# A Survey of LoRaWAN for IoT: From Technology to Application
## 6 MAC Layer Performance Evaluation
### LoRaWAN Network Models
#### 6.1.2 Empirical Based  
Apart from theoretical approach, other system models are based on empirical approach by doing controllable measurements with certain number of nodes and generating models based on outcomes. In [75], authors performed measurements for co-SF interference in a controllable setup, where received signal strength and time difference between interferer and interfered signal were changed. Based on the measurements, it is found that the most fragile parts of a packet are the preamble and physical header with main three outcomes [75]:  
* If the interferer starts after the preamble and the RSSI from the interferer is at the same level or lower than the interfered transmission, then the interfered transmission will be received correctly. * If the interferer starts after the end of the preamble and the header time and has a higher RSSI at the receiver, then the first transmission will be received with the wrong payload CRC. * If the last six symbols of the transmitter preamble are received correctly, the receiver can synchronize with the transmitter. Similar results were achieved by [PERSON] et al [78] accounting for the pseudo-orthogonality of SFs. Based on these outcomes a system model was created to assess scalability of the system. It is shown that for multi-SF single gateway deployments LoRaWAN can have three times lower losses compared to Aloha for 1000 end nodes per gateway. As the model does not consider the inter-SF interference (SF orthogonality is assumed), this can be seen as top border of performance, as in this case the inter-SF interference is under determined. Similar approach was followed in [47], where LoRa capture effect was determined by empirical measurements. Another empirical based system level model has been presented in [68] that considers inter-SF interference. In addition, authors used a corrected Okumura-Hata path loss model (based on coverage measurements) as well as log-normal shadowing effects in their model. Differently from empirical approaches, in [40], LoRa interference model is constructed based on extensive complex base band bit error rate simulations. The interference model is combined with LoRaWAN MAC protocol to design system level model for LoRaWAN. A packet is received correctly if the SINR level (interference from other SFs are considered too) is above the receiving threshold for that SF. Table 5 lists all the models together with the interference scenarios that they consider. In Figure 7, different interference scenarios are shown based on what type of interference are considered. In Figure 7a, the case where interferer using same SF with highest signal strength reception (red end node) in the gateway is shown. Figure 7b shows the case where all interferers using the same \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Study** & **Model** & \multicolumn{8}{c}{**Considered Interference**} \\ \hline  & & **Dominant** & **Cumulative** & **Dominant** & **Cumulative** & **Co and** & **Path Loss** & **Channel** & **Other** \\  & & **Co-SF** & **Co-SF** & **Inter-SF** & **Inter-SF** & **Inter-SF** & **Model** & **Fading** & **Interference** \\ \hline
[34] & Mathema. & No & No & No & No & No & None & No & No \\ \hline
[69] & Mathema. & Yes & No & No & No & No & Yes & No & No \\ \hline
[70] & Mathema. & Yes & No & No & No & No & Yes & No & No \\ \hline
[71] & Mathema. & Yes & No & No & No & No & Yes & No & No \\ \hline
[72] & Mathema. & Yes & Yes & No & No & No & Yes & No & No \\ \hline
[25] & Mathema. & Yes & Yes & No & No & No & Yes & Yes & Yes \\ \hline
[73] & Mathema. & Yes & Yes & Yes & Yes & Yes & Yes & Yes & No \\ \hline
[77] & Mathema. & & & & & & & & \\ \hline
[75] & Empir. & Yes & No & No & No & No & Yes & No & No \\ \hline
[47] & Empir. & Yes & No & No & No & No & No & No & No \\ \hline
[68] & Empir. & Yes & Yes & Yes & Yes & Yes & Yes & No & No \\ \hline
[40] & Simu. & Yes & Yes & Yes & Yes & Yes & Yes & No & No \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Proposed system models for LoRaWAN.