## 5 Simulation Results and Analysis
### Spectrum Reconstruction Results  
The result of the azimuth spectrum reconstruction is shown in Figure 9. From Figure 9a, the under-sampled azimuth echo signal will result in serious spectrum ambiguity without the azimuth multichannel spectrum reconstruction processing. Then, pairs of ghost objects occur on both sides of the targets after the azimuth pulse compression, which seriously affects the imaging quality of the targets.  
The proposed spectrum reconstruction algorithm is used to restore the uniform azimuth signal. The azimuth pulse response of the reconstructed result is shown in Figure 9b. It can be observed that the ambiguous energy from pairs of ghost objects is effectively suppressed, and the normalized amplitude is close to \(-65\) dB relative to the true point targets. Meanwhile, the azimuth response of single channel sampling with a high PRF is compared with the equivalent single channel sampling with  
Figure 8: Point targets distribution for SAR imaging simulation.  
Figure 9: The azimuth response of DPCAM SAR for hypersonic platform: (**a**) without spectrum reconstruction; (**b**) with spectrum reconstruction.  
a low PRF after the spectrum reconstruction, where the target signal is well retained, and the sidelobe signal of the false targets is effectively suppressed for the equivalent single channel SAR system.  
### Spectrum Reconstruction Results  
Combining the SAR system parameters setting and the locations of targets in the imaging scene, the ETF imaging algorithm is further studied. The imaging results of multi-point targets are shown in Figure 10.  
As shown in Figure 10, the integrate SAR image is obtained after the ETF image processing for each sub-swath and the subsequent images mosaic processing. Meanwhile, the multi-point targets located in a wide swath are well focused. Here, consider that the point targets located at the center of the imaging scene can be precisely focused, thus the imaging results of the point targets near swath edge are further analyzed. As shown in Figure 11, the range and the azimuth response of the point targets \(T_{1}\) and \(T_{15}\) are given in detail, respectively.  
Moreover, as shown in Table 2, the performance parameters such as the impulse response width (IRW), peak sidelobe ratio (PSLR) and the integrated sidelobe ratio (ISLR) are calculated to estimate the imaging quality of the multi-point targets, which represents the different locations in the SAR scene. Meanwhile, according to Equation (7) and the parameter of the signal bandwidth listed in Table 1, the ideal IRWs of the hypersonic platform SAR are 0.886 m in range and 0.66494 m in azimuth, respectively.  
As shown in Table 2, when the ETF imaging algorithm is utilized to process the SAR echo signal of the hypersonic platform with curved trajectory, the imaging quality of the point targets is close to the theoretical value in range. Meanwhile, the point targets approaching the scene center derive a high imaging performance, while the corresponding quality of the point targets near swath edge is slightly lower, but it can basically meet the requirement of azimuth resolution.  
Figure 10: Point targets imaging results for hypersonic platform SAR.