## 4 Numerical Results
At the same time, as it was expected, BA-PTSM and GO provides  
Figure 4: SNR in RR polarization for a spaceborne GNSS-R receiver obtained using BA-PTSM (solid lines) and GO (dashed lines) for wind speed \(5\) m/s (blue lines), \(15\) m/s (red lines), and \(25\) m/s (green lines). (a) \(\phi_{s}=0^{\circ}\); (b) \(\phi_{s}=45^{\circ}\); (c) \(\phi_{s}=90^{\circ}\); (d) \(\phi_{s}=120  
very similar results at and around the specular direction, where small-scale roughness scattering is negligible compared to large-scale roughness scattering. For the purposes of accurate simulation of GNSS-R signals, distinguished comments apply to the spaceborne and airborne scenarios. Indeed, for spaceborne GNSS-R equipped with an LHCP receiving channel (Figure 3), it emerged that SNR is larger than 0 dB only in an angular region surrounding the specular direction, where GO and BA-PTSM provide very similar results. Conversely, departure of GO from BA-PTSM is significant at far-from-specular directions, specified by \(\phi_{s}>90^{\circ}\) or \(\theta_{s}>60^{\circ}\). However, in such acquisition geometries, both scattering models predict SNR values well below 0 dB, and, then, the incoherently-averaged DDM would be dominated by thermal noise. Accordingly, accuracy of the scattering model in these acquisition geometries would not be an issue. Figure 5: SNR in RL polarization for an airborne GNSS-R receiver obtained using BA-PTSM (solid lines) and GO (dashed lines) for wind speed 5 m/s (blue lines), 15 m/s (red lines), and 25 m/s (green lines). (**a**) \(\phi_{s}=0^{\circ}\); (**b**) \(\phi_{s}=45^{\circ}\); (**c**) \(\phi_{s}=90^{\circ}\); (**d**) \(\phi_{s}=120^{\circ}\); (**e**) \(\phi_{s}=150^{\circ}\); (**f**) \(\phi_{s}=180^{\circ}\). Spaceborne GNSS-R equipped with RHCP channel (Figure 4) experiences SNR values well below 0 dB regardless of the acquisition geometry and sea state. Again, DDM products would be dominated by thermal noise and their simulation would be scarcely affected by the choice of the sea scattering model. Finally, according to results shown in Figures 3 and 4, accurate simulation of spaceborne GNSS-R signals over open sea can be carried out by relying on the classical GO model with anisotropic sea surface model. It is worth noting that, even assuming much larger coherent integration times (on the order of 100 ms or larger), GO might still be accurate enough for simulation purposes regardless of the acquisition geometry and sea state. In the airborne scenario, the much lower receiver altitude with respect to spaceborne GNSS-R leads to much higher SNR values in all acquisition geometries and sea states, with LHCP channel providing larger signal strength compared to the RHCP one, see Figures 5 and 6. SNR values as large as about 46 dB are obtained in the forward-scattering direction for low wind speed (Figure 5). The much larger received signal strength calls for sea scattering models more accurate than GO, which is no longer reliable for proper simulation of sea-reflected GNSS signals. As a matter of fact, GO might lead to inaccurate results even for in-plane scattering (Figure 5a), where for large \(\theta_{s}\) values and low wind speed, severe discrepancies between GO and BA-PTSM are visible. For out-of-plane scattering and in backscattering, GO becomes more and more inaccurate as \(\phi_{s}\) increases, i.e., as the scattering direction goes far from the specular one. As a result, application of GO is questionable for acquisition geometries specified by \(\phi_{s}>90^{\circ}\), where GO would lead to severe underestimations of the sea clutter contribution. Similar comments apply for simulation of the RHCP channel (Figure 6), where GO offers limited applicability in far-from-specular directions. However, the reduced sea signal strength makes the application of GO less problematic especially for low wind speeds, see Figure 6d-f.