## 6 Appendix-Spatial Resolution  
In this section, Equations (1) and (2) are derived starting from the relationships found in [13]. The hypotheses of flat Earth and same satellite heights hold true. We make reference to the geometry shown in Figure 7.  
Figure 7: Geometry for evaluating the bistatic spatial resolution. T, R and P represent the positions of transmitter, receiver and target, respectively. By assuming the incidence plane as a reference, let us consider a three-dimensional Cartesian coordinates system in which the (\(x\),\(z\))-plane is coincident with the incidence one and the (\(x\),\(y\))-plane is considered to be the (flat) Earth surface. Let us fix: \(i\)) the transmitter position T (\(x_{T}\), \(y_{T}\), \(H\)) in such a reference frame; \(ii\)) the incidence angle \(\theta_{i}\), \(iii\)) the elevation \(\theta_{s}\) and azimuth \(\varphi_{s}\) scattering angles. Then, we can determine, as function of these parameters, the following ones: \(iv\)) the ground target position P (\(x_{T}+\theta_{i}\), 0, 0); \(v\)) the receiver position R (\(x_{T}+H\)tan\(\theta_{i}+H\)tan\(\theta_{s}\)cos\(\varphi_{s}\), \(y_{T}+H\)tg\(\theta_{s}\)sin\(\varphi_{s}\), \(H\)). Denoting by \(\mathbf{x}_{0}\), \(\mathbf{y}_{0}\) and \(\mathbf{z}_{0}\) the versors of the considered Cartesian system, the vectors directed from the transmitting (\(\mathbf{u}_{T}\)) and receiving (\(\mathbf{u}_{R}\)) antennas to the target are (see Figure 7):  
\[\mathbf{u}_{{}_{T}}=H\tan\theta_{i}\mathbf{x}_{0}-H\mathbf{z}_{0} \tag{3}\]  
\[\mathbf{u}_{{}_{R}}=-H\tan\theta_{{}_{s}}\cos\varphi_{s}\mathbf{x}_{0}-H\tan \theta_{{}_{s}}\sin\varphi_{s}\mathbf{y}_{0}-H\mathbf{z}_{0} \tag{4}\]  
The transmitter-to-target and receiver-to-target ranges are the modules of \(\mathbf{u}_{T}\) and \(\mathbf{u}_{R}\), respectively:  
\[\left|\mathbf{u}_{{}_{T}}\right|=H/\!\cos\theta_{{}_{i}} \tag{5}\]  
\[\left|\mathbf{u}_{{}_{R}}\right|=H/\!\cos\theta_{{}_{s}} \tag{6}\]  
Now we can consider the relationship for the ground range resolution proposed in [13]:  
\[\rho_{gr}=\frac{c}{2B_{{}_{W}}\left|\Gamma_{xy}\mathbf{u}_{{}_{eff}}\right|} \tag{7}\]  
where \(c\) denotes the velocity of light, \(B_{w}\) is the pulse bandwidth and \(\Gamma_{xy}\) is the projector onto the horizontal plane. \(2\mathbf{u}_{{}_{eff}}\) is defined as [13]:  
\[2\mathbf{u}_{{}_{eff}}=\!\left(\frac{\mathbf{u}_{{}_{T}}}{\left|\mathbf{u}_{{ }_{T}}\right|}+\frac{\mathbf{u}_{{}_{R}}}{\left|\mathbf{u}_{{}_{R}}\right|}\right) \tag{8}\]  
Accounting for Equations (3)-(6) it turns out:  
\[2\mathbf{u}_{{}_{eff}}=\!\left(\sin\theta_{{}_{s}}\cos\varphi_{s}-\sin\theta_ {{}_{i}}\right)\mathbf{x}_{{}_{0}}+\sin\theta_{{}_{s}}\sin\varphi_{{}_{s}} \mathbf{y}_{{}_{0}}+\!\left(\cos\theta_{{}_{i}}+\cos\theta_{{}_{s}}\right) \mathbf{z}_{{}_{0}} \tag{9}\]  
The application of the \(\Gamma_{xy}\) operator leads to the following relationship:  
\[2\Gamma_{xy}\mathbf{u}_{{}_{eff}}=\!\left(\sin\theta_{{}_{s}}\cos\varphi_{{}_ {s}}-\sin\theta_{{}_{i}}\right)\mathbf{x}_{{}_{0}}+\sin\theta_{{}_{s}}\sin \varphi_{{}_{s}}\mathbf{y}_{{}_{0}} \tag{10}\]  
By substituting the norm of \(2\Gamma_{xy}\mathbf{u}_{{}_{eff}}\) in (7), we can derive the final expression of \(\rho_{gr}\):  
Figure 7:0  
Considering that the ground range resolution of a conventional monostatic radar is \(c/(2B_{w}\)sin\(\theta)\), the \(\rho_{gr}/\rho_{gr}{}^{back}\) ratio is given by (1). It is worth noting that, if \(\theta_{s}\) is equal to \(0^{\circ}\), the \(\rho_{gr}/\rho_{gr}{}^{back}\) ratio does not depend on \(\varphi_{s}\) and is equal to 2 for every \(\theta_{i}\). Moreover, if we consider \(\varphi_{s}\) equal to \(0^{\circ}\) (or around it), when \(\theta_{s}\) increases starting from \(0^{\circ}\), the \(\rho_{gr}/\rho_{gr}{}^{back}\) ratio grows too much and is always larger than 2.