# Spaceborne Sparse SAR Imaging Mode Design: From Theory to Implementation
## 3 Design and Performance Analysis of Sparse SAR Imaging Mode
### System Performance Analysis of Scan Mode  
**System Parameter Calculation**. According to the timing diagram in Figure 3d, we compare the essential system parameters of sparse and traditional Scan modes. The basic system parameters of sparse and traditional Scan modes are calculated in Table 2. To illustrate the differences between them, we focus on subswath 1 (SS1) as the example. In the traditional mode, SS1 has a swath width of 60.02 km with a PRF of 1375 Hz. In contrast, the designed sparse Scan mode reduces PRF to 1031 Hz, resulting in a wider swath width of 80.05 km. By reducing the PRF to 75% of its original value, the swath coverage of each subswath in sparse Scan mode increases from 60 km to 80 km. This leads to a total swath width increase from 180 km to 240 km, without any changes to other parameters such as azimuth resolution and beamwidth.  
**Azimuth Ambiguity Analysis**. The relationship between AASR and PRF for SS1 in Table 2 is shown in Figure 8, and the corresponding variation curves are given for azimuth positions at 0 m, 500 m, and 1 km, respectively. From Figure 8, it can be seen that the AASR value increases with the azimuth position. In addition, because of the reduced PRF, AASR deteriorates from \(-16\)\(\sim\)\(-25\) dB to \(-6\)\(\sim\)\(-14\) dB. Thus, it is necessary to suppress the azimuth ambiguity using the sparse imaging method.  
**Range Ambiguity Analysis**. The RASR of the Scan mode is calculated in the same way as in Stripmap, as the Scan mode has no extra processing in the range direction. However, since the PRF is different for each subswath, the RASR of each subband is also different. The relationship between RASR and the incidence angle for each subswath in traditional and sparse Scan modes is shown in Figure 9. The red line is the traditional Scan mode, and the blue line is the sparse one. It is seen that the RASR of each subswath of the sparse mode is lower than that of the traditional one. Then, we take SS1 for example to analyze RASR. The relationship between RASR and PRF for SS1 in Table 2 is shown in Figure 10. It is seen that in the sparse mode, the RASR varies from \(-43.9\) dB to \(-51.9\) dB due to changes in the incidence angle and PRF, which indicates that the range ambiguity is suppressed in the sparse mode.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline  & **SS1** & **SS2** & **SS3** \\ \hline Sparse Scan imaging mode & & & \\ \hline PRF [Hz] & 1031 & 1170 & 950 \\ Incident angle (near) [deg] & 28.63 & 33.58 & 38.10 \\ Incident angle (far) [deg] & 33.65 & 38.19 & 42.31 \\ Middle look angle [deg] & 27.33 & 31.34 & 34.93 \\ Platform velocity [m/s] & 7465 & 7465 & 7465 \\ Range resolution [m] & 8 & 8 & 8 \\ Azimuth resolution [m] & 15 & 15 & 15 \\ Subswath width [km] & 80.05 & 80.15 & 80.14 \\ Total swath width [km] & & \(\sim\)240 & \\ \hline Traditional Scan imaging mode & & & \\ \hline PRF [Hz] & 1375 & 1460 & 1257 \\ Incident angle (near) [deg] & 31.63 & 35.14 & 38.44 \\ Incident angle (far) [deg] & 35.26 & 38.53 & 40.21 \\ Platform velocity [m/s] & 7465 & 7465 & 7465 \\ Range resolution [m] & 8 & 8 & 8 \\ Azimuth resolution [m] & 15 & 15 & 15 \\ Subswath width [km] & 60.02 & 60.04 & 60.08 \\ Total swath width [km] & & \(\sim\)180 & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters of designed sparse Scan mode and traditional Scan mode.