# Experimental Performance Analysis of Wi-SUN Channel Modelling Applied to Smart Grid Applications
## 5 Measurement Setup
In Figure 10, it is shown that the characteristics of Wi-SUN channel approximation in the same modulation type and frequency (2 FSK, 433.92 MHz) are different in each data rate, even though the experimental data was taken from the same experimental area. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number** & **Alias** & **r\({}_{\mathbf{s}}\)** & **\(\sigma\)** & **K-factor (dB)** & **RMSE** \\ \hline
1 & 2 FSK-433-50 & 7.57963 & 17.9817 & \(-10.514\) & \(0.031926604\) \\ \hline
2 & 2 FSK-433-100 & 3.61237 & 17.8572 & \(-16.8907\) & \(0.02828176\) \\ \hline
3 & 2 FSK-433-200 & 13.503 & 16.2121 & \(-4.59848\) & \(0.03407693\) \\ \hline
4 & 2 FSK-443-50 & 13.6994 & 13.6518 & \(-2.98007\) & \(0.03418891\) \\ \hline
5 & 2 FSK-443-100 & 1.65492 & 15.8254 & \(-22.6219\) & \(0.704776627\) \\ \hline
6 & 2 FSK-443-200 & 18.371 & 12.4326 & \(0.381117\) & \(0.023459429\) \\ \hline
7 & 2 FSK-448-50 & 14.5991 & 17.6363 & \(-4.65193\) & \(0.034126905\) \\ \hline
8 & 2 FSK-448-100 & 7.72779 & 18.4444 & \(-10.5665\) & \(0.030325362\) \\ \hline
9 & 2 FSK-448-200 & 9.55073 & 17.556 & \(-8.29808\) & \(0.030628617\) \\ \hline
10 & 2 FSK-923-50 & 26.2517 & 16.7561 & \(0.88939\) & \(0.023764168\) \\ \hline
11 & 2 FSK-923-100 & 40.9284 & 14.4616 & \(6.025868\) & \(0.030386638\) \\ \hline
12 & 2 FSK-923-150 & 6.03959 & 17.8988 & \(-12.4466\) & \(0.037302199\) \\ \hline
13 & 2 FSK-923-200 & 10.3359 & 17.8441 & \(-7.75323\) & \(0.038247233\) \\ \hline
14 & 2 FSK-2440-50 & 17.329 & 16.2678 & \(-2.46141\) & \(0.030903469\) \\ \hline
15 & 2 FSK-2440-150 & 21.5597 & 13.9068 & \(0.79801\) & \(0.059350678\) \\ \hline
16 & 2 FSK-2440-200 & 13.2688 & 14.2688 & \(-3.64142\) & \(0.026787834\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Conventional fitted Rician parameter. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number** & **Alias** & **r\({}_{\mathbf{s}}\)** & **\(\sigma\)** & **K-factor (dB)** & **RMSE** & **RMSE Changed (\%)** \\ \hline
1 & 2 FSK-433-50 & 9.66897 & 17.6084 & \(-8.21709\) & \(0.031739791\) & \(-0.58513\) \\ \hline
2 & 2 FSK-433-100 & 5.08686 & 17.7703 & \(-13.8752\) & \(0.02811935\) & \(-0.60048\) \\ \hline
3 & 2 FSK-433-200 & 14.207 & 15.9743 & \(-4.02869\) & \(0.033911397\) & \(-0.48576\) \\ \hline
4 & 2 FSK-443-50 & 14.5326 & 13.357 & \(-2.27761\) & \(0.032979213\) & \(-3.53827\) \\ \hline
5 & 2 FSK-443-100 & 1.37446 & 15.9317 & \(-24.2929\) & \(0.704715123\) & \(-0.00873\) \\ \hline
6 & 2 FSK-443-200 & 18.8941 & 12.167 & \(0.812554\) & \(0.022394608\) & \(-4.53899\) \\ \hline
7 & 2 FSK-448-50 & 15.8887 & 17.2146 & \(-3.70647\) & \(0.034031097\) & \(-0.28074\) \\ \hline
8 & 2 FSK-448-100 & 11.2216 & 17.7849 & \(-7.01023\) & \(0.030280683\) & \(-0.14733\) \\ \hline
9 & 2 FSK-448-200 & 10.9664 & 17.2438 & \(-6.94168\) & \(0.030327182\) & \(-0.98416\) \\ \hline
10 & 2 FSK-923-50 & 26.9703 & 16.3685 & \(1.327238\) & \(0.02369494\) & \(-0.29131\) \\ \hline
11 & 2 FSK-923-100 & 40.8299 & 14.5448 & \(5.955111\) & \(0.030023154\) & \(-1.1962\) \\ \hline
12 & 2 FSK-923-150 & 7.68147 & 17.6876 & \(-10.2548\In Table 4, the RMSE parameters in all aliases are very low, which fairly implies that the Rician distribution approximation is fit to the measured RSSI distribution. Therefore, K-factor, \(\mathrm{r_{s}}\) and \(\mathrm{\sigma}\) derived from the conventional Rician distribution approximation could be fairly used to model the 2 FSK Wi-SUN channel. However, in Table 5, it is shown that RMSE parameters are further decreased by applying the bias function in Equation (8), which are smaller than RMSE parameters shown in Table 4. For instance, on average, RMSE parameters were decreased for 0.557%, 2.695%, 0.47%, 0.666% and 3.827% in 433.92 MHz, 443 MHz, 448 MHz, 923 MHz and 2440 MHz, respectively. The K-factor(dB) of the biased approximation is also lower than the K-factor of the conventional approximation that has arisen from the fact that the \(\mathrm{r_{s}}\) and \(\mathrm{\sigma}\) of the conventional Rician distribution approximation was reduced.