## 2 Selection of a Bistatic Configuration
### Spatial Resolution Analysis  
The ground range and azimuth resolutions could be very poor in some bistatic configurations, thus implying a bad radar image quality. For instance, the ground range resolution is critical in specular configuration [1, 12]. Basing on these considerations, we have performed an evaluation of the bistatic spatial resolutions in order to put an additional constraint to the sensor configurations selected in [2]. It is worth noting that no adequate model has been found in the literature for such an exercise, because only few cases addressed the spaceborne receiver configuration. In [1], this matter was analyzed, but only for a two-dimensional (2-D) configuration restricted to the bistatic plane. General considerations and formulas valid for the 3-D case were provided in [13].  
Starting from the relationships found in [13], we have derived the formulas for evaluating the ground range (\(\rho_{gr}\)) and azimuth (\(\rho_{u}\)) bistatic resolutions, by doing the following assumptions: _i_) flat and fixed Earth; _ii_) satellites orbiting at the same height (and therefore flying with the same velocity); _iii_) equal coherent integration times. Then, we have normalized the bistatic resolutions to the monostatic ones, obtaining equations depending on the relative geometry of the satellites carrying the sensors and independent from orbital and antenna parameters. In this section, we do not report all the mathematical manipulations, for the sake of conciseness, but only the result. More details can be found in the Appendix. The final equations are the following:  
\[\frac{\rho_{gr}}{\rho_{gr}}^{back}= \frac{2\sin\theta_{i}}{\sqrt{\sin^{2}\theta_{i}+\sin^{2}\theta_{ s}-2\sin\theta_{i}\sin\theta_{s}\cos\varphi_{s}}}\] (1) \[\frac{\rho_{a}}{\rho_{a}}^{back}=\frac{2\cos\theta_{  
complementary to those identified by the unit vector normal to the incidence plane and the velocity vectors (see Appendix).  
Starting from the above formulas, and supposing that the satellites' velocity vectors are directed normally to the incidence plane (_i.e._, \(\delta_{T}=\delta_{R}=\)90\({}^{\circ}\)), maps of \(\rho_{g^{\prime}}/{\rho_{g^{\prime}}}^{back}\) and \(\rho_{a}/{\rho_{a}}^{back}\) have been generated as function of \(\theta_{s}\) (in the range [0\({}^{\circ}\)-60\({}^{\circ}\)]) and \(\varphi_{s}\) (in the range [0\({}^{\circ}\)-180\({}^{\circ}\)]), for a fixed value of \(\theta_{i}\). Figure 2 shows the maps for the minimum and maximum values of \(\theta_{i}\) recommended for estimating soil moisture (_i.e._, 15\({}^{\circ}\) and 35\({}^{\circ}\)).  
By observing Figure 2, it can be noted that the ground range resolution is more critical than the azimuth one. The latter does not exceed 2\({\rho_{a}}^{back}\), while \(\rho_{g^{\prime}}\) can be several times larger than \({\rho_{g^{\prime}}}^{back}\), especially near the specular direction (as expected). As an additional constraint to the bistatic sensors configurations selected in [2], we have chosen \(\rho_{g^{\prime}}<{\rho_{g^{\prime}}}^{back}\), thus finding that \(\varphi_{s}\) must be limited in the interval [90\({}^{\circ}\)-270\({}^{\circ}\)], that is in the backward quadrant (see Figure 1 right panel and the Appendix). We have therefore considered the following ranges for the zenith and azimuth scattering angles: \(\theta_{s}\in[0^{\circ}\)-8\({}^{\circ}\)] and \(\varphi_{s}\in[90^{\circ}\)-270\({}^{\circ}\)].  
Figure 2: Maps of \(\rho_{g^{\prime}}/{\rho_{g^{\prime}}}^{back}\) (left panels) and \(\rho_{a}/{\rho_{a}}^{back}\) (right panels), for \(\theta_{i}=15^{\circ}\) (upper panels) and \(\theta_{i}=35^{\circ}\) (lower panels) in the (\(\theta_{s}\),\(\varphi_{s}\))-plane. Ground range resolution has been upper limited to 4 times the backscattering value for the sake of figure clarity.