*4.1. Imaging Quality*

According to the analysis of the TDFS-TS algorithm in Sections 2.2.2 and 2.2.4, the simplification in the range dimension leads to a distortion of the azimuth profile including the main lobe broadening and position offset (in the squint mode), and the residual RCM introduced by the simplification in the azimuth dimension affects both the range and the azimuth profile. In addition, the inherent limitations of jamming signal, namely the Doppler bandwidth loss of the fake scatter far away from the jammer in the azimuth dimension, will broaden the azimuth main lobe. In summary, we can draw the following conclusions on the TDFS-TS algorithm:


These phenomena can be seen clearly in Table 2: *P*<sup>0</sup> and *P*<sup>1</sup> are both at the azimuth center of the block, thus they have the same imaging quality parameters in the range dimension; the imaging quality parameters of *P*<sup>2</sup> and *P*<sup>3</sup> in the range dimension are the same, and worse than that of *P*<sup>0</sup> and *P*<sup>1</sup> because the two points are both in the azimuth edge of the block; the situation in the azimuth dimension is more complicated: affected by both the range and azimuth position, the four points have different degrees of azimuth distortion, where *P*<sup>3</sup> is the worse and *P*<sup>0</sup> is the best; the impact of residual RCM

in the azimuth dimension is greater than that of azimuth chirp rate error by comparing the imaging quality parameters of *P*<sup>1</sup> and *P*2.

From Table 2 it can be seen that, in the broadside mode, the main lobe positions of *P*<sup>2</sup> and *P*<sup>3</sup> in the range dimension are slightly shifted. This is caused by the residual RCM as well. Due to the existence of residual RCM, the curve of jamming signal after RCM correction in the range-Doppler domain is not a straight line but a parabola which is expressed as Equation (22), thus the main lobe in the range dimension will shift towards the negative direction besides broadening. In the squint mode, the effect of residual RCM is more complicated, which can be seen in Table 3. Due to the nonlinear nature of the RCM error shown in Equation (22), the offset in the range dimension expressed in Equation (34) is just an approximation. In fact, it can hardly be eliminated completely, thus the images of *P*1, *P*2, and *P*<sup>3</sup> shift to varying degrees in the range dimension. In addition, by comparing the range offset of *P*<sup>1</sup> and *P*2, we can consider that the range coordinate has a greater effect on the range offset in the squint mode. Although the TDFS-TS algorithm cannot correct the range offset accurately, the maximum residual offset shown in Table 3 is approximately equal to the range resolution, and has little impact on the deceptive image shown in Figures 11–13.

In the squint mode, the offset in the azimuth dimension caused by the frequency modulation rate error can be effectively corrected by the TDFS-TS algorithm; the results are shown in Table 3. As a comparison, the RDS algorithm divides the template in the range dimension as well, thus the problem of frequency modulation rate error still exists. Without a correction algorithm, the main lobe position of the RDS algorithm shift severely in the azimuth dimension and the image is distorted. In short, the imaging quality of the TDFS-TS algorithm can be guaranteed both in the broadside mode and in the squint mode with a small squint angle.

### *4.2. Computational E*ffi*ciency*

According to the results in Section 3.3, in the broadside mode, the TDFS-TS-WSC algorithm has a quite high computational efficiency, and the squint correction is time-consuming. This is because the range coordinate correction is related to the azimuth coordinate and the azimuth coordinate correction is also related to the range coordinate. Therefore, the range and azimuth coupling terms are added, resulting in a large number of calculations needing to be completed in the real-time calculation stage, and the computational efficiency becomes worse. However, due to the calculation of each block being completely independent in the TDFS-TS algorithm and the introduction of matrix operations, it is convenient to apply parallel computing technology to greatly increase the calculation speed. Therefore real-time jamming is feasible. In summary, compared with the RDS algorithm, the TDFS-TS algorithm is more efficient in the broadside mode, and the application scenario can be extended to the squint mode.

#### **5. Conclusions**

In this paper, the large-scene electromagnetic deception of SAR is studied. The primary focus is to reduce the computational burden during the jamming process. For this purpose, the TDFS algorithm is proposed, which can improve the computational efficiency significantly. In addition, the focus capability of the jamming signal must be considered. In order to ensure the deceptive image quality of the TDFS algorithm in a large scene, the template is divided into several blocks according to the SAR parameters and imaging quality control factor. The correction algorithm in squint mode is introduced so that the TDFS-TS algorithm can be used to the SAR with a low squint angle and medium aperture length. Finally, simulation results and computational complexity analyses show that, compared to other jamming algorithms, the TDFS-TS algorithm has higher computational efficiency with less image quality decline in the broadside mode. Furthermore, the application of parallel computation can partially compensate for the computational performance decline in the squint mode.

The TDFS-TS algorithm is applicable to space-borne SAR operating at broadside mode or a low squint angle mode. In the future, we will investigate the rapid jamming method against the SAR

with a significant squint angle and long synthetic aperture. Additionally, other problems such as intelligence gathering and gain control will also be studied.

**Author Contributions:** Conceptualization and supervision, W.Y.; formal analysis, F.M.; methodology, K.Y. and F.M.; experiment, G.L. and Q.T.; writing, K.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Science and Technology on Complex Electronic System Simulation Laboratory, grant number DXZF-JC-ZZ-2017-007.

**Conflicts of Interest:** The authors declare no conflict of interest.
