*2.3. TDFS-TS Algorithm Procedure*

The prerequisite for the successful implementation of SAR deceptive jamming is to obtain relevant intelligence on the jamming object, which mainly includes the follows aspects.


The specific detection methods of the parameters above will not be discussed in this paper; we simply suppose that the parameters have been obtained in advance.

As shown in Figure 4, the entire procedure includes two parts: preprocessing and real-time calculation. The first step in the preprocessing stage is template segmentation: according to the parameters including synthetic aperture length *L*, signal bandwidth *B*, shortest slant range of the jammer *RJ*<sup>0</sup> and the given factors ε and η, we divide the template into several blocks based on the limitation of Equation (28); then, we perform offline calculation and calculate the time-delay matrixes **Hr**<sup>1</sup> and **Hr**<sup>2</sup> according to Equations (38) and (39). In the real-time calculation stage, we calculate frequency-shift matrixes **Ha***q*1, **Ha***q*<sup>2</sup> according to Equations (40) and (41); then, we calculate the JSF on each block based on Equations (30) and (42); finally, we add the JSF on all blocks to obtain the JSF on the entire scene.

**Figure 4.** Time-delay and frequency-shift with template segmentation (TDFS-TS) algorithm procedure.

### **3. Simulation Results**

In this section, the effectiveness of the TDFS-TS algorithm is verified by simulating the imaging results of false point targets and fake scenes, and the computational complexity is analyzed. The simulation results of the range dimension segmentation (RDS) algorithm proposed by Zhou et al. [11] are used as a comparison. The main parameters of the radar, which reference the satellite RADARSAT-1, are listed in Table 1.

#### *3.1. Fake Point Scatters Case*

In order to analyze the imaging result of fake point scatter at different positions after imaging, a deceptive scene template containing only four-point scatters is set as shown in Figure 5. The four points *P*<sup>0</sup> ∼ *P*<sup>3</sup> are arranged in a rectangular shape with a distance of 6 km in the range dimension and 2 km in the azimuth dimension. According to the calculation results in Section 2.2.2, we set the length of blocks to 2.5 km in the range dimension and 1.5 km in the azimuth dimension. Since the imaging quality of fake scatters is only related to the position in the block, for the purpose of analyzing the jamming effect of the algorithm comprehensively, the template segmentation scheme is shown by the dashed line in Figure 5, meaning that *P*<sup>0</sup> is located at the center of block 1, *P*<sup>1</sup> is at the edge of block 3 in the range dimension, *P*<sup>2</sup> is at the azimuth edge of block 4, and *P*<sup>3</sup> is at the edge of block 6 in both range and azimuth dimensions. In addition, the position of the jammer (i.e., the origin position) is set at the point *P*0; actually, the position of the jammer has little effect on the imaging result. In the simulation of the RDS algorithm, the template is divided into three segments with the same segmentation length (2.5 km) in the range dimension and is no longer segmented in the azimuth dimension.

**Figure 5.** The deceptive scene containing four-point scatters.

Figures 6–9 show the imaging results of the four scatters by the RDS and TDFS-TS algorithm in the broadside mode and squint mode with the squint angle θ = 5 ◦ , including the close-up image, range profile, and azimuth profile. Tables 2 and 3 list the imaging quality parameters of range and azimuth dimensions in the two modes, including 3 dB impulse response width (IRW), main lobe position offset (MLPO), peak sidelobe ratio (PSLR), and integrated sidelobe ratio (ISLR). It can be seen that, compared with the RDS algorithm, the performance of the TDFS-TS algorithm is basically equivalent, the RDS algorithm is more advantageous on IRW, while TDFS-TS is dominant over MLPO. The IRW of TDFS-TS algorithm is increased especially for the azimuth dimension in squint mode; however, the maximum broadening does not exceed 3.6%. In the squint mode, the MLPO of the RDS algorithm can reach up to −80.32 m in the azimuth dimension, which can be eliminated basically by the TDFS-TS algorithm due to the corresponding correction. Because of the influence of the residual RCM, the MLPO in the range dimension cannot be completely corrected, but the overall image is affected very little. In short, the simulation of fake point scatters shows that the TDFS-TS algorithm is effective and has certain advantages in several areas.

**Figure 6.** Simulation results of the RDS algorithm for false point scatters in broadside mode. (**a**–**c**) are the close-up image, range profile, and azimuth profile of *P*0, respectively; (d–f) are the close-up image, range profile, and azimuth profile of *P*<sup>1</sup> respectively; (g–i) are the close-up image, range profile, and azimuth profile of *P*2, respectively; (j–l) are the close-up image, range profile, and azimuth profile of *P*3, respectively.

**Figure 7.** Simulation results of the TDFS-TS algorithm for false point scatters in broadside mode. (**a**–**c**) are the close-up image, range profile, and azimuth profile of *P*0, respectively; (d–f) are the close-up image, range profile, and azimuth profile of *P*1, respectively; (g–i) are the close-up image, range profile, and azimuth profile of *P*2, respectively; (j–l) are the close-up image, range profile, and azimuth profile of *P*3, respectively.

**Figure 8.** Simulation results of the RDS algorithm for false point scatters in squint mode with a squint angle θ = 5 ◦ . (a–c) are the close-up image, range profile, and azimuth profile of *P*0, respectively; (d–f) are the close-up image, range profile, and azimuth profile of *P*1, respectively; (g–i) are the close-up image, range profile, and azimuth profile of *P*2, respectively; (j–l) are the close-up image, range profile, and azimuth profile of *P*3, respectively.

**Figure 9.** Simulation results of the TDFS-TS algorithm for false point scatters in squint mode with a squint angle θ = 5 ◦ . (a–c) are the close-up image, range profile, and azimuth profile of *P*0, respectively; (d–f) are the close-up image, range profile, and azimuth profile of *P*1, respectively; (g–i) are the close-up image, range profile, and azimuth profile of *P*2, respectively; (j–l) are the close-up image, range profile, and azimuth profile of *P*3, respectively.


**Table 2.** Comparison of imaging quality parameters between the RDS algorithm and TDFS-TS algorithm in broadside mode.

**Table 3.** Comparison of imaging quality parameters between the range dimension segmentation (RDS) algorithm and TDFS-TS algorithm in squint mode with squint angle θ = 5 ◦ .

