## 4 Results and Discussion  
### Simulated Results of High-Resolution SAR Imaging  
The simulation is carried out in order to analyze the degree of deterioration of SAR image caused by the relative motion between the space-borne X-band SAR and space targets. The simulated parameters of non-uniform hybrid sampling technology are given in Table 2. The range of hybrid samplings interval (\(t_{\text{hs}}\)) is calculated based on Equation (9), and the parameters setting are shown in Table 3, indicating that the hybrid sampling interval (\(t_{\text{hs}}\)) decreases as the qualification factor (\(Q\)) increases. According to the parameters of the SAR system, the hybrid sampling intervals (\(t_{\text{hs}}\)) for different qualification factors (\(Q\)) are set as 50 us, 28 us and 15 us. Simulated results of space-borne high-resolution SAR imaging for single point target are shown in Figure 5. The simulation results show that all the targets are well focused in the range direction, while the focusing performance in the azimuth direction significantly deteriorates with the increase in the hybrid sampling interval (\(t_{\text{hs}}\)). Considering the system characteristics of ultra-wideband signal and long synthetic aperture time, the back projection (BP) algorithm is used to image the target [20]. The simulation raw SAR data with 2.5 GSPS sampling rate are firstly processed by hybrid sampling technology to form the pre-processed data with 10 GSPS sampling rate, and then focused into a two-dimensional SAR image after pulse compression and back projection processing. Figure 5a is the imaging result of single point target with Nyquist real-time sampling (the real-time ADC sampling rate is 10 GSPS), and there is no phase disturbance in slow time. Figure 5b-d shows the imaging results with hybrid sampling intervals of 15 us, 28 us and 50 us, respectively. The quantitative analysis of imaging quality for single-point target is compared in Table 4, including impulse response width (IRW), peak side lobe ratio (PSLR) and integrated side lobe ratio (ISLR) in both the range (R) and azimuth (A) directions [21]. The imaging quality with a hybrid sampling interval of 15 us is comparable to the imaging results using Nyquist real-time sampling, whereas the azimuth imaging quality with a hybrid sampling interval of 28 us and 50 us deteriorates in the azimuth direction, especially for the 50 us interval. \begin{table}
\begin{tabular}{c c} \hline
**Description** & **Value** \\ \hline Relative speed & 1 km/s \\ Size of the antenna & 0.14 m (A) \(\times\) 0.14 m (R) \\ Equivalent PRF & 20 kHz \\ Pulse width of the transmitted signal & \(t_{\text{P}}\) = 2 us \\ Center frequency & 9.75 GHz \\ Bandwidth of the SAR signal & 3.5 GHz \\ \hline \end{tabular}
\end{table} 
Table 2: Simulated parameters of the proposed non-uniform hybrid sampling technology. \begin{table}
\begin{tabular}{c c} \hline \hline
**Description** & **Value** \\ \hline Real-time sampling rate of the high-speed ADC & 2.5 GSPS \\ The number of hybrid sampling for obtaining one entire echo & \(N=4\) \\ Equivalent-time sampling interval & \(t_{\rm int}=100\) ps \\ Qualification factor for the phase disturbance & \(Q=2/3,6/5,2\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 5: The SAR simulated results of single point target with different \(Q\) factors: (**a**) Nyquist real-time sampling; (**b**) \(Q=2\), \(t_{\rm hs}=15\) us; (**c**) \(Q=6/5\), \(t_{\rm hs}=28\) us; (**d**) \(Q=2/3\), \(t_{\rm hs}=50\) us. In addition, simulation is designed for point array targets with different qualification factors. Figure 6 shows the point array targets with an interval of 15 cm. The imaging results are demonstrated in Figure 7. Figure 7a is the imaging results using Nyquist real-time sampling, and Figure 7b-d are the imaging results using the proposed non-uniform hybrid sampling technology with 15 us, 28 us and 50 us intervals, respectively. Comparing Figure 7a,b, point targets can clearly be distinguished in both the range and azimuth direction.