# Pre-Flight SAOCOM-1A SAR Performance Assessment by Outdoor Campaign
## 2 Outdoor Experiment Concept, Design, and Simulations  
The well-known far field condition on the distance \(R\) for an antenna with size \(L\) operating at central wavelength \(\lambda\), is:  
\[\frac{\lambda}{L}R>>L \tag{1}\]  
In the case of the SAOCOM-1A SAR instrument, we refer to the SAR antenna, a planar array with the total size along azimuth \(L\) equal to 9.94 m. The antenna is made by seven tiles with the size of 1.42 m \(\times\) 3.48 m (azimuth \(\times\) elevation), and the center frequency is 1.275 GHz (\(\lambda=\frac{c}{f}\) is equal to 23.53 cm). The far field distance results are in the order of 40 m. Moreover, the SAR instrument cannot receive echoes returning to the antenna while the chirp transmission is still active. Considering a minimum chirp length of 10 \(\upmu\)s, and another 10 \(\upmu\)s of guard time between the end of transmission and the start of echo reception, the minimum distance of a \"visible\" target is 3.3 km. Compared to the SAR acquisition in space, here the antenna is not moving along an orbit, so there is no synthetic aperture. The area illuminated by the antenna is limited by the range resolution \(\rho_{g}\) and by the real antenna aperture in azimuth \(\frac{\lambda}{L_{a}}R\). Considering a homogeneous reflective scenario (e.g., bare soil or short vegetation) in front of the radar, with reflectivity equal to \(\sigma_{T}^{0}\), the radar cross-section (RCS) of each resolution cell is computed as:  
\[\sigma_{c}=\frac{\rho_{g}\lambda R}{L_{a}}\sigma_{T}^{0} \tag{2}\]  
Considering the bandwidth range equal to 50 MHz and one tile of the antenna with a length equal to 1.42 m, the resolution cell at the SAOCOM central frequency is as large as 1600 m\({}^{2}\). Assuming a reflectivity of \(-\)15 dB, the obtained RCS is 17 dBsm. (We indicate with dBsm the ratio of the area with respect to 1 m\({}^{2}\), expressed in logarithmic scale). This large backscattered power can be considered either as a signal--if stable--or as a noise--if unstable. Water and leaves are highly unstable; however, their contribution is effectively reduced if averaged for seconds. Slower-moving targets could provide long-term noise contributions that affect the measure. We then decided that the observed scenario might not be stable enough for an accurate measurement, so we inserted a trihedral corner reflector in the scene. Figure 1 shows the schematic representation of the overall concept of the SAOCOM outdoor test (ODT): the SAOCOM SAR antenna points towards a known point target (trihedral corner reflector), moving along the line of sight, with a linear motion, thanks to a linear actuator. The acquired data are downloaded and processed to extract signal characteristics and to assess the phase and gain stability of the instrument. The reason for target motion is to effectively limit the size of the corner reflector to reasonable values. The target, moving with controlled and known motion, can be separated from the background and other moving targets provided that the motion is significant with respect to half the wavelength. The RCS of the trihedral corner reflector with length \(d\) can be modeled as:  
\[\sigma_{x}^{2}=\frac{4}{3\pi}\frac{d^{4}}{\lambda^{2}} \tag{3}\]  
In order to distinguish it from the background and to have sufficient accuracy in the phase and amplitude measurement, we ask for a signal to clutter ratio \(\frac{\sigma_{x}^{2}}{\sigma_{c}^{2}}\) of at least 30 dB. With the computed RCS of the clutter as above, this would lead to a target with a size greater than 8 m.  
Let us then assume that the corner reflector is mounted on a rail, and moves with time, say of an extent much less than a range resolution cell.