# Reflection Characteristics Measurements of Indoor Wireless Link in D-Band
## 2 Principle of Reflection Measurements and Theoretical Model  
### Reflection Measurement  
The received power of LoS transmission in free space can be obtained by the Friis transmission equation as follow:  
\[P_{LoS}=P_{t}\cdot\left(\frac{\lambda}{4\pi d_{LoS}}\right)^{2}\cdot G_{r} \cdot G_{t}, \tag{1}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Year** & **Materials** & **Dielectric Properties** & **Equipment** & **Frequency** & **Results** \\ \hline \multirow{4}{*}{2014} & \multirow{4}{*}{Four wood species} & \multirow{4}{*}{Complex permittivity} & Quasioptical Mach-Zahnder Interferometer with backward-wave oscillator & \multirow{4}{*}{100–500 GHz range is 1.60–1.89 [26].} \\  & & & & \\ \cline{1-1} \cline{5-5}  & & & & \\ \cline{1-1} \cline{5-5}  & & & & \\ \cline{1-1} \cline{5-5}  & & & & \\ \hline \multirow{2}{*}{2019} & \multirow{2}{*}{Gypsum} & \multirow{2}{*}{Permittivity} & Frequency-modulated continuous-wave radar sensors & \multirow{2}{*}{122–169 GHz} & \multirow{2}{*}{2.595 [27]} \\ \cline{1-1} \cline{5-5}  & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: _Cont._  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & **Frequency** & **Permittivity** \\ \hline Wood & 1–100 GHz & 1.99 [28] \\  & 110–170 GHz & 1.60–1.89 [26] \\ \hline \multirow{2}{*}{Plexiglass} & 143 GHz & 2.60 [25] \\  & 60–300 GHz & 2.581–2.602 [29] \\ \hline \multirow{2}{*}{Drywall (plaster)} & 68–92 GHz & 2.80 [30] \\  & 122–167 GHz & 2.595–2.602 [27] \\ \hline Concrete board & 1–95.9 GHz & 6.2–7.0 [24] \\ \hline Red brick & 1–100 GHz & 3.75 [31] \\ \hline \hline \end{tabular}
\end{table}
Table 3: Permittivity Review of Indoor Materials.  
where \(P_{t}\) is the power of transmitting antenna, \(G_{t}\) and \(G_{r}\) represent the gains of the transmitting and receiving antenna respectively, \(\lambda\) denotes wavelength, and \(d_{LoS}\) defines the LoS propagation distance [32; 33].  
When the electromagnetic wave hits the object at a certain angle, it usually reflects and forms a reflected wave. The ratio of the amplitudes of the reflected wave to the incident one is defined as the reflection coefficient \(|\Gamma|\). The received power after reflection can be regarded as the LoS value for the unfolded path length multiplied by \(|\Gamma|^{2}\), assuming that the size of the reflecting boundary is much larger than distances \(d_{1}\) and \(d_{2}\), and the surface area is much larger than the illuminated part [34], as shown in (2),  
\[P_{ref}=P_{t}\cdot\left(\frac{\lambda}{4\pi(d_{1}+d_{2})}\right)^{2}\cdot G_{r }\cdot G_{t}\cdot|\Gamma|^{2}, \tag{2}\]  
where \(d_{1}\), \(d_{2}\) are the distances from Tx/Rx antenna to reflected object, and \(|\Gamma|\) refers to the reflection coefficient. Figure 1 illustrates this more intuitively. Equation (3) is obtained by dividing (2) by (1),  
\[|\Gamma|=\frac{d_{1}+d_{2}}{d_{LoS}}\cdot\sqrt{\frac{P_{ref}}{P_{LoS}}}=\frac {d_{1}+d_{2}}{d_{LoS}}\cdot 10^{\left[P_{ref}\ (\mathrm{dBm})-P_{LoS}\ (\mathrm{dBm})\right]/20}, \tag{3}\]  
where \(P_{ref}\) (dBm) and \(P_{LoS}\) (dBm) are received power in reflection and LoS path in dBm, respectively. It shows that the measured reflection coefficient is determined by the difference between two kinds of received power. Additionally, the ratio of the transmission distances acts as a weighting coefficient.