An Interrupted Sampling Scattered Wave Deception Jamming Method against Three-Channel SAR GMTI

An important problem is how to generate false moving targets, whose relocated azimuth position is similar to that of real moving targets. To solve this problem, an interrupted sampling scattered wave deception jamming method against three-channel synthetic aperture radar ground moving target indication (SAR GMTI) is proposed. A stationary jammer uses a controllable jammer antenna to generate verisimilar moving targets by controlling velocity and initial position of jammer beam footprint. The antenna sampled moves along the diﬀerent tracks. For each track, the slant history of jamming signal is changed varying with diﬀerent pulse recurrence intervals (PRI), and the movement of the footprint will introduce a Doppler frequency in jamming the signal. By analyzing parameters’ diﬀerence between echoes and jamming signal, the velocity and the initial position of the footprint will be calculated, and then the verisimilar false targets are generated. The eﬀectiveness of the method is veriﬁed by simulation experiments.


Introduction
Synthetic aperture radar ground moving target indication (SAR GMTI) is able to get high resolution images of sensitive areas and information of moving targets at all-time under all-weather condition [1][2][3][4]. Displaced phase center antenna (DPCA) and along track interferometry (ATI) are a type of three-channel SAR GMTI. DPCA technique can detect slow moving targets, and ATI technique can acquire velocity of moving targets. Furthermore, ATI technique can obtain the relocated azimuth position of targets which can be used to relocate the moving target to the correct positions and distinguish real moving targets and false targets [5][6][7][8].
Because of their ease of use, they are widely used in civilian and military field. So, an important research topic is how to effectively protect information of moving targets against DPCA and ATI techniques [9][10][11]. In addition, research on jamming and antijamming method will be on the improved radar system in the future [12,13]. e jamming methods are generally classified into barrage jamming methods and deception jamming methods. High noise-like jamming signal is retransmitted to cover the working band of SAR, and then a signal-tonoise ratio (SNR) is reduced in whole SAR images to prevent detecting targets from three-channel SAR GMTI. However, the barraged jamming method requires higher power than a deception jamming method to achieve a low signal-to-noise ratio (SNR) in SAR imaging results [14,15]. In addition, because the azimuth jammer filter is generated by utilizing DPCA technique, the false target will be cancelled near the jammer. So, an improved barraged jamming method, which uses two jammers, is used to cover the whole DPCA images [16]. However, the distance between the jammers is also required to control and set before the jamming area, and this reduces the flexibility of the method. According to the path of jamming signal, deception jamming includes direct-path deception jamming methods and multipath deception jamming methods. In direct-path jamming methods, the jammer generates false targets by intercepting, modulating, and retransmitting radar signal. However, because false targets are all generated by a stationary jammer, false targets near the jammer will be cancelled by DPCA technique and those all have the same relocated azimuth position by ATI technique [16][17][18][19][20][21].
is result is obviously different from the detecting result of moving targets, and false targets are easy to be recognized. To solve this disadvantage, deception jamming methods is proposed by utilizing multiple coherent jammers [9,22,23]. e phase difference of jamming signal in the different received antenna of the radar is controlled to adjust against the suppression of interferometric synthetic aperture radar (InSAR) and SAR GMTI. Every false target has the desired relocated azimuth position. However, because the phase is needed to be summed by every multiple jammers, it is difficult to control the additional phase terms in the received antenna. In addition, the distance between the jammers also need to control and set before SAR working. In other way, scattered wave jamming is a kind of multipath jamming method. e intercepted signal is scattered by scatterers of the ground to form jamming signal [10,[24][25][26]. In our previous work, a novel method is proposed to generate a verisimilar moving target by controlling a jammer velocity and a jammer beam footprint [27]. Although this method can effectively generate a verisimilar moving target after DPCA technique, there are some problems that we need to further address as follows. First, sometimes, it is difficult to control a moving jammer with the desired accurate speed, and the jammer speed always has a relatively large error compared with ideal speed. Second, after ATI technique, multiple false moving targets generated with this method cannot simulate the multiple moving targets with the desired relocated azimuth positions. Final, jamming effect against ATI technique is not analyzed.
An important problem is how to generate false moving targets, whose relocated azimuth positions are similar to the relocated azimuth position of real moving targets. So, an improved deception jamming method with a controllable jammer antenna is proposed to solve this problem. e improvement is that a stationary jammer with a controllable jammer antenna. e footprint moves in the calculated initial position and at a calculated velocity, and then the track is formed. e intercepted and retransmitted signal is scattered by the scattered points on the ground to form jamming signal. e jammer beam footprint intercepted sampling moves along the different tracks to generate multiple false moving targets. For each track, the slant history of jamming signal is changed varying with different pulse recurrence intervals (PRI), and the movement of the footprint will introduce a Doppler frequency in the retransmitted jamming signal. By analyzing parameter difference between the false target and the moving target, including position, Doppler rate, amplitude after DPCA technique, and the relocated azimuth position after ATI technique, the velocity and initial position of the footprint are calculated to determine the track, and then jamming signal forms a verisimilar false moving targets. e remainder of this paper is organized as follows. Section 2 introduces the geometry of the proposed method. e difference between echo of the moving target and the jamming signal are also compared. In Section 3, parameter difference between a real moving target and a false target is analyzed. In addition, the process of selecting the position and velocity of footprint is also summarized to eliminate the difference and generate verisimilar false moving targets. Section 4 gives experiment results of the proposed method compared with a traditional deception jamming method. In Section 5, conclusion is given.

Geometry of a Scattered Wave Deception Jamming Method Based on Controllable Jammer Antenna
As shown in Figure 1, radar flies along with X-axis, which is the azimuth direction. Its ideal velocity is v and its altitude is H. Y-axis is the ground range direction, and Z-axis is the altitude direction. e three antenna of radar are denoted by the A 1 , A 2 , and A 3 , and their coordinates are (vt a − D, 0, H), (vt a , 0, H), and (vt a + D, 0, H), respectively. t a is slow time and D is a distance among antenna. Radar transmits signal from antenna A 1 and antenna A 2 . A 3 receives echo. P is a moving target, and its coordinate is (x P + v x t a , y P + v y t a , 0). J is a stationary jammer, and its coordinate is (x J , y J , h). e intercepted signal is transmitted and amplified by J, and then it is illuminated to the area under the jammer beam. By controlling the jammer beam, the jammer beam footprint moves at a calculated velocity with a calculated initial position. I is the center of the footprint and its coordinate is (x I + v x ′ t a , y I + v y ′ t a , 0). e intercepted signal scattered by the scattered points covered by I to form the jamming signal. By adjusting parameters of the velocity and the initial position, jamming signal will be similar to echo, and then F will be similar to P.

Echoes.
e P's slant range of antenna A 1 and A 3 are, respectively, given by Equations (3)- (5) can be expanded as a Taylor series around t a at D/v, 0, and − (D/v), and then they are, respectively, given by 2 Mathematical Problems in Engineering Because DPCA and ATI techniques are used to detect the slow moving target, which means P is always slower than radar, v x ≪ v, v y ≪ v, and D ≪ R 2 can be hold. en, the slant range can be, respectively, given by Linear frequency modulation signal is used by the radar as follows: where t r is fast time, f 0 is center frequency, c is chirp rate, is pulse envelope, and T r is pulse duration. e baseband echo from P of antenna A 1 and A 3 are, respectively, expressed as follows: where λ is wavelength, σ P is radar cross section (RCS) of P, muth position of P, and T a is target exposure time. Figure 1: Geometry of the proposed method.

Jamming Signal.
To generate moving targets at the same time, the jammer beam interrupted sampling scans and illuminates the ground along the different tracks, as shown in Figure 2, which tracks are determined by the footprint parameters of the velocity and the initial position, and then the verisimilar false moving targets will be generated. For example, the jammer beam footprint interrupted sampling scans and illuminates along two tracks. As shown in Figure 3, PRI is pulse recurrence interval, τ � PRI is the slice width and the duration of illumination for each track, and T � N·PRI is the time interval between adjacent intercepted slice, where N presents the number of tracks. During T, the jammer beam can illuminate different tracks to form multiple targets.
In other words, the jamming signal is likely performed by interrupted sampling modulation, as shown in Figure 3 [28]. It can be given by where rect(·) is the rectangular window function. Slant ranges of jamming signal received by antennae A 1 and A 3 are, respectively, expressed as follows: Equations (11)-(17) can be expanded as a Taylor series around t a at 0, 0, D/v, 0, and − (D/v), and then they can be described as follows:

Mathematical Problems in Engineering
Considering 4 . en, the slant ranges for antennae A 1 and A 3 can be described as follows: e baseband jamming signal received by antennae A 1 and A 3 are, respectively, expressed as follows: where x F ′ is the azimuth position of F and σ I � G 1 G 2 σ I , where G 1 is a jammer amplified factor and σ I is an averaged RCS of the scattered point covered by I. Because amplitude of jamming signal is weakened by interrupted sampling modulation, G 2 � N is used to compensate amplitude. To generate F as P, results of jamming signal and echo should be same after SAR, DPCA, and ATI technique.

Analyze of Parameter Difference between Echo and Jamming Signal
e proposed method depends on controlling factors, including the footprint's velocity and initial position, to form the false target as the moving target. By analyzing parameter difference between the false target and the moving target, such as position, Doppler rate expression, amplitude after . Range position of F will be expressed as follows [24]: Similarity, P's range position will be expressed as follows: By adjusting I's initial range position, | (R F + cΔt j )/(2 − R P )| < P r should be satisfied, where P r is range resolution and Δt j is the delay of jammer. e jamming signal is not required to perform and store, and then the time delay within the jammer is too small to be noticed [9,24,29].

Azimuth Position. F's azimuth position is determined by
the Doppler frequency at t a � 0 [24]. It will be expressed as follows: Similarity, P's azimuth position will be given as follows: By controlling I's velocity, v x ′ and v y ′ , |x F ′ − x P ′ | < P a should be satisfied, where P a is azimuth resolution.

Doppler Rate Mismatch.
e second order term of slant ranges, which contains velocity of targets, will lead to defocusing in SAR images [24]. en, F's Doppler rate expression will be given as follows: Similarity, P's Doppler rate expression will be given as follows: By controlling I's velocity, v x ′ and v y ′ , K F /K P ≤ 0.9 should be satisfied.

DPCA Technique.
After SAR processing, F can be described as follows: where B a is the Doppler bandwidth.

Mathematical Problems in Engineering
Because the interrupted sampling jamming signal forms multiple targets, the main target, n � 0, is considered to simulate the moving target.
DPCA technique can detect slow moving targets by substracting the coregistered SAR images, which belong to A 1 and A 3 [9]. Flowchart of DPCA technique is shown in Figure 4 [30,31].
F's DPCA result is described as follows: Similarity, after SAR processing, P is described as follows: en, P's DPCA result is expressed as follows: Because the jammer is near the protected area, R 1 ≈ R 4 can be satisfied. Comparing (28) with (30), if the initial azimuth position of the footprint x I approximately equals that of moving target x P , F and P have an approximate amplitude after DPCA technique. |x I − x P | < P a should be satisfied.

ATI Technique.
ATI technique abstracts the interferometric phase information between two coregistered SAR images to resolve the relocated azimuth position of slow-moving targets [9]. Flowchart of ATI technique is shown in Figure 5 [30,32].
D, λ, and R 1 and the phase of the false target are known parameters for SAR GMTI, and x F ′ can be obtained from the SAR image. So, F's relocated azimuth position will be detected after ATI technique. F is described as follows: where * represents the complex conjugate. F's interferometric phase is given by where arg · { } represents the acquiring phase term operation. F's estimate azimuth position will be relocated to Similarly, P is described as follows: P's interferometric phase is given by P's the relocated azimuth position will be estimated by Based on the above analysis, if initial azimuth position of the footprint x I approximately equals that of moving target x P , F and P have an approximate relocated azimuth position after ATI technique.

Realization.
e steps of generating a verisimilar false moving target will be represented as follows. First, I's initial azimuth position, x I , should be adjusted to be equal to that of P. Second, by controlling I's initial position in the ground range direction, y I , F's range position is similar to that of P in images.
ird, by controlling I's velocity, v x ′ and v y ′ , F's Doppler rate mismatch and the azimuth position will be similar to those of P, K F ≈ K P and x F ′ ≈ x P ′ . Henceforth, according to the calculated initial position and velocity of jamming beam footprint, the track will be decided. Fifth, according to the azimuth velocity and number of false targets, which intend to generate, the time interval T between the adjacent jamming footprints is calculated. e beam interrupted sampling illuminates the ground along the track. en, F has the same amplitude and the relocated azimuth position as P.

Simulation
Parameters of radar are listed in Table 1.

A False Moving Target Simulation.
In this section, we examine that a false target generated with the proposed method can be imaged as a moving target, and detected results of the simulated moving target are provided for contrast analysis. e moving target's initial position is (10 m, 10,050 m, 0 m), and its velocity are v x � 0.5 m/s and v y � 0.5 m/s. A jammer is the assumed set at (0 m, 10,000 m, 10 m). e jammer beam footprint's initial position is (10 m, 10,044.3 m, 0 m) and its velocity are v x ′ � 1.1 m/s and v y ′ � 0.2 m/s. e SAR imaging results of the real target and the false target are shown in Figure 6, and their azimuth sectional plots are shown in Figure 7. ey are well focused and imaged in the SAR image, and they are almost the same, which verifies the effectiveness of the proposed method. In addition, the errors, which contain position error, the impulse response width (IRW) error and the peak side lobe ratio (PSLR) error, are listed in Table 2 [29]. e positions of the real target and false target are the same. e error of IRW is too small to be recognized by the radar. PSLR of false target is slightly better than that of the moving target, which contributes to mislead radar decision. So, the proposed method has the ability to generate a verisimilar false target against SAR. e DPCA results are shown in Figure 8, and their azimuth sectional plots are shown in Figure 9. Targets are well focused and imaged in the DPCA image, which verifies the effectiveness of the proposed method. e quality results are listed in Table 3.
Imaging quality parameters of the moving target is similar to those of the false target. So, the proposed method has ability to generate a false target against DPCA technique.
Next, Figure 10 shows interferograms of targets utilizing ATI technique. en, the relocated azimuth position can be estimated.
After ATI technique, their relocated azimuth positions are detected and are listed in Table 4. e relocated azimuth position error between the false target and the moving target is too small to be noticed. So, the proposed method has the ability to generate a false target which is similar to a moving target against ATI technique. Figure 4: Flowchart of DPCA technique.   [9,21], which is a traditional deception jamming based on signal jammer and is able to generate multiple false targets. Two moving targets are simulated by utilizing the traditional method and the proposed method to generate two false moving targets. eir initial azimuth positions are 30 m and 40 m. e DPCA results are shown in Figure 11. Figure 12 shows interferograms of false targets detected by ATI technique. en, the velocity in ground direction and the relocated azimuth position will be detected.
Although DPCA results are the same in Figure 11, the interferograms are different in Figure 12. e false targets, which are generated with the traditional deception jamming method, all have the similar relocated azimuth position, as shown in Table 5, which is difficult to simulate moving targets and misleads the decision-making of the radar. However, false targets generated with the proposed method         have the different relocated azimuth positions, which are similar to the initial azimuth positions of the moving targets. So, the proposed method is able to generate multiple false moving targets.

Conclusions
An important problem is how to generate false targets with the same initial azimuth positions as those of moving targets. To solve this problem, a scattered wave deception jamming method with a controllable jammer antenna is proposed. e improvement is that a stationary jammer is set affront of the protected area with a controllable antenna to generate very similar moving targets by controlling jammer beam footprint's velocity and initial position. e footprint moves along the different calculated tracks. For each track, slant ranges of the jamming signal are changed varying with different PRI, and the movement of the jammer antenna beam would introduce a Doppler component. By analyzing parameter difference between the false target and the moving target, the velocity and initial position of the footprint are calculated, and then the track will be determined. In addition, during the time interval between adjacent intercepted slice, the jammer beam can be controlled to illuminated different tracks, and then targets are generated. Simulation experiments use the jamming quality parameters, which contain position information, IRW, PSLR, and the relocated azimuth position, to evaluate jamming effect. e effectiveness of the method is verified by experiment results.

Data Availability
No data were used to support this study because all experiments were simulated based on equations of the proposed method.

Conflicts of Interest
e authors declare that they have no conflicts of interest.