# Performance Comparison of NB-Fi, Sigfox, and LoRaWAN
## 5 Numerical Results
NB-Fi networks operating using 50 and 400 bps and Sigfox networks demonstrate the lowest maximal rates because the total duration of block transmission is much longer than the frame duration. Such a high ratio is the result of randomizing time interval \(T_{P}\) between transmissions within a large interval because in this scenario, \(T_{start}=10\,\mathrm{ms}\), and \(T_{end}=100\times T_{frame}\), where \(T_{frame}\) is the frame duration. Moreover, such randomization has a significant effect on the average delay. Figure 13 shows the average delay for different scenarios. The average delay for the Unreliable Transmission of Long Packets Scenario with the randomization is significantly higher than for the same scenario without the randomization. For example, NB-Fi operating at 50 bps demonstrates an average delay of almost 1500 s because the time interval between each frame is uniformly distributed within the window of \([0.01;576]\) s, meaning a 43 times increase compared to the same scenario without randomization and 256 times increase compared with the unreliable transmission of short frames scenario. On the other hand, even with the randomization, NB-Fi at 25,600 bps demonstrates an average delay comparable with LoRaWAN networks due to a much lower frame duration. However, given that initial research showed that such randomization does not affect the PLR significantly, but notably lowers the maximal rate and increases the average delay, such randomization is unnecessary. Therefore, to consider a wider range of rates and to lower the average delay, we consider for the next scenario that \(T_{start}=T_{end}=T_{G}^{min}\), where \(T_{G}^{min}=10\)ms is the lowest gap duration between frames in a multiple frames U-procedure or different procedures, allowed by the Sigfox standard [21]. Figure 12: PER for the unreliable transmission of long packets scenario. Figure 14 shows the dependence of PLR on the rate for the Reliable Transmission of Short Packets Scenario. For rates below \(100\,\mathrm{packets}/\mathrm{s}\), NB-Fi networks demonstrate the lowest PLR because the duration of the receive window and time interval from which the random backoff is drawn if no ACK was received in NB-Fi are much longer than the frame duration, and since new packets are not generated until the sensor is finished the previous transmission procedure, the BS has a lot of time to transmit ACK and the channel is not overloaded with unnecessary retransmissions. In LoRaWAN networks, the durations of receive and retry windows are close to the durations of the frames, which results in redundant retransmissions, overloading the channel and, consequently, higher PLR. Sigfox sensors operate according to multiple frame U-procedure, which means that they transmit every frame thrice with the same payload. This procedure ensures reliability; however, it does not perform as well as acknowledgment mode and demonstrates higher PLR. Figure 15 shows the dependence of PER on the rate for the Reliable Transmission of Short Packets Scenario. PER in the LoRaWAN network is the highest compared to other considered networks for the same reason as PLR is the highest one. Sigfox and NB-Fi networks demonstrate similar PER at lower rates because of the similar channel access procedure and the same modulation in these technologies. At lower rates, PER is primarily determined by the probability of success during the first transmission attempt, which depends on the probability of frames overlapping both in time and frequency. Since in the considered scenario all sensors in Sigfox and NB-Fi networks use one bitrate, this probability does not depend on the chosen bitrate and, in our case, on the technology because frame duration is inversely proportional to the occupied frequency band. However, at higher rates, NB-Fi provides higher PER than Sigfox because of the frequency selection algorithm used in NB-Fi for downlink transmission.