frames are not acknowledged, therefore resulting in lower PER at higher rates. Figure 14: PLR for the reliable transmission of short packets scenario. Figure 15: PER for the reliable transmission of short packets scenario. Note that the curves in Figures 14 and 15 stop at some maximal rate. NB-Fi networks, where sensors operate using bitrates of 50 and 400 bps, demonstrate the lowest maximal rates. Specifically, the rate does not achieve higher values than approximately 80 packets/s for 50 bps and 120 packets/s for 400 bps because at such rates the devices operate in saturation: they generate new frames after a delay that is much lower than the total duration of data frames, receive windows, and the window from which the random delay is drawn. At the same time, NB-Fi networks that use bitrates of 3200 and 25,600 bps can generate more packets and thus achieve higher rates. In addition, at high rates, NB-Fi networks that use 3200 or 25,600 bps bitrates demonstrate higher PLR than Sigfox networks because of the high probability of overlap in frequency and a relatively small ratio of the receive and retry durations to the frame duration. Figure 16 shows the average delay for the Reliable Transmission of Short Packets Scenario. Since Sigfox networks operate without acknowledgments, the average delay is constant for any rate and equals \(3\times T_{frame}+2\times T_{G}^{min}\). In NB-Fi and LoRaWAN networks, at lower rates, the average delay is primarily determined by the round-trip time, which is inversely proportional to the bitrate. When the rate increases, so does the number of retries required for the successful frame transmission, which significantly increases the average delay. In LoRaWAN networks, the average delay starts increasing more rapidly and at lower rates than in NB-Fi networks because of the collision avalanche caused by an inefficient collision resolution approach [37]. However, the increase rate significantly lowers at approximately 200 packets/s, which correlates with PLR reaching a plateau at the same rates. In NB-Fi networks operating at 3200 and 25,600 bps, the average delay decreases after reaching the maximal value because, at such a rate, the PLR is high and frames are either lost and do not affect the average delay or are transmitted successfully without many retries. Let us conclude the numerical results. Even though the considered technologies have similarities, such as, for example, channel access in NB-Fi and Sigfox, and acknowledgment mode in NB-Fi and LoRaWAN, the technologies perform best in different scenarios. Sigfox is the most reliable in the scenario where only short packets are transmitted in an un  
Figure 16: The average delay for the reliable transmission of short packets scenario. reliable way. LoRaWAN performs better if only long packets are transmitted in a network, while NB-Fi is more suitable if short packets have to be transmitted most reliably.