## 5 Case Study Example  
The analysis of the bistatic geometry of a PR based on TerraSAR-X was carried out, because of the similar characteristics of PAZ and TerraSAR-X. The central point of the area of interest was located at the University of Alcala campus, on the roof of the Polytechnic School, with the following coordinates \(40^{\circ}30^{\prime}48.44^{\prime\prime}\) N, \(3^{\circ}20^{\prime}55.30^{\prime\prime}\) W and an altitude of 587 m.  
An acquisition in spotlight mode was assumed. This mode simplifies the geometry of the system, because it allows the definition of a constant coverage area during SAR sensor operation. It has been selected in order to focus on the description of the parameters to be considered in the analysis. Once the methodology has been explained, it can be straightforwardly applied to ScanSAR and stripmap modes, taking into consideration the movement of the footprint and the increase in the achievable coverage area. A spotlight image acquisition covering an area of \(10\times 10\) km\({}^{2}\), with a bandwidth of 300 MHz, an incidence angle of \(24.75^{\circ}\), and an acquisition time of \(1.5\) s was assumed (Figure 18). Due to the slight movement of the beam along the cross-range direction, an effective inner illuminated area of \(5\times 5\) km\({}^{2}\) was considered (Figure 20). The PR receiver was located at the center of the area of interest. This solution minimized the required sensitivity, taking into consideration that, as has been already mentioned, the coverage was composed of two independent ovals centered on the OI and the PR receiver, respectively. The considered area laid completely in the unambiguous detection region defined by the LFM pulse train CAF, which is around 480 km long for the monostatic case. The date and time parameters of the case of study were: 13 April 2015, 17:58:50. From the TLE parameters provided by the SGP4 model, during the acquisition time of \(1.5\) s, the main features of the satellite movement where estimated:  
* The satellite moved from \(40^{\circ}10^{\prime}20.00^{\prime\prime}\) N, \(5^{\circ}51^{\prime}56.00^{\prime\prime}\) W to \(40^{\circ}15^{\prime}57.00^{\prime\prime}\) N, \(5^{\circ}53^{\prime}24.00^{\prime\prime}\) W.
* Satellite altitude remained approximately constant and equal to 513.4 km. Figure 19: Coverage area of PAZ as the OI depending on the sensitivity of the system and the incidence angle of the satellite’s illumination beam. * The acquisition started at the time when the elevation angle of the satellite with respect to the PR receiver location was maximum. The elevation variations were of some hundredths of degree around \(65.25^{\circ}\). * The azimuth of the satellite with respect to the North varied \(3^{\circ}\), from \(260^{\circ}\) to \(263^{\circ}\). This variation was higher due to the polar orbit of the sensor. Knowing the position of the OI during the acquisition time, a bistatic system geometry analysis was carried out throughout the coverage area (Figure 20) with the following considerations:  
* The area of interest was divided into \(5\times 5\) m\({}^{2}\) cells. * The system geometry was calculated assuming that a non-moving ground target was located at the center of each cell. * The system geometry was recalculated each 0.01 s (150 time slots were analyzed) in order to take into account the satellite dynamics. The bistatic angle at the acquisition starting time for each \(5\times 5\) m\({}^{2}\) cell of the defined coverage area is presented in Figure 21a. The total variation of the bistatic angle during the whole acquisition time is represented in Figure 21b. The maximum bistatic angle variations is equal to \(1.17^{\circ}\). Figure 21: Study of the spatial and time variation of the bistatic angle: (**a**) initial value at each \(5\times 5\) m\({}^{2}\) cell of the coverage area; (**b**) total variation during the acquisition time. Figure 20: Case study geometry analysis scheme. The bistatic range resolution, which is a function of the bistatic angle, was also analyzed.