# A Novel Spaceborne Sliding Spotlight Range Sweep Synthetic Aperture Radar: System and Imaging
## 5 Comparisons
### Total Sample Number  
As stated at the beginning of this paper, the advantage of the SSS-RSSAR over the traditional SSS-SAR is that the SSS-RSSAR can image a tilted ROI with a much narrower ROI-matched BIS and hence contribute to less total data amount. If the data acquisition were made using the traditional SSS-SAR, the BIS would be parallel to the satellite orbit. For this case, the most simple and effective geometry corresponds to a CBP with a zero squint angle for and being vertical to the parallel-to-orbit BIS. To fully cover the BIS of the SSS-RSSAR, the cross-BIS swath of the traditional SSS-SAR, denoted as \(W_{\tau\tau}\) in Figure 2, yields  
Figure 7: Integrate system parameter design flowchart for the SSS-RSSAR.  
\[W_{\rm rT}=W_{\rm a}\sin\theta+W_{\rm r}\cos\theta \tag{54}\]  
By replacing \(W_{\rm r}\) in Equation (37) with \(W_{\rm rT}\), the echo length of the traditional SSS-SAR \(\tau_{\rm wT}\) yields  
\[\tau_{\rm wT}=\frac{2W_{\rm rT}\sin\beta_{\rm c}}{c}+T_{\rm p} \tag{55}\]  
Different from SSS-RSSAR, the sampling rate of the traditional SSS-SAR, denoted as \(F_{\rm sT}\), should be calculated by substituting the bandwidth \(B_{\rm r}\) in Equation (32), instead of the dechirped one \(B_{\rm rm}\) in Equation (33), into Equation (34) as  
\[F_{\rm sT}=\frac{\sigma c}{2\rho_{\rm r}\sin\beta_{\rm c}} \tag{56}\]  
The least required range sample number \(N_{\rm minT}\) can be achieved by multiplying \(\tau_{\rm wT}\) and \(F_{\rm sT}\) as  
\[N_{\rm minT}=\frac{\sigma W_{\rm rT}}{\rho_{\rm r}}+\frac{\sigma cT_{\rm p}}{ 2\rho_{\rm r}\sin\beta_{\rm c}} \tag{57}\]  
On the other aspect, for an expected along-strip azimuth resolution \(\rho_{\rm a}\), the minimum Doppler bandwidth of a target, denoted as \(B_{\rm aT}\), is  
\[B_{\rm aT}=\frac{V_{\rm s}}{\rho_{\rm a}} \tag{58}\]  
To avoid the azimuth aliasing, the maximum constant pulse interval, denoted as \(PI_{\rm T}\), for the azimuth sampling should be  
\[PI_{\rm T}=\frac{\rho_{\rm a}}{\sigma V_{\rm s}} \tag{59}\]  
By employing the same beam width \(\varphi_{\rm a}\) and the central beam slant range \(R_{\rm c0}\), the least required data acquisition period, denoted as \(t_{\rm aT}\), can be estimated by  
\[t_{\rm aT}=\frac{W_{\rm aT}+R_{\rm c0}\varphi_{\rm a}}{V_{\rm s}} \tag{60}\]  
where \(W_{\rm aT}\) denotes the along-track BIS swath of the traditional SSS-SAR as shown in Figure 2 as  
\[W_{\rm aT}=W_{\rm a}\cos\theta+W_{\rm r}\sin\theta \tag{61}\]  
The minimum azimuth sampling number, denoted as \(N_{\rm minT}\), can be computed by dividing \(t_{\rm aT}\) in Equation (60) by \(PI_{\rm T}\) in Equation (59) as  
\[N_{\rm aminT}=\sigma\frac{W_{\rm aT}+R_{\rm c0}\varphi_{\rm a}}{\rho_{\rm a}} \tag{62}\]  
By multiplying \(N_{\rm minT}\) and \(N_{\rm aminT}\), the total sample number for the traditional SSS-SAR, denotes as \(N_{\rm totalT}\), yields  
\[N_{\rm totalT}=\sigma^{2}\frac{W_{\rm aT}+R_{\rm c0}\varphi_{\rm a}}{\rho_{ \rm a}}\left(\frac{W_{\rm rT}}{\rho_{\rm r}}+\frac{cT_{\rm p}}{2\rho_{\rm r} \sin\beta_{\rm c}}\right) \tag{63}\]  
Comparatively, the total sample number for the SSS-RSSAR, denoted as \(N_{\rm total}\), can be computed by multiplying \(N_{\rm min}\) in Equation (38) and \(N_{\rm amin}\) in Equation (43) as  
\[N_{\rm total}=\sigma^{2}\frac{2f_{\rm c}\sin\beta_{\rm c}W_{\rm a}W_{\rm r}}{ c\rho_{\rm r}}\left(\tan\alpha\left(\frac{N_{\rm a}}{2}\right)-\tan\alpha\left(- \frac{N_{\rm a}}{2}\right)\right)\left(1+\frac{2W_{\rm r}\sin\beta_{\rm c}}{ cT_{\rm p}}\right) \tag{64}\]