# LoRa Communication Using TVWS Frequencies: Range and Data Rate
## 3 LoRa Radio Propagation Model
### Propagation Models  
In the context of signal propagation, three major scenarios can be considered free space, outdoors, and indoors. A free-space scenario can be described as a line-of-sight transmission from the transmitter to the receiver over a certain distance, and the path loss can be modeled using the commonly used free space path-loss model [17; 18]. The free space path loss \(Lp_{FSPL}\) --is given as  
\[Lp_{FSPL}=32.44+20\log_{10}(f)+20\log_{10}(d_{FSPL}) \tag{4}\]  
where \(f\) is the frequency of transmission in MHz, \(d_{FSPL}\)--is the distance between the transmitter and receiver in km. The maximum distance can be obtained from the maximum path loss as given in (5),  
\[d_{FSPL}=10^{(Lp_{FSPL}-32.44-20\log_{10}(f))/20} \tag{5}\]  
The widely accepted Okumura-Hata model is considered to study the range for LoRa transmissions using TVWS frequencies in outdoor urban environments [17]. It is an empirical model for rural, suburban, and urban settings, typically in the 150-1500 MHz frequency range, considering losses due to diffraction, reflection, and scattering without any prominent objects within the transmitter and receiver [19]. For urban settings  
\[L_{u}=69.5+26.16\ log_{10}f-13.82\ log_{10}h_{b}-C_{H}+[44.9-6.55\ log_{10}h_{ B}]log_{10}d_{u} \tag{6}\]  
For small and medium cities  
\[C_{H}=0.8+(1.1\ log_{10}f-0.7)h_{M}-1.56\ log_{10}f \tag{7}\]  
For big cities  
\[C_{H}=\left\{ \begin{array}{ll}8.29\ (log_{10}(1.54h_{M}))^{2}-1.1\,&if\ 150\ \leq f\ \leq 200\\ 3.2\ \left(log_{10}(11.75h_{M})\right)^{2}-4.97\,&if\ 200\ \leq f\ \leq 1500\end{array} \right\} \tag{8}\]  
where \(L_{u}\) is the path loss in urban regions (dB), \(f\) is the transmission frequency (MHz), \(h_{B}\) is the base station antenna height (m), \(h_{M}\) is the mobile station antenna height (m), \(C_{H}\) is a factor for antenna height correction, \(d_{u}\) is the distance between the transmitter and receiver in kilometers. For rural settings  
\[L_{o}=L_{u}-4.78(log_{10}f)^{2}+18.33(log_{10}f)-40.94 \tag{9}\]  
where \(L_{o}\) is the path loss in open regions (dB), \(L_{u}\) is the average path loss from a small city form of the model (dB), and \(f\) is the transmission frequency in MHz. Signal propagation and coverage in indoor systems depend on the building geometry, reflection from and diffraction around objects in the rooms, movement of people inside the room, and transmission loss through walls and other obstacles [20]. The indoor \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Transmission power \(P_{t}\) & 12.5 dBm \\ Transmitter antenna gain \(G_{t}\) & 2 dBi \\ Transmitter cable losses \(L_{t}\) & 2 dB \\ Receiver antenna gain \(G_{r}\) & 2 dBi \\ Receiver cable losses \(L_{r}\) & 2 dB \\ Transmitter height \(h_{b}\) & 24 m \\ Receiver height \(h_{m}\) & 1 m \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._dominant path-loss model has been used to study signal propagation at frequencies such as 2.4 GHz [16] and TV signal frequencies [21]. The indoor dominant path-loss model considers the main path between the transmitter and the receiver and includes path loss, loss due to walls, and interaction loss due to changes in the direction of the propagating signal. The indoor path loss \(L_{p_{in}}\) is given as. \[L_{p_{in}}=L_{p}(d_{0})+10 nlog_{10}\bigg{(}\frac{d_{in}}{d_{0}}\bigg{)}+\sum_{x }L_{wx}+\sum_{y}L_{iy} \tag{10}\]  
where \(L_{p}(d_{0})\) represents the path loss at a distance \(d_{0}\), and \(n\) is the path-loss exponent. The wall loss is the sum of losses \(L_{wx}\) caused by each wall along the main path. The interaction loss is the sum of losses \(L_{iy}\) caused by the change in the direction of the transmitting signal.