# Performance Comparison of NB-Fi, Sigfox, and LoRaWAN
## 4 Scenario and Problem Statement  
We consider that the server operates on the BS, and the 10,000 sensors operating in each network are distributed uniformly in a circle around the BS. NB-Fi, Sigfox, and LoRaWAN have different coverage ranges for each bitrate; however, within the 1 km range, sensors can use any bitrate. Thus, we consider a circle with a radius of 1 km. The sensors and BS are static. The LoRaWAN BS allocates two main channels and one downlink channel with 125 kHz bandwidths. In NB-Fi networks, the uplink band is 204.8 kHz wide, and the downlink band is 102.4 kHz wide; in Sigfox networks, the uplink band is 192 kHz wide. The sensors generate new frames according to an exponential distribution with a parameter \(\lambda\) after completing the previous transmission procedure. All sensors use the transmission power of 25 mW. As in [34], we use the Okumura-Hata model [35] to evaluate signal propagation. We consider that the noise at the receiver has a power of \(-157\) dBm for 50 Hz. The frames are received successfully only if the signal-to-interference-and-noise ratio (SINR) for the transmitted frame exceeds the threshold \(SINR_{min}\). For Sigfox and NB-Fi networks, \(SINR_{min}\) is equal to 7 dB, where 2 dB is the BS noise factor, and 5 dB is the \(SNR\) required to achieve reliable transmission. LoRaWAN devices use the LoRa modulation [28], which requires much lower \(SINR_{min}\) to successfully receive a frame. Table 4 lists \(SINR_{min}\) values depending on the \(SF\). In Sigfox and NB-Fi networks, the sensors use the bitrate, assigned to them during the initialization. For Sigfox and NB-Fi, we consider a scenario where all the sensors in the network use the same bitrate. Each LoRaWAN sensor is allocated one \(SF\) during its initialization with a probability, which is inversely proportional to the duration of a frame transmitted with this \(SF\). Such allocation of \(SF\)s ensures a low packet error rate that is uniformly distributed among \(SF\)s [36]. Let us consider the following three scenarios. 1. In the first scenario (further referred to as _the Unreliable Transmission of Short Packets Scenario_), the payload size of all frames is 8 bytes. NB-Fi and LoRaWAN sensors transmit frames in the unacknowledged mode. Sigfox sensors transmit each frame only once. A similar scenario is used in the case of collecting data on a daily basis when the goal is to have relevant data but not necessarily the most recent. 2. In the second scenario (further referred to as _the Unreliable Transmission of Long Packets Scenario_), the payload is generated in portions of 48 bytes, which means that LoRaWAN sensors transmit data in a single frame, while NB-Fi and Sigfox sensors operate using block transmission. To transmit 48 bytes of payload, NB-Fi sensors generate six frames, while Sigfox sensors--that can transmit up to 12 bytes in a single frame--generate four frames. Since the Sigfox specification does not mention block transmission or fragmentation, we assume that the fragmentation occurs on the application layer, which means that every frame in the block belongs to a separate transmission procedure. The time interval \(T_{P}\) between procedures is uniformly distributed within the window \([T_{start},T_{end}]\). The delay \begin{table}
\begin{tabular}{c c} \hline \hline \(\mathbf{SF}\) & \(SINR_{min}\) dB \\ \hline
12 & -20 \\
11 & -17.5 \\
10 & -15 \\
9 & -12.5 \\
8 & -10 \\
7 & -7.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Minimal SINR required at the LoRaWAN receiver input. between transmissions of different frames in one block in the NB-Fi network is randomized by the same rules as in Sigfox. Since the block transmission is successful only if all frames from the block are transmitted successfully, this randomization increases the probability of successful transmission. 3. In the third scenario (further referred to as _reliable transmission of short packets scenario_), the payload size is 8 bytes.