# Ultra-Low-Power Wide Range Backscatter Communication Using Cellular Generated Carrier +
## 3 Propagation Models
### ITU Outdoor D2D Model  
The radio communication sector of international telecommunication union (ITU-R) provides the guidance and recommendations for outdoor short range communication. In a technical report ITU-R P.1411-10 [50], the ITU-R presents a path loss model for outdoor D2D type of communication, where the devices can be located below the roof-top height close to the street level. The ITU-R presents a general model for both line of sight (LoS) and non-LoS (NLoS) conditions. The path loss in LoS is given by Equation (1), where \(PL_{LoS,AB}\) is the path loss in \(dB\) value for LoS condition, \(PL_{LoS,dB}^{Medim}\) is the median value of path loss in LoS case, and \(\Delta_{LoS}\) is the LoS location correction factor. \(PL_{LoS,dB}^{Medim}\) is calculated, as given in Equation (2), where \(f_{c,MHz}\) is the carrier frequency in \(MHz\), and \(d_{km}\) is the separation between the terminals/devices in kilometers. The \(\Delta_{LoS}\) is the function of the location percentage \(p\), and it includes the impact of shadowing, as shown in Equation (3). Shadowing is generally modelled as a Gaussian random variable with zero mean and \(\sigma_{LoS}\) is the standard deviation of the shadowing in LoS condition. The reported value of \(\sigma_{LoS}\) is 8.5 dB at [50]. ITU defines location percentage as the percentage of locations in which the the predicted path loss exceeds the actual path loss. The location percentage can have any value between 1-99%. \[PL_{LoS,dB}=PL_{LoS,dB}^{Median}+\Delta_{LoS} \tag{1}\]  
\[PL_{LoS,dB}^{Median}=32.45+20\log_{10}(f_{c,MHz})+20\log_{10}(d_{km}) \tag{2}\]  
\[\Delta_{LoS}=1.5624\sigma_{LoS}(\sqrt{-2\ln{(1-p/100)}-1.1774}) \tag{3}\]  
Similarly, the path loss in NLoS condition can be computed using Equation (4), where \(PL_{NLoS,dB}\) is the path loss in \(dB\) value for NLoS condition, \(PL_{NLoS,dB}^{Median}\) is the median value of path loss, and \(\Delta_{NLoS}\) is the location correction factor for NLoS condition, respectively. \(PL_{NLoS,dB}^{Median}\) is calculated, as given in Equation (5), where \(L_{urban}\) is the environment correction factor, and the recommended value of \(L_{urban}\) is 0 dB and 6.8 dB for suburban and urban environment, respectively [50]. For a given location percentage, the \(\Delta_{NLoS}\) can be computed by Equation (6), where \(\sigma_{NLoS}\) is the standard deviation of shadowing in the NLoS condition and \(N^{-1}(. )\) is the inverse normal cumulative distribution function. The recommended value of \(\sigma_{NLoS}\) is 8.5 dB given at reference [50]. \[PL_{NLoS,dB}=PL_{NLoS,dB}^{Median}+\Delta_{NLoS} \tag{4}\]  
\[PL_{NLoS,dB}^{Median}=9.5+45\log_{10}(f_{c,MHz})+40\log_{10}(d_{km}+L_{urban}) \tag{5}\]  
\[\Delta_{NLoS}=\sigma_{NLoS}N^{-1}(p/100) \tag{6}\]  
Finally, the basic path loss at any distance \(d\) with location percentage \(p\) is given as:  
\[PL(d,p)= \begin{cases}PL_{LoS,dB}(d,p)&d<d_{LoS}\\ PL_{NLoS,dB}(d,p)&d>d_{LoS}+w\\ PL_{T,dB}(d,p)&else\end{cases}  \tag{7}\]  
where, in Equation (7), \(d_{LoS}\) is the LoS distance for which the \(PL_{LoS,dB}(d,p)\) is applicable, and it is the function of location percentage \(p\), as shown in Equation (8), \(w\) is the transition distance for the device to move away from LoS condition to completely NLoS condition, and \(PL_{T,dB}(d,p)\) is the basic path loss for transition state distance i.e., for \(d\geq d_{LoS}\) and \(d\leq d_{LoS}+w\), where \(PL_{T,dB}(d,p)\) is computed by linear interpolation of path loss between the LoS and NLoS condition, as shown in Equation (9). \[d_{LoS}(p)= \begin{cases}212[\log_{10}(p/100)]^{2}-64\log_{10}(p/100)&p<45\\ 79.2-70(p/100)&else\end{cases}  \tag{8}\]  
\[PL_{T,dB}(d,p)=PL_{LoS,dB}(d_{LoS},p)+(PL_{NLoS,dB}(d+w,p)-PL_{LoS,dB}(d,p)(d -d_{LoS})/w) \tag{9}\]  
Figure 2 shows the basic path loss for an urban environment at 500 MHz frequency as a function of distance for different values of location percentage \((p)\).