## 2 Design of the Space-Borne X-Band SAR System  
The imaging scene of the proposed space-borne high-resolution SAR system for space target in this paper is shown in Figure 1. The best imaging scene of the SAR satellite platform for space target is that the low-orbit SAR satellite platform flies in the same direction as the space target, or flies in the direction of a cross-angle (\(\beta_{\text{st}}\)), and \(|\beta_{\text{st}}|\) generally less than 30\({}^{\circ}\). When the satellite and the space target fly in opposite directions, the relative velocity in the azimuth direction is as high as 15 km/s [1]. The SAR Doppler bandwidth (\(B_{\text{dop}}\)) is calculated by the following formula:  
\[B_{\text{dop}}=2V_{\text{st}}/D_{\text{A}} \tag{1}\]  
where \(V_{\text{st}}\) and \(D_{\text{A}}\) are the relative velocity and the actual aperture of SAR antenna in the azimuth direction, respectively. Thus, the doppler bandwidth is about 60 KHz for a SAR antenna with 0.5 m aperture. The pulse repeated frequency (PRF) of SAR system is 84 KHz according to the requirement of 1.4 times oversampling rate. The pulse width of the SAR signal is less than 10 us, which limits the average power of SAR system, resulting in poor imaging performance of long-distance space targets. When the absolute value of \(\beta_{\text{st}}\) is less than 30\({}^{\circ}\), the relative velocity in the azimuth direction is generally less than 2 km/s so the doppler bandwidth is less than 8 KHz, and the PRF of SAR system is less than 12 KHz. The requirement of PRF can provide sufficient time resource for the transmission of SAR system with high average power and the non-uniform hybrid sampling of wideband echoes. The parameters of SAR systems are determined by bandwidth, PRF and imaging distance. In order to identify and classify space targets, the bandwidth of SAR signals is set to 3.5 GHz, the center frequency is set to 9.75 GHz, and the imaging resolution should reach centimeter level. According to the sampling rate requirement, the PRF should be greater than 1.4 times the doppler bandwidth. Finally, the imaging distance is from 30 km to 50 km. The block diagram of the hardware structure is illustrated in Figure 2. The antenna of X-band SAR, signal generator of X-band SAR, circulator (transmit/receive switch), radio frequency receiver, clock generator and distributor, main control system are included. The SAR antenna is used to transmit and receive wideband SAR signals, the polarization is VV polarized, the working frequency is from 8 GHz to 11.5 GHz, and the center frequency is 9.75 GHz. The wideband chirp signals are generated by signal generator and transmitted when the rising edge of the trigger pulse arrives. The peak power of transmitted chirp  
Figure 1: Imaging scene of space-borne SAR for space target. SAR signal is 0 dBm, the peak power of SAR signal is amplified to 40 dBm after the power amplifier. The radio frequency receiver is designed for primary amplification, mixing, band-pass filtering, secondary amplification of the echoes. The primary amplification gain is 20 dB to 40 dB, and the gain can be controlled by the main control system. The gain of secondary amplification is 40 dB. The local frequency of the mixer is 7.5 GHz. The output frequency after mixer is from 0.5 GHz to 4.0 GHz, and the center frequency is 2.25 GHz. The entire gain of radio frequency receiver is from 50 dB to 70 dB. The clock generator and distributor provide 7.5 GHz local oscillator frequency, 2.5 GHz ADC sampling clock, and FPGA working master clock for X-band SAR signal generator, radio frequency receiver, main control system, respectively. The main control system is used to control the parameters of the signal generator, the triggering time of launch and the gain of the radio frequency receiver. Meanwhile, it is used to control the receiving timing of the non-uniform hybrid sampler and the delay amount of the programmable delay line. It is also used to process and save the sampling echoes.