A Multiple-Jammer Deceptive Jamming Method Based on Particle Swarm Optimization against Three-channel SAR GMTI

Traditional deceptive jamming methods effectively generate false targets against three-channel synthetic aperture radar ground moving target indication (SAR GMTI). However, effectiveness of traditional methods is limited to azimuth distance between two jammers. When the distance requirement is not satisfied, the jamming amplitude coefficients will be too high to be used by jammers. To overcome this disadvantage, a novel multiple-jammer deceptive jamming method is proposed. The intercepted radar signal is retransmitted and performed by amplitude and time-delay modulation. Then, jamming signal is first modeled as a polynomial function where the polynomial order is equal to the number of jammers. The interferometric phase difference between a moving target and a false target is utilized as an objective function, the azimuth relocated position difference between a moving target and a false target is utilized as the constraint to reduce computational burden, and the optimal jamming amplitude coefficients are estimated by solving the optimization problem based on the particle swarm optimization (PSO). Hereby, the optimal jamming amplitude coefficients and gain calculated with the proposed method will be lower than those calculated with traditional methods when the distance requirement is not satisfied. By utilizing the optimal coefficients and jamming amplitude gain, a false target generated with the proposed method will be detected by displaced phase center antenna (DPCA) technique and be relocated in the desired position by along-track interferometry (ATI) technique. Experimental results verify the effectiveness of the proposed method.


I. INTRODUCTION
Synthetic aperture radar ground moving target indication (SAR GMTI) has been widely utilized in both civil and military applications ranged from a city traffic monitoring to an airport surface surveillance and a battleground surveillance [1][2][3][4][5]. SAR GMTI is able to detect information of moving targets from sensitive areas. Displaced phase center antenna (DPCA) technique and along-track interferometry (ATI) technique are two important techniques of three-channel SAR GMTI. DPCA technique detects slow moving targets from strong clutter by subtracting two coregistered SAR images, and ATI technique estimates initial azimuth positions of moving targets by exploiting interferometric phase between two coregistered SAR images [6][7][8][9]. To prevent moving targets from being detected and relocated by DPCA technique and ATI technique, research on jamming methods against SAR GMTI has been an important subject in electronic countermeasure (ECM).
In general, jamming methods are classified as barrage noise jamming methods and deceptive jamming methods [10]. However, to be against DPCA technique and ATI technique, jamming methods are classified into multiplejammer jamming methods and single-jammer jamming methods according to the number of jammers.
Single-jammer jamming methods are proposed to enlarge jamming area, reduce computational burden, enhance focus capability, fortify electromagnetic fidelity and raise correlation coefficient [11][12][13][14][15][16][17][18]. These goals may conflict. For example, a deceptive jamming method with high electromagnetic fidelity may require too many modulations, and radar parameters are obtained by jammers with high accuracy which increases computational burden. Tradeoffs between fidelity and computational burden, between jamming area and focus capability, and so on, are issues in ECM.
However, single-jammer jamming methods are difficult to prevent DPCA technique and ATI technique from detecting and relocating ground moving targets. There are two obvious disadvantages. First, with DPCA technique, an azimuth jamming filter is generated based on the additional phase terms of jamming signal in different channels, and then jamming effect will be suppressed by the filter [19]. Second, all false targets will have the same azimuth relocated position which cannot be controlled with single-jammer jamming methods. Then they will be recognized and cannot mislead radar decision-making [20]. The jamming effectiveness will be significantly reduced. To address these weaknesses, the single jammer is set on an unmanned aerial vehicle (UAV). By controlling velocity of jammer and the position of jammer beam 'footprint' which is a area illuminated by the jammer beam, the intercepted radar signal scattered by scatterers performs jamming signal which is the same as the echo of the real moving target. However, jammer power is limited to the scattering coefficient of scatterers [21].
To overcome these disadvantages, multiple-jammer jamming methods are proposed. The barrage noise jamming method based on double jammers is an effective jamming method [19]. Noise covers the whole detection result with DPCA technique, and then the protected target cannot be relocated with ATI technique. Because the noise-like signal cannot obtain SAR processing gain, this method requires high transmitting power. To reduce jamming power, jamming signal should be coherent in range and azimuth to obtain the SAR processing gain, and then the multiplejammer deceptive jamming methods are proposed to control initial azimuth positions of false targets. By setting jamming complex coefficient for every jammer, the intercepted radar signal is performed by the phase modulation and the timedelay modulation to generate jamming signal, which is similar to the echo of a moving target in every channel. Then, the detection results of a false target will be equal to those of a real moving target with DPCA technique and ATI technique, including the range position, the azimuth position, the impulse response width (IRW), the peak sidelobe ratio (PSLR) and correlation coefficient.
An important problem faced by jammers is how to solve jamming complex coefficients. Considering the complex jamming coefficients can be separated into the jamming amplitude coefficients and the jamming phase coefficients, the method proposed by Zhang et al. turns the two-dimension search problem into two simple one-dimension search problems [22,23]. However, the method need to analyze the monotonicity of the interferometric phase expression varying with amplitude coefficients and the jamming phase coefficients. It makes the processing of solution too complex and trivial. Sun et al. directly makes the sum of the intercepted and modulated signal equal to that of the echo of the real moving target in every channel. Hence, the jamming complex coefficients will be solved by a matrix solution [24]. Chang et al. proves that the jamming amplitude coefficients can precisely control azimuth relocated positions of false targets without the jamming phase coefficients, which can reduce the computational complexity. The jamming amplitude coefficients can be directly obtained by solving a quadratic equation with one unknown [25]. Although traditional methods are able to solve jamming coefficients, there is a disadvantage in these methods. The jamming coefficients are solved as a unique solution, and the distance between jammers must be satisfied. When the distance required by traditional methods is not satisfied, the jamming amplitude coefficients could be too high to be used by jammers. Thus, an important problem faced by jammers are that the limitation of the azimuth distance between jammers should be removed, which will lead to reduce the jamming amplitude coefficients.
To overcome this disadvantage, a multiple-jammer deceptive jamming method based on particle swarm optimization (PSO) is proposed against three-channel SAR GMTI. Compared with previous works, the contribution of this paper is that a novel jamming problem modeling idea is proposed based on an optimization problem. By establishing a jamming geometry, the interferometric phase difference between a moving target and a false target is utilized as an objective function, the azimuth relocated position difference between a moving target and a false target is utilized as the constraint to reduce computational burden, and the optimal jamming amplitude coefficients are estimated by solving the optimization problem based on the particle swarm optimization (PSO). After multiple episodes which satisfy decision-making time, coefficients are grouped into the candidate coefficients set. Then the optimal coefficients, which are the lowest coefficients, will be chosen from the candidate coefficients set.
The reminder of this paper is organized as follows. Section II introduces a jamming geometry of the multiple-jammer deceptive jamming method against three-channel SAR GMTI. The detection result of a moving target is derived. Moreover, a multiple-jammer deceptive jamming method is presented. In addition, an important problem about how to solve jamming complex coefficients is analyzed, and a multiple-jammer deceptive jamming method is proposed based on PSO in Section III. The experimental results are given in Section IV. Finally, conclusions are drawn in Section V.

II. A MULTIPILE-JAMMER DECEPTIVE JAMMING METHOD AGAINST THREE-CHANNEL SAR GMTI
In this section, a jamming geometry of a multiple-jammer deceptive jamming method is first presented. Then, the deceptive jamming method is described in detail by analyzing the detection results of DPCA technique and ATI technique.

A. JAMMING GEOMETRY OF A MULTIPLE-JAMMER DECEPTIVE JAMMING METHOD AGAINST THREE-CHANNEL SAR GMTI
Because radar is a non-cooperative objective, it is hard to obtain the accurate 2-D impulse response of a moving target. Therefore, a jamming geometry is established, and then the algorithm process and the technique used by radar are analyzed based on intelligence support [26]. In addition, with the help of the real-time parameter measurement, the 2-D impulse response of a moving target could be estimated [16,24]. If the jamming geometry is similar to the real jamming geometry, the verisimilar 2-D impulse response of a moving target will be obtained.
As shown in Fig. 1, a radar works at the board-side mode. It flies at a constant velocity v along with X-axis. X-axis represents the azimuth direction at altitude H, Y-axis represents the ground range direction, and Z-axis represents altitude direction. The three antenna are denoted by the points A1, A2, and A3. Their coordinates are ( Especially, jammers can only rely on intelligence support to acquire distance D [26]. The signal is transmitted from antenna A2, and then echo is received by antenna A1 and A3. A moving target is denoted by the point M, and its coordinate is (  y ma y v t , 0). Assume that the number of stationary jammers is N. The nth jammer is denoted by the point n J and its coordinate is ( n x , n y , n h ), where n is an integer and it serves as the index for each jammer. They modulate the intercepted signal to generate a verisimilar false moving target F, which is similar to the moving target M in the detection result with DPCA technique and ATI technique.

B. THE DETECTION RESULT OF THE MOVING TARGET
The linear frequency modulation (LFM) signal used by the radar can be expressed as follows: where r t is the fast time, 0 f is the radar center frequency, γ is the chirp rate, tT is the pulse envelope of the signal, and r T is the pulse duration. A symbol like Rt is defined as the distance between M and A1 varying with a t . It is used to explain the different paths. The slant range of moving target M varying with a t for antenna A1, A1 and A3 are respectively expressed as follows: In SAR images, the azimuth position of the moving target M is determined by the Doppler frequency at 0  a t [12]. Then, the azimuth position of the moving target M is described as follows: The baseband echo from a moving target M to antenna A1 and A3 are respectively expressed as follows: This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2021.3118899, IEEE Access VOLUME XX, 2017 9 where  is the wavelength of the LFM signal,  M is the scattering coefficient of the moving target M, is the azimuth envelope, and a T is the target exposure time.
After SAR processing, the SAR images of antenna A1 and A3 are expressed as follows: is bandwidth of LFM.
Based on the DPCA technique, the difference between the two adjacent coregistered SAR images will be expressed as follows [6,20] Based on the ATI technique, the interferometric phase of the moving target M will be described as follows [6,20] (8) and (15), the moving target M will be relocated as follows: Then the detection processing of radar is presented in detail, and the key idea of the proposed method is to simulate detection result of the moving target M by jammers.

C. THE MULTIPLE-JAMMER DECEPTIVE JAMMING METHOD
The slant range of the nth jammer varying with a t for antenna A1, A2 and A3 are respectively expressed as follows:  This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.  (24) where G is jamming amplitude gain,  denotes the convolution operation, and  n is the jamming amplitude coefficients.
Then, after SAR imaging processing, the SAR images of false target F obtained based on (11) and (12) can be shown as follows: In order to generate a verisimilar false moving target, based on the DPCA technique, the detection result of the false moving target F should be equal to that of the moving target M by controlling variables G and  n . It will be illustrated as follows: Because the detection result and the inteferometric phase of the false moving target F are equal to those of the moving target M, jammers will generate the verisimilar false moving target F that will be detected with DPCA technique and relocated in the desired positions with ATI technique.
Therefore, how to solve jamming amplitude coefficients n  and jamming amplitude gain G becomes an important issue in this paper.

III. A MULTIPLE-JAMMER DECEPTIVE JAMMING METHOD BASED ON PARTICLE SWARM OPTIMIZATION
The proposed method contains three main parts. First, a novel jamming problem modeling idea is proposed based on an optimization problem. Second, the candidate variables  n is calculated by PSO, and the best coefficients are selected from the candidate coefficients set based on the amplitude evaluation indicator. Finally, the implementation flowchart is presented.

A. JAMMING OPTIMIZATION PROBLEM PRUDUCTION
The detection result of the false target F generated by multiple jammers consists of high order terms according to (26) and (27). It is reasonable to model the jamming result based on a polynomial function, where the jamming amplitude coefficients n  represents the polynomial coefficients. Hence the jamming problem can be solved via estimating the polynomial coefficients  n . The number of the jammers N is equal to the polynomial order, and the estimated polynomial coefficient vector can be reformed as Then, (26) and (27) can be respectively changed as follows: where  ˆ=   N F M f Ρ is a particle fitness.

B. PSO-BASED POLYNOMIAL COEFFICIENTS SOLUTION METHOD
Compared with conventional optimization techniques like GAs and quasi-Newton algorithm, PSO is more of simplicity and robustness [27,28]. Hence, a PSO-based global optimization method is used in this section. The estimated polynomial coefficient vector ˆN Ρ can be denoted by the particles. The procedure of PSO is presented in [29]. The update equations of each particle's position and velocity are described as follows: is the best solution that the nth particle has been found after 1 l  iterations, is the best solution that the whole swarm has been found.  is the inertia weight coefficient. According to (36), the smaller the cost function is, the better the corresponding particle is.
However, the smaller the cost function is, the more the computational burden is. Thus, the threshold of   N f Ρ is accepted as follows [19]: where a P is the azimuth resolution of the SAR images. Its advantage is that time used to obtain the candidate coefficient vectors is decreased. Moreover, the more times PSO is used, the more coefficient vectors can be acquired. Then, the lowest jamming amplitude coefficient vector can be selected from the candidate coefficient vectors sets.
The amplitude gain G makes the false target similar to the moving target in the detection result with DPCA technique.
G is related with ˆN Ρ . According to (30), (32) and (33), G is expressed as follows: Assume that the number of episodes is E which is related to the jamming decision-making time. Thus, during the process, there will be a sequence of the candidate variables where e is the index of episode.

C. IMPLEMENTATION FLOWCHAR
An implementation flowchart of the proposed method is summarized as shown in Fig. 2.
Jamming global optimization problem production Jammer 1 Jammer 2 The process of the proposed method has the following three steps: First, based on the jamming geometry, DPCA technique and ATI technique, an optimization problem is established by making interferometric phase of a moving target M and that of a false target F equal.
Second, the PSO-based method is implemented in loop to estimate the candidate amplitude gain the false target will be detected in the desired azimuth position based on DPCA and ATI technique.

IV. EXPERIMENT RESULTS AND ANALYSIS
In this section, compared with the effect of the traditional method in [24], several simulated experiments are designed to verify the effectiveness of the proposed method. The azimuth and ground range length of the illuminated area are 200 m and 100 m, respectively. The Signal Noise Ratio (SNR) is assumed as 13.2 dB where detection probability is 0.9 and false-alarm probability is 6 10  [30]. The simulation parameters are shown in TABLE I.

A. A POINT TARGET SIMULATION
The real moving target is set in the illuminated area for contrast analysis. Its coordinate is (20020, 20, 0) with the azimuth velocity x v = 0.2 m/s and the range velocity y v = 0.15 m/s. Assume that four jammers, N=4, are used to generate the verisimilar false moving target, which is the same as the real moving target. The coordinates of four jammers 1 J , 2 J , 3 J , and 4 J are listed in TABLE II. In addition, after 30 episodes with 100 iterations in each episode, the jamming amplitude coefficients and amplitude gain are also listed.  The SAR imaging results of the real moving target and false moving target are shown in Fig.3 and both of them are well imaged and focused in the SAR images. To evaluate the jamming effect, the correlation coefficient, which is the detailed jamming performance evaluation indicator, is calculated in this paper [14]. The correlation coefficient of the jamming results is 0.9999 which is approximately equal to 1, that is to say, the false moving target are nearly the same as the real moving target.
Especially, the proposed method aims at generating moving targets against prescreening and detection before being focused and recognized. Thus, the defocused target is directly detected by suppressing the stationary target, and the detected targets will be further focused by estimating moving target parameters. If the false target is similar to the moving target, the computational burden of radar will be raised and making-decision will be misled. Focusing is not concerned in this paper, so the simulated targets are not very well focused. In addition, the defocused target will not cause difficulties in evaluating the effectiveness of the proposed method. The jamming signal and echo are processed as the same detection result by the same SAR processing, DPCA technique and ATI technique. That is to say, the proposed method will generate the same detection result, even the moving target is defocused. The corresponding azimuth sectional plots are presented in Fig. 4 for contrast analysis.  As seen from the figure, the real moving target and the false moving target are almost similar to each other. Detailed jamming evaluating indicators, including the range position, the azimuth position, the impulse response width (IRW), and the peak sidelobe ratio (PSLR) are calculated in  As shown in TABLE III, the range position, the azimuth position and IRW are the same. Errors are obviously small, that is to say, the imaging result of the false target obtained has almost the same quality as that of the real target. So the proposed method is able to generate a false moving target with high fidelity against SAR.
After DPCA technique, the detection results are shown in Fig. 5. As seen in the figure, contour plots of the real moving targets and that of the false moving target look the same, and the correlation coefficient of the jamming results is 0.9987, which means the detection results of the false target are the same as those of the real moving target. For further comparison analysis, the azimuth sectional plots are presented in Fig. 6. In addition, the corresponding evaluating indicators are listed in TABLE IV.   As presented in TABLE IV, the range position and the azimuth position are the same. The IRWs and PSLRs of the real targets and the false targets are also almost the same with only several hundredths of a decibel difference. Therefore, the proposed method is able to generate false moving target with high fidelity in the detection results based on DPCA technology.
When the moving target is detected, its moving parameters, interferophase, initial azimuth position, and the ground range velocity, are also estimated based on ATI technology. Radar will use the initial azimuth position to relocate the targets. The estimations of target velocity and initial azimuth position are listed in TABLE V. The interferophase of the real targets and the false targets are also nearly the same with only several hundredths of a decibel difference. Then, the low error interferophase will lead to the low error of initial azimuth position, which is obviously small. In addition, the velocities of the real moving targets and the false moving targets are the same.
In other words, SAR imaging result, the detection result and moving parameters of the false moving targets obtained can have almost the same quality as those of the real moving target. Therefore, the proposed method is able to generate false targets based on ATI technology.

B. COMPARING THE PROPOSED METHOD AND THE TRADITIONAL METHOD
Assume that two jammers, 1 J and 4 J , are used by the traditional method in [24] to generate a verisimilar false moving target which simulates a real moving target. In addition, two jammers, 2 J and 3 J , are added with the proposed method to generate a false moving target which simulates the same real moving target for contrast analysis. Then, the coordinates and variables of the jammers are shown in  In TABLE VII, the false target 1 is generated with the proposed method, and the false target 2 is generated with the traditional method. Meanwhile, the estimations of the target velocity and initial azimuth position are also shown in the table. Interferophase, initial azimuth position, and the ground range velocity, are nearly the same. Thus, both the proposed method and the traditional method are able to generate the verisimilar false moving target. However, according to the coefficients shown in TABLE VII, when the distance between 1 J and 4 J required by the traditional jamming method is not satisfied, the jamming power is higher than that required by the proposed method. The less jamming power is, the easier realization is. Therefore, the proposed jamming method is able to generate verisimilar false moving targets with low power and easy realization.

VI. CONCLUSIONS
It is difficult to estimate jamming coefficients using mathematical analysis which makes the processing of solution too complex and trivial, such as monotonicity. Moreover, coefficients estimated by solving equation that are constructed by making interferometric phase of a false target and a moving target be equal will lead to obtain a unique solution of jamming coefficients with a constraint of distance between jammers. To remove the distance limitation, compared with previous works, the contribution of this paper is that a novel jamming problem modeling idea is proposed based on an optimization problem. Therefore, a PSO-based method is proposed to estimate the coefficients. When the distance between jammers required by the traditional jamming method is not satisfied, the jamming power required by the proposed method is lower than that required by traditional methods. By using the jamming evaluating indicators, including the range position, the azimuth position, IRW, PSLR, and correlation coefficient, the proposed method is able to generate the verisimilar false moving target. Furthermore, the proposed method introduces a novel jamming coefficient acquirement structure, which could be suitable for this problem in the field of ECM. Although the PSO-based method could introduce a heavy computational burden, device capabilities could be improved to meet this challenge, and the improved method based on paralleled PSO algorithm is expected to reduce parameter acquisition time in the future.