## 2 Scenario Definition  
In this section, we describe the scenario for GNSS-R coherent reflections that we have considered for this work. By doing so, we summarize all of the relevant assumptions that are needed to define the received GNSS signal model at the output of the receiver front-end. As expected, the properties of the reflected signal when impinging the receiver antenna will strongly depend on the scenario geometry and on the reflecting surface itself [61]. It is precisely that dependency that allows us to retrieve useful information from the signal. In this paper, we study a scenario similar to the one defined in [7]. In such a scenario, the GNSS-R receiver is ground-based and stationary during the data acquisition. This receiver has a single antenna simultaneously receiving the line-of-sight (LOS) signal and a single reflected signal, where the latter has been forwardly scattered from the specular reflection point on the surface. The geometry of our scenario is shown in Figure 1. The reflection surface is assumed to be a horizontal planar surface with a homogeneous layered structure, i.e., the dielectric permittivity of the medium will only depend on the depth, i.e., the \(z\)-axis. These conditions could be fulfilled by surfaces, such as bare soil, snow- or vegetation-covered soil, or a calm water surface. Because of the large distance separating the satellite and the receiver, the elevation angle of the incident signal at the specular reflection point and at the receiver antenna can be considered both equal to the angle \(\theta_{el}\). In addition, we consider the reflection surface in our scenario to be smooth according to the Rayleigh criterion [61], and thus, the standard deviation of the surface height \(\sigma_{s_{h}}\), i.e., the surface roughness, satisfies:  
\[\sigma_{s_{h}}<\frac{\lambda}{8\sin(\theta_{el})}, \tag{1}\]  
where \(\lambda\) is the carrier wavelength. By default, we will assume a \(\sigma_{sh}=0.01\) m, low enough to fulfill the Inequality (1) for the GNSS L1 and L5 carrier frequencies and \(\theta_{el}\leq 35^{\circ}\). The reflected signals are usually characterized as the sum of two contributions or components: one specular and another one diffuse [61]. Under the smooth surface assumption, the coherent component reflected from the specular reflection point will clearly dominate, and as a consequence, the contribution of the diffuse component will be disregarded in our analysis. Under such an assumption, we can consider the energy reflected mainly coming from the first Fresnel zone [7; 61], and the reflected signal can be well approximated by a single delayed and complex-attenuated replica of the LOS signal. The first Fresnel zone describes an ellipse on the reflection surface (denoted as \(S\) in Figure 1) with:  
\[a=\frac{b}{\sin(\theta_{el})};\quad b=\sqrt{\frac{\lambda\,h}{\sin(\theta_{el} )}+\left(\frac{\lambda}{2\sin(\theta_{el})}\right)}, \tag{2}\]  
where \(a\) represents the semi-major axis, oriented towards the satellite's azimuth; and \(b\) is the ellipse's semi-minor axis. As was also pointed out in [7; 61], the waves carrying the GNSS signals will acquire some degree of depolarization upon their reflection on dielectric mediums. While the wave corresponding to the LOS signal will be considered as purely right-hand circularly polarized (RHCP), the reflected wave can be described as a mix of both RHCP and left-hand circular polarization (LHCP) components. The receiver's antenna radiation pattern is assumed to be known, and its effect under different polarizations of the incoming signals is included within the modeling of the amplitude of the received signals. Furthermore, we make no assumption about the maximum height for the receiver's antenna phase center position in our scenario, as long as the smooth criterion defined by Inequality (1) is still respected. Without loss of generality, we constrain our analysis to the single-satellite and single-signal scenario in each case.