# GNSS-R Observations of Marine Plastic Litter in a Water Flume: An Experimental Study
## 2 Materials and Methods
### GNSS-R-Like System
#### 2.1.4 Reflection Geometry  
A key aspect of the GNSS-R experiment implemented at Deltares premises was the location of the transmitting antennas to achieve different incidence angles to study the sensitivity of GNSS-R signals to the presence of surface plastics. As it can be seen in Figure 3, the longitudinal separation between the mast holding the receiving antennas was 3.46 m. Since the receiving antennas were at 1 m height, the height of the elevation antennas to achieve reflection angles of 30\({}^{\circ}\), 45\({}^{\circ}\), and 60\({}^{\circ}\) in elevation \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Angle [\({}^{\circ}\)]** & **Frequency** & **Polarization** \\ \hline \multirow{4}{*}{TX antennas} & \multirow{2}{*}{Elevation} & 30 & 1540–1610 & RHCP \\  & 45 & 1490–1700 & RHCP/LCHP \\  & 60 & 1540–1610 & RHCP \\ \cline{2-4}  & \multirow{2}{*}{Azimuth} & 30 & 1540–1610 & RHCP \\  & 45 & 1530–1580 & RHCP/LHCP \\  & 60 & 1540–1610 & RHCP \\ \hline \multirow{2}{*}{RX antennas} & \multicolumn{2}{c}{Up-looking} & 1540–1610 & RHCP \\ \cline{2-4}  & \multicolumn{2}{c}{Down-looking} & 1500–1600 & RHCP/LHCP \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Antennas’ specifications. Figure 2: Block diagram with the transmitter and receiver parts of the GNSS-R-like system developed for the GLIMPS experiment at Deltares. E and A: transmitting antennas in Elevation and Azimuth, R: receiving antennas, G: amplifier’s gain, and L\({}_{\text{var}}\): insertion losses of a variable attenuator. were 1 m, 2.46 m, and 5 m, respectively. To achieve azimuthal angles of 30\({}^{\circ}\), 45\({}^{\circ}\), and 60\({}^{\circ}\), the longitudinal separation of the transmitting antennas with respect to the receivers were 7.52 m, 4.34 m, 2.50 m, respectively. Because of the small distances involved, the reflected signal comes from a small area that in many cases does not even include a single \"long\" wave period. Therefore, as will be evidenced later, a strong coherent component is expected. When a coherent reflection occurs, the area from which the signals are coming from is given by the so-called \"first Fresnel zone\" [2; 3]. The first Fresnel zone is the ellipsoidal area surrounding the specular point where the path difference with respect the specular point is less than half wavelength (\(\Delta r\leq\frac{\lambda}{2}\)), or less than a phase shift of \(\Delta\phi\leq 180^{\circ}\):  
\[R_{1}=\sqrt{\lambda\cdot\frac{D_{10}\cdot D_{20}}{D_{10}+D_{20}}},\ R_{2}= \frac{R_{1}}{sin\theta_{el}}, \tag{1}\]  
where \(R_{1}\) is the radius of the first Fresnel zone, and \(R_{2}\) is its projection (i.e., \(R_{1}\) and \(R_{2}\) are the semi-axes of the ellipse), \(\lambda\) is the electromagnetic wavelength, \(D_{10}\) is the distance between the transmitter and the specular point, \(D_{20}\) is the distance between the receiver and the specular point, and \(\theta_{el}\) is the local elevation angle. From the distances between the transmitters and the receivers, the radii of the first Fresnel zone are calculated and shown in Table 2.  
Antenna pattern sphericity effects are analyzed in [11]. Since the distance from the transmitting antenna to the specular reflection point is larger than the width of the first Fresnel zone. Therefore, the subtended angle is small enough so that the plane wave assumption approximately holds. To ensure the presence of plastics inside the first Fresnel zone, during the execution of some particular tests, plastics had to be attached with the help of a thin nylon rope and \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Angle [\({}^{\circ}\)]** & **D\({}_{\textbf{10}}\) [m]** & **D\({}_{\textbf{20}}\) [m]** & **R\({}_{\textbf{1}}\) [m]** \\ \hline  & 30 & 2.00 & 2.00 & 0.87 \\ Elevation & 45 & 3.48 & 1.41 & 0.62 \\  & 60 & 5.77 & 1.16 & 0.49 \\ \hline Azimuth & 30 & 5.02 & 5.02 & 1.38 \\ (Elevation angle = 30\({}^{\circ}\)) & 45 & 3.55 & 3.55 & 1.16 \\  & 60 & 2.90 & 2.90 & 1.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: First Fresnel zones specifications.