# Experimental Performance Analysis of Wi-SUN Channel Modelling Applied to Smart Grid Applications
## 3 Channel Modeling Methodology  
A channel model is a simplified mathematical expression for a communication channel, which represents the channel characteristic and the performance of a specific communication technology operating in such a channel. It is used to simulate the channel emulation, evaluate the performance of communication technologies and be applied to network planning, especially in the wireless network design. Basically, the wireless network transmits and receives information through the air as a media. Hence, the wireless propagation under a realistic condition is modelled, which is extremely challenging. With the knowledge of boundary conditions, one can derive the channel model by solving Maxwell's equations from all physical objects and the environment; however, it is considerably hard to obtain such information accurately, especially in the multi-path fading channels. Therefore, the channel model should be alternatively focused on the main propagation effects, such as the reflection, diffraction and scattering, and ignore the rest for the complexity reduction of the problem. The reflection occurs when the signal impinges on a surface whose dimensions are much larger than the wavelength of the incident wave. It depends on the angle of the incidence, wave polarization, material properties and the carrier frequency. The diffraction occurs when the signal passes through aperture or edges or sharp corners of obstacles, which reduce the field strength. The scattering occurs when the signal pass through small obstacles, which are much smaller than the wavelength. The signal is scattered in all directions from the obstacles. The multi-path propagation is caused by receiving signals in  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Regulatory Domain** & **Frequency Band (MHz)** & **Data Rates (kbps)** \\ \hline China & 470–510, 779–787 & 50, 100, 200 \\ Europe & 863–870 & 50, 100, 200 \\ US & 902–928 & 50, 150, 200 \\ Korea & 917–923.5 & 50, 150, 200 \\ Japan & 920–928, 950–958 & 50, 100, 200, 400 \\ Worldwide & 2400–2483.5 & 50, 150, 200 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Data rates and frequency bands of MR-FSK PHY layer in different countries.  
many directions, i.e., a direct path, a reflection, a diffraction and a scattering, are combined with a random amplitude, phase and delay. The fading in wireless communication can be classified into two groups, namely, large-scale fading and small-scale fading [20; 21; 22]. Large-scale fading represents the slow-changing signal, which is due to the effects of path loss and shadowing. On the other hand, small-scale fading represents the rapid-changing signal in a small scale based on the influence of three foundations, including a delay spread of the signal, a time variance of the channel and a transmission bandwidth of the channel. Therefore, the small-scale fading is of interest and challenging for channel simulation in realistic conditions.  
The channel modeling approaches are classified into two categories, including a physical model and an analytical model. The physical model is the channel model estimated by the measurement of the transmitted and received signals. On the other hand, analytical models recreate the statistical properties of the channel modeling by mathematics or analysis, by which physical models are not considered [23]. The physical channel modeling can be classified into two types, as follows.