## 2 Scenario Definition
This assumption is reasonable given the low crosstalk among different GNSS signals, as well as the low cross-correlation among the different satellite spreading codes [62; 63]. In this paper, we have focused only on the GPS L1 C/A and GPS L5 (both L5I and L5Q) signals, as well as on the Galileo E1 (E1B: data; and E1C: pilot) and the full Galileo E5 signals. Table 1 summarizes the characteristics of the signals considered, and Figure 2 shows their normalized autocorrelation (real part). Figure 1: Scenario geometry depicting the LOS (**blue**) and the specular reflection (**red**) signal propagation paths. RX represents the position of the receiver’s antenna phase center, located at a height \(h\), defined as its orthogonal distance to the reflection surface. The point \(P\) marks the specular reflection point. The values \(\theta_{el}=30^{\circ}\) and \(h=2\) m are used in this case as the example. Although the GNSS signals in Table 1 have different typical received powers [64; 65; 66], for comparison purposes, we assume a default carrier-to-noise ratio (C/N\({}_{0}\)) of 45 dB-Hz for the LOS signal in all of the cases, before considering the antenna gain. Signal Model at the Output of the Receiver Front-EndFor the single-satellite scenario described, we collect \(\mathbf{x}\in\mathbb{C}^{N\times 1}\), a vector representing the complex baseband signal received, sampled at the output of the receiver's front-end over a total observation time interval of \(T_{obs}\) seconds. We assume the sampling rate \(f_{s}\), such that \(T_{obs}=Nf_{s}^{-1}\). The \(n\)-th sampling instant is defined as \(t_{n}\,=\,t_{0}+nf_{s}^{-1}\), where \(t_{0}\) is the time where the first measurement was taken. The vector \(\mathbf{x}\) can then be expressed as: \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Signal** & \(f_{c}\) **(MHz)** & **Modulation** & \(f_{chip}\) **(MHz)** & **Main Lobe BW(MHz)** & \(B_{Tx}\) **(MHz)** \\ \hline GPS L1 C / A & 1575.42 & BPSK (1) & 1.023 & 2.046 & 30.69 \\ GPS L5 & 1176.45 & BPSK (10) & 10.23 & 20.46 & 24 \\ Galileo E1 OS & 1575.42 & CBOC (6,1,1/11) & 1.023 & 14.322 & 24.55 \\ Galileo E5 full & 1191.795 & AltBOC (15,10) & 10.23 & 51.15 & 51.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: GNSS signal characteristics considered [64; 65; 66]. \(f_{c}\) is used to refer to the signal’s carrier frequency; \(f_{chip}\) is the modulation’s primary code chip rate; and \(B_{Tx}\) is the considered transmitted signal bandwidth. \(B_{Tx}\) has been selected to be equal to the receiver’s reference bandwidth, defined in the corresponding Interface Control Documents for each signal. For the GPS L1 C/A signal, we have considered the reference bandwidth defined for the Block III satellite vehicles. Figure 2: **(Top)** Normalized autocorrelation function of the transmitted GNSS signals considered (real part). The \(x\)-axis showing the delay \(\tau\) has been normalized to \(T_{chip}=(1.023\times 10^{6})^{-1}\) s; **(Bottom)** PSD of the signals. See Table 1 for more details. \[\mathbf{x}=\underbrace{\sum_{m=0}^{M-1}\mathbf{r}_{m}}_{\mathbf{r}}+\mathbf{n}, \tag{3}\]  
where the GNSS signal, described by the vector \(\mathbf{r}\), has been expressed as \(M\) superimposed independent signal components \(\mathbf{r}_{m}\), each one corresponding to a different propagation path. In Equation (3), \(\mathbf{n}\) is circularly-symmetric complex Gaussian noise with covariance \(\mathbf{C}\). Thus, \(\mathbf{x}\) is a random vector distributed as \(\mathcal{CN}\left(\mathbf{r},\mathbf{C}\right)\). Each \(\mathbf{r}_{m}\) component can be expressed as:  
\[\mathbf{r}_{m}=u_{m}\mathbf{d}_{m}e^{\mathrm{i}\phi_{m}}, \tag{4}\]  
where \(u_{m}\) and \(\phi_{m}\) are, respectively, the amplitude and the phase at the instant \(t_{0}\) (referenced to the receiver's local oscillator) of the \(m\)-th individual component. \(u_{m}\) and \(\phi_{m}\) are assumed to remain constant during observation intervals of up to a 1-s duration.