# Towards an Efficient Method for Large-Scale Wi-SUN-Enabled AMI Network Planning
## 4 Proposed Method
### Link Received Power  
The link received power (LRP) is used as the metric to establish the connection between a smart meter and a candidate position. The LRP is computed based on the transmission power, antenna gains, and channel path loss model. To estimate the link power loss (LPL), we consider the link path loss and diffraction Loss. The LPL considers the detailed terrain profile, which is constructed as follows: initially, the coordinates and length of the path between the smart meter and the CP are identified; the path is divided into 100 equidistant points, and the terrain elevation at each point is obtained; with the elevation measurements and the position of each point, the detailed profile of the terrain is obtained. The use of a detailed terrain profile analysis avoids (or minimizes) the need for empirical terrain classification, as it is very difficult (or imprecise) to define whether, for a specific region, the terrain is, e.g., totally hilly or flat, or just 50% hilly with light or heavy tree density, and so on. The International Telecommunication Union (ITU) ([[https://www.itu.int/](https://www.itu.int/)]([https://www.itu.int/](https://www.itu.int/)) (accessed on 8 May 2022)) presents models for determining the diffraction losses of radio links in its recommendations. The Delta-Bullington method is presented in ITU-R P.526-13 [37]. It aims to determine the diffraction of a radio link considering the multiple obstacles determined by the terrain profile between the transmitter and receiver points. The Bullington diffraction loss for the path is given by (7):  
\[L_{b}^{\text{dB}}=L_{uc}^{\text{dB}}+(1-e^{-L_{uc}^{\text{dB}}/6})\times(10+0.0 2\times d) \tag{7}\]  
where \(L_{uc}^{\text{dB}}\) is the knife-edge loss for the Bullington point, and \(d\) is the distance (in km) between the transmitter and the receiver. The model includes three types of diffraction loss (DL) (more details in [37]):  
* Bullington DL for the actual path profile (\(L_{ba}^{\text{dB}}\)): For the calculation of \(L_{ba}^{\text{dB}}\), the Bullington method is applied using Equation (7) considering the actual terrain profile with all its elevations. The obstacle that causes the greatest diffraction is considered for the calculation. * Bullington DL for a smooth path profile (\(L_{bs}^{\text{dB}}\)): This diffraction loss considers a terrain without elevations. For the calculation of \(L_{bs}^{\text{dB}}\), the Bullington method is applied using Equation (7) considering an equivalent obstacle with equivalent heights of the transmitter and receiver antennas. * Spherical-Earth Diffraction Loss (\(L_{sph}^{\text{dB}}\)): This diffraction loss takes into account the Earth curvature and it is calculated as the interpolated diffraction loss, given by (8): \[L_{sph}^{\text{dB}}=\left[\boldsymbol{1}-\boldsymbol{h}/\boldsymbol{h}_{req} \right]\boldsymbol{A}_{\boldsymbol{h}}\] (8) where \(\boldsymbol{h}\) is the smallest clearance height between the curved-earth path and the ray between the antennas, \(\boldsymbol{h}_{req}\) is the required clearance for zero diffraction loss, and \(\boldsymbol{A}_{\boldsymbol{h}}\) is the diffraction loss for the path using the modified Earth radius. If \(\mathbf{A_{h}}\) is negative, the diffraction loss for the path is zero, and no further calculation is necessary. The link diffraction loss (\(LDL\)) for the general path is:  
\[LDL\ (\mathrm{dB})=L_{ba}^{\mathrm{dB}}+\max(L_{sph}^{\mathrm{dB}}-L_{bs}^{ \mathrm{dB}},0). \tag{9}\]  
The path loss (\(PL\)) corresponds to the reduction in power density of a radio wave as it propagates through the channel [38]. This signal attenuation is usually the result of physical propagation phenomena such as reflection, refraction, diffraction, and scattering [39]. Considering the radios' operating frequency, the diffraction phenomenon is particularly relevant for precise path loss estimation.