## 5 Data Processing and Experimental Results: SAR Mode
### Data Processing  
The SAR data collected onboard, typically named raw-data, are arranged, as in the Sounder case, in a two-dimensional matrix representing the radar echoes as a function of the range and azimuth coordinates. The main rationale of the processing chain applied to focus these raw data is shown in Figure 9. It basically consists of the cascade of three steps. The first step is the same as that described for the Sounder case, that is, an azimuth pre-summing aimed at improving the signal-to-noise ratio. In this regard, it is noted that the Doppler bandwidth achievable with the available azimuth beam (\(20^{\circ}\) and \(10^{\circ}\) for the SAR-Low and SAR-High modes, respectively, see Table 1) and the platform velocity (on the order of 40 m/s) is, for both the SAR operational modes, on the order of 40 Hz, that is, significantly smaller than the PRF (which, according to Table 1, becomes 500 Hz when considering each separate polarimetric channel). Accordingly, the pre-summing factor can be safely set on the order of 10 or even more. In the cases at hand, a factor of 8 has been applied. Also the second processing step is the same as that of the Sounder processing chain (see again Figure 9): it carries out the range focusing of the data through the chirp pulse compression procedure [(62; 63)], which may include also the application of a spectral windowing aimed at reducing the level of the secondary lobes of the impulse response relevant to the range-f  
Figure 8: As for Figures 6 and 7, but for TS4. Mean flight velocity: 45 m/sec. Mean flight altitude: 2081 m. Mean terrain height: 745 m.  
Figure 7: As for Figure 6, but for TS2. Mean flight velocity: 36 m/sec. Mean flight altitude: 2104 m. Mean terrain height: 770 m.  
Figure 9: SAR data processing. at hand, the Hamming filtering has been applied. Moreover, for the SAR-Low mode data, application of an additional band pass filtering procedure was necessary to cut strong interference contributions well concentrated around the lower frequencies of the bandwidth of the transmitted pulse. In particular, a 25% reduction of the 40 MHz pulse bandwidth has been applied, which has led to a range resolution of about 5 m.  
Following this step, azimuth focusing of the data, which includes the correction of the range cell migration effect [63], has been applied. For each target of the considered scene, this procedure basically consists in the compensation of the phase terms that depend on the so-called range history, i.e., the distance between the target and the phase center of the moving radar antenna. In this regard, we note that when the SAR sensor moves along a rectilinear trajectory, as it happens in the spaceborne case (at least theoretically, within a synthetic azimuth length [63]), for all the observed targets the range history is independent of the terrain topography [63]. Differently, when deviations from an ideal straight trajectory occur, as it always happens for aerial platforms (due to the unavoidable presence of atmospheric turbulences), the range history relevant to the observed targets becomes dependent on both the trajectory deviations and the terrain topography [72; 73]. Thus, in the latter case, exploitation of external Digital Elevation Models (DEMs) of the observed area, as well as the flight data recorded by the navigation system mounted onboard [72; 73], is necessary to precisely compensate the range history of the observed targets. In the last decades a number of accurate and computationally efficient algorithms, which operate in the spectral domain, have been originally devised to focus spaceborne SAR data [63; 74] and subsequently modified in order to deal with aerial SAR data as well, through the inclusion of the so-called MOtion COmpensation (MOCO) procedures [72; 73]. However, such MOCO procedures involve some approximations [75] necessary to preserve the high computational efficiency of the spectral domain focusing algorithms.