## 4 Numerical Results  
For numerical analysis we assumed typical GNSS-R receivers, namely SGR-ReSi and GOLD-RTRR for spaceborne and airborne configurations, respectively. The former has been adopted in past and current spaceborne GNSS-R missions, e.g., TechDemoSat-1 and CYGNSS; the latter has been used in more than 40 flights over oceans, lakes, and land. Related GNSS-R data are made available on the missions websites. Noise and processing parameters are listed in Table 1 for both receivers. For more details about SGR-ReSi and GOLD-RTR receivers, the interested reader is referred to [36; 37], respectively. Numerical results for the SNR are shown in Figures 3-6. More specifically, Figures 3 and 4 show the SNR for a spaceborne GNSS-R equipped with SGR-ReSi receiver and an LHCP and RHCP channel, respectively. Similarly, Figures 5 and 6 show results for an airborne GNSS-R equipped with a GOLD-RTR receiver and an LHCP and RHCP channel, respectively. For each scenario, SNR of the sea surface return is displayed as a function of the zenith scattering angle for different wind speeds-namely 5 m/s (gentle breeze, blue lines), 15 m/s (near gale, red lines), and 25 m/s (storm, green lines), and for different azimuth scattering angles, ranging from 0\({}^{\circ}\) (forward-scattering, where conventional GNSS-R operates) to 180\({}^{\circ}\) (back-scattering, where unconventional GNSS-R is conceived to work). For a more comprehensive analysis, results obtained with BA-PTSM (solid lines) are compared with classical GO model (dashed lines), wherein the same sea surface slopes PDF described in Section 2 has been adopted for both scattering models. The evaluation of the sea scattering area has been accomplished by assuming the receiver along-track and across-track HPBW values reported in Table 1.  
Largest SNR values are reasonably obtained in the forward-scattering configuration and in the LHCP receive channel, regardless of sea state and receiver altitude. Indeed, this is due to a favorable combination of the following phenomena: first, sea surface geometry makes the impinging EM energy be largely reflected in a rather narrow angular region around the specular reflection direction, whose width increases with increasing wind speed; second, bistatic GNSS-R acquisition geometry is characterized by resolution cells whose sizes heavily depend on the delay-Doppler coordinates of the surface point and are largest at the specular reflection point. As a result, both sea surface NRCS and scattering area  
Figure 3: SNR in RL 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**) \(\phi_{\mathrm{s}}=0^{\circ}\); (**b**) \(\phi_{\mathrm{s}}=45^{\circ}\); (**c**) \(\phi_{\mathrm{s}}=90^{\circ}\); (**d**) \(\phi_{\mathrm{s}}=120^{\circ}\); (**e**) \(\phi_{\mathrm{s}}=150^{\circ}\); (**f**) \(\phi_{\mathrm{s}}=180^{\circ}\). are largest in correspondence of the forward-scattering direction. Moreover, polarization inversion over seawater leads to an LHCP signal component larger than the RHCP one. BA-PTSM better estimates the diffuse component of sea scattering at far-from-specular observation directions, i.e., for large \(\phi_{s}\) values or \(\theta_{s}\) not close to \(\theta\), where GO severely underestimates sea surface NRCS due to the tangent plane approximation. Major differences between the two models can be appreciated for \(\phi_{s}=180^{\circ}\), that includes the backscattering direction. In such configurations, the underestimation of the sea-reflected signal SNR is as large as several tens of dB for large zenith scattering angles regardless of sea state and receiver altitude, whereas for zenith scattering angles less than about \(10^{\circ}\) GO offers good accuracy in RL polarization, see Figures 3f and 5f. Additionally, in far-from-specular directions, including backscattering, GO reveals less accurate in modeling the RR channel rather than the RL one.