## 2 Monostatic-Bistatic Geometry for Stereo-Radargrammetric Reconstruction
### Monostatic-Bistatic Observation Strategies  
Geometric parameters characterizing the bistatic geometry are the baseline, \(B\), that is the inter-antennae distance, and the bistatic angle, \(\beta\), that is the transmitter-target-receiver angle [25]. It is worth noting that the bistatic angle plays the same role in monostatic-bistatic radargrammetry as the stereo-intersection angle in monostatic repeat-pass one. A general analysis of bistatic SAR resolution is reported in [26; 27], based on the gradient method and on the derivation of bistatic ambiguity function; literature results will be used in the next sections, whereas simplified expressions, based on [23], will be introduced here in order to assess basic rules for mission design. Assuming two space platforms operating at the same altitude in parallel trajectories, the bistatic ground range, \(\Delta r_{g}\)\", and azimuth, \(\Delta x\)\" resolution can be related to the monostatic ones (\(\Delta r_{g}\)' and \(\Delta x\)', respectively) [23; 25]:  
\[\Delta r_{g}^{\bullet} = \frac{2\Delta r_{g}^{\prime}\sin\eta^{\prime}}{\sin\eta^{\prime}+ \sin\eta^{\bullet}} \tag{1}\] \[\Delta x^{\bullet} = \frac{2r^{\bullet}}{r^{\prime}+r^{\bullet}}\Delta x^{\prime} \tag{2}\]where \(\eta\)' and \(\eta\)\" are monostatic and bistatic incidence angles; \(r\)' and \(r\)\" are monostatic and bistatic slant ranges. Note that \(\eta\)\" must be considered negative in opposite-side geometry (see Figure 1). Theoretically, under the considered hypotheses, three different observation strategies can be realized (see Figure 1, where it is assumed constant the position of the monostatic SAR, and the different baselines are achieved thanks to adequate positioning of the bistatic receiving-only antenna):  
* same-side with monostatic sensor closer to the target;
* same-side with bistatic satellite closer to the target;
* opposite-side. Figure 2 shows the bistatic-to-monostatic ground range and azimuth resolution ratios with varying bistatic angle and observation strategy, considering a formation operating at 620 km altitude with constant 25 degrees monostatic off-nadir angle. Opposite-side geometry degrades bistatic ground range resolution considerably, whereas small variations of azimuth resolution can be estimated even if the worst values are realized for same-side configurations with monostatic sensor closer to the target. Bistatic slant range ambiguities depend on system timing and monostatic/bistatic antenna patterns and observation geometries [25, 28]. An immediate way to evaluate the ambiguity level is to consider the time interval required for the bistatic antenna to receive the monostatic swath width in elevation, which is the time interval between reception of far range and near range echoes in bistatic geometry. Figure 3 shows the time intervals required for bistatic swath acquisition considering a footprint in elevation of 40 km. As expected, increasing baseline in opposite-side observation geometry makes very difficult to separate the backscattered signals from the different regions of the illuminated area. This condition is even worse when dealing with surface relief variations. Indeed, the actual terrain slope can produce locally the specular observation condition in which the bistatic range ambiguity is total [25]. Finally, assuming a Lambertian model both for monostatic and bistatic backscattering coefficients [3] the ratio between bistatic and monostatic SNR can be evaluated as in [31]:  
\[\frac{\mathit{SNR}^{\pi}}{\mathit{SNR}^{\prime}}\cong 4\,\frac{{r^{\prime}}^{2} }{{r^{\prime}}\big{(}{r^{\prime}}+{r^{\prime}}\big{)}}\,\frac{\cos\eta^{\pi}} {\cos\eta^{\prime}}\frac{\sin\eta^{\prime}}{\sin\eta^{\prime}+\sin\eta^{\prime}} \tag{3}\]  
Figure 1: Observation strategies for monostatic-bistatic acquisition. The transmitting-receiving (Tx/Rx) and the receiving-only (Rx/o) antennae are supposed to operate at the same altitude in parallel trajectories (not to scale for clarity).