# A Novel Spaceborne Sliding Spotlight Range Sweep Synthetic Aperture Radar: System and Imaging
## 6 Simulation and Discussion
Figure 9: Variations of: (**a**) CBSR; and (**b**) PI array with respect the azimuth time. Based on the new PA technique, the azimuth-dependent carrier frequency and chirp rate are shown in Figure 11a,b, respectively. Figure 12 compares the range wavenumber \(K_{\mathrm{Y}}\) when using and not using the new PA method. The red and blue lines denote the upper and lower limits of the range wavenumber spectrum and the green lines denote the upper and lower limits of range wavenumber of the valid data after the RVP removal. Figure 12a denotes the case where the new PA technique is used. The maximum and minimum values of \(K_{\mathrm{Y}}\) almost overlap with \(K_{\mathrm{Ymax}}\) and \(K_{\mathrm{Ymin}}\) respectively, resulting in a range bandwidth of the wavenumber domain \(\Delta K_{\mathrm{Y}}\) around \(8.8\) rad/m. Note that as this bandwidth is actually wider than the real range wavenumber bandwidth of the valid data \(\Delta K_{\mathrm{Ys}}\) because the echoes of different targets have been aligned to the referential target (swath center) by the RVP removal manipulation. Based on Equations (19), (21) and (46), \(\Delta K_{\mathrm{Ys}}\) can be estimated as  
\[\Delta K_{\mathrm{Ys}}\approx\frac{4\tau\gamma_{0}T_{\mathrm{p}}\sin\beta_{c}} {c} \tag{66}\]  
By substituting the parameters in Table 4 into Equation (66), \(\Delta K_{\mathrm{Ys}}\) is calculated as \(6.28\) rad/s, which is not to be altered by the range interpolation. Comparatively, in Figure 11b where the carrier frequency and chirp rate always equal to their constant referential values \(f_{\mathrm{<0}}\) and \(\gamma_{0}\), respectively, both the maximum and minimum values of \(K_{\mathrm{Y}}\) are characterized with large spatial varieties and the range bandwidth of the wavenumber domain \(\Delta K_{\mathrm{Y}}\) is around \(0.33\) rad/m, much narrower than the range wavenumber bandwidth of the valid data \(\Delta K_{\mathrm{Ys}}\). For this case, \(\Delta K_{\mathrm{Ys}}\) equals to \(\Delta K_{\mathrm{Y}}\). Figure 11: Azimuth dependent: (**a**) carrier frequency; and (**b**) chirp rate when the new parameter adjusting technique is employed. Figure 12: Range wavenumber when: (**a**) using the parameter adjusting technique; and (**b**) not using the parameter adjusting technique. The difference of the range wavenumber bandwidth of the valid data will lead to different range resolution performances as shown in Figure 13, where the central swath target \(T_{33}\) is adopted for the resolution inspection. For the case where the new PA technique is used in Figure 13a, the range resolution of the focused image is 1.035 m. Comparatively, for the case where the traditional constant parameter strategy is used in Figure 13b, the range resolution is 18.846 m, degraded by around 18.8 times. By noticing that that the range wavenumber bandwidth of the valid data achieved with the new PA technique is 18.8 times high than that without the new PA technique, we can conclude that the improvement of the range resolution performance is caused by the expansion of the range wavenumber bandwidth contributed by the new PA technique. By comparing Figure 13a,b, we find the azimuth resolutions of the two cases are almost the same. This is because the azimuth samples corresponding to the beam dwell time of \(T_{33}\) are within the region restricted by \(A_{1}-A_{2}\) in Figure 12b. For the azimuth samples outside the \(A_{1}-A_{2}\) region, there would be no valid data after the range interpolation. Therefore, for the azimuth marginal targets such as \(T_{11}\), \(T_{31}\), \(T_{51}\), \(T_{15}\), \(T_{35}\), \(T_{55}\), etc., the azimuth resolutions would be degraded. Based on the results in Figures 11-13, the benefits of applying the new PA technique for the SSS-RSSAR data acquisition have been demonstrated.