Rotational micro-motion modulated jamming for countering ISAR based on intermittent sampling repeater.
The inverse synthetic aperture radar (ISAR) collects modulated pulses and coherently processes them to reconstruct a two-dimensional (2-D) intensity image of moving targets (such as aircraft and ships) [1-3]. ISAR imaging plays an important role in many military applications such as target classification, recognition and identification . Surveillance systems such as US ALCOR radar , the AN/APS-137B(V) radar  and the ground based radar (GBR)  possess the capability of detecting, classifying and tracking by using the ISAR imaging mode. ISAR image, characterized by high resolution along both the range and cross-range directions, can also be used to launch weapon systems . The need for countering wideband ISAR imaging radars remains a high priority in electronic warfare [8,9].
In most of the conventional work on the inverse synthetic aperture radar (ISAR) imaging, the target is assumed to have rigid-body motion. Actually, non-rigid-body targets can often be found in real-world situations, such as the rotating rotor blades of a helicopter, the scanning antenna of a ship and the wheel of a ground vehicle [10-12]. These mechanical rotations or vibrations are referred as micro-motion dynamics. Micro-motion dynamics of an object or structures on the object may introduce additional time-varying frequency modulations on the radar echoes which are called micro-Doppler (m-D) effect [13,14]. On the one hand, the ISAR image may be contaminated due to the interference from the additional time-varying m-D modulations when the backscattering of the micro-motion part is emphatic enough [15-17]. On the other hand, micro-Doppler features can be regarded as a unique signature of an object with movements, providing additional information for the classification, recognition, and identification of the object. Some methods for separation of the m-D effect or extract the m-D features from the radar echoes are proposed [10, 18-21]. Thus, the micro-motion dynamics can be used in the countermeasures of ISAR which may decrease the readability of radar images or make the separation and extraction of m-D signatures difficult and spurious.
A jamming method based on the rotating angular reflector is presented in . With the characteristic of rotation, the frequency modulated radar echoes along azimuth lead to smeared imaging in ISAR. But it can only blur the image in the cross-range and the achieved barrage jamming along the down-range needs a reflector array as the author has pointed out. Actually, the jamming method based on the rotating angular reflector is a passive jamming technique and the reflector array may be difficult to set up especially in some aerospace targets, such as aircraft and ballistic targets on which space is limited. The digital radio frequency memory (DRFM) is widely used in radar active coherent jamming [6, 23-26]. With the capability of high speed sampling, DRFM reduces production costs and achieves a wide bandwidth. Associated with the micro-motion dynamics, Zhu et al. [27,28] put forward the synthesizing equivalent micro-motion point jamming (SEMPJ) to ISAR based on DRFM. First, the intercepted ISAR signal samples are modulated by sinusoidal increments in the slow time. Second, all the samples are retransmitted to the radar. It can produce time-varying Doppler frequency modulations in the cross-range after ISAR imaging. Multiple point-scatterers will be induced in the down-range by utilizing the time-delay or frequency-shifted processing. One obvious problem of the SEMPJ is that the jamming signal retransmitted to the radar usually is delayed at least one pulse duration compared with the target echoes. Based on the delay time, false targets may be identified by the radar easily . High isolation of the two receive-transmit antennas is another problem in the coherent jamming. Based on a receive-transmit time-sharing antenna, the intermittent sampling repeater jamming (ISRJ) was proposed and developed . It samples the arrived ISAR chirp signals intermittently for a constant time that is less than the pulse duration and then turns on the transmitter to retransmits all the samples immediately to the radar. Then the transmitter is turned off and the receiver is turned on to go on sampling the remainder signal. The steps of switching between the receiver and transmitter are alternated until the whole pulse has been sampled and retransmitted. Since the intermittent sampling is done in the fast time, false point scatterers will be introduced only in the down-range where each point spread function (PSF) is a scaled sinc function. As ISAR is a method of reconstructing a 2-D intensity image of a target, a jamming method that can contaminate the ISAR image in both the down-range and the cross-range is needed.
Based on the combination of the intermittent sampling in the fast time and the m-D modulation in the slow time, an ISAR jamming method is presented in this paper, which can introduce a smeared 2-D ISAR image. The remainder of this paper is organized as follows. The principles and the imaging results of jamming are derived in Section 2. Section 3 is dedicated to the analysis of important parameters and their selection criteria. In Section 4, numerical simulation results are presented and analyzed. In Section 5, the jamming simulations based on the measured data are discussed. Finally, in Section 6, some conclusions and perspectives are presented.
2. PRINCIPLES OF THE JAMMING
2.1. Intermittent Sampling in the Fast Time
Once the jammer receives the ISAR transmitted signal, it samples the pulse intermittently in the fast time and transmits all the samples immediately to the radar. Assume that the intermittent sampling function noted as p (t) is a rectangular envelope pulse train with pulse duration [tau] and pulse repetition interval (PRI) [T.sub.s], as Fig. 1 illustrates, is defined as 
p(t) = rect (t/[tau]) x [+[infinity].summation over (n=-[infinity])] [delta] (t - n[T.sub.s]) (1)
Consider an ISAR that transmits a linear frequency modulated pulse where the frequency is swept upwards cross the pulse. The waveform of the transmitted signal in the fast time and the slow time domain can be expressed as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
and [??] is the fast time, t the full time, [T.sub.p] the pulse width in seconds, [f.sub.0] the carrier frequency in Hz, and k the chirp rate.
The imaging geometry of a target with a jammer is shown in Fig. 2 where the coordinate XOY is established with the axis y is the light of sight (LOS). Suppose the translational motion has been compensated and the target is a turntable model with angular velocity [omega] (rad/s) around the imaging centre O. [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the instantaneous slant range between O' (phase centre of the jammer) and radar. In a small accumulation angle [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] can be expressed as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
where O'([x.sub.J],[y.sub.J]) denotes the range between the jammer and the rotating centre, and [t.sub.m] is the slow time satisfying that [t.sub.m] = t - [??].
The delay time caused by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] can be expressed as
[[tau].sub.m] = [2[absolute value of [[??].sub.0]]/c] + [2[y.sub.J]/c] + [2[x.sub.J][omega]/c] [t.sub.m] (5)
where c is the speed of electromagnetic wave.
Denote the delay time of jammer by [[tau].sub.r], then the delay time caused by retransmission and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] can be computed as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
where [[tau].sub.0] = [[tau].sub.r] + [tau] + [2[y.sub.J]/c].
Take the radar transmitting signal's time as the starting time, and then the unit amplitude intermittent sampling jamming signals can be written as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
Integer values of a radar pulse after the intermittent sampling are generated as
N = [[T.sub.p]/[T.sub.s]] (8)
where N = [x] indicates the greatest integer no less than or equal to x. It is clear that the jamming signals are made up of N segment LFM signals, whose frequency modulation slope is k, pulse width is [tau], and frequency modulation bandwidth is [B.sub.J] = k[tau].
2.2. Micro-motion Modulation in the Slow Time
The m-D of a rotating scatterer in addition to the target's bulk movement is a sinusoidal FM signal . Let the modulation micro-Doppler be
[f.sub.d] = [2/[lambda]] [omega][x.sub.d] + (2/[lambda]) [omega]'r' cos ([omega]'[t.sub.m]) (9)
where [lambda] denotes the wave length, [x.sub.d] the modulation rotating centre away from the jammer along the X axis, r' the rotation radius, and [omega]' the rotation rate
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)
Usually, ISAR targets are relatively small. For a wideband LFM signal, dechirping processing is an acceptable method to achieve a high resolution range profile (HRRP) . Let the reference point be the imaging center O, then the jamming signals after dechirping can be expressed as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)
2.3. ISAR imaging of the jamming signals
There are two steps of ISAR imaging: the range compression and the azimuth focusing. The jamming signals after the range compression in the fast-time domain are given by
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)
where sinc (x) [??] sin ([pi]x/[pi]x). Suppose that no range migration occurs during the imaging time then the approximation form of (12) satisfies
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and Z = [4[pi]/[lambda]] r'.
Carrying out the FT in the slow-time domain, we can obtain the ISAR image [13, 15]
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (14)
where [T.sub.M] denotes the imaging time and [J.sub.l] (Z) the Bessel function of first kind.
From (14), one can conclude that the image of jamming signals is a series of scaled sinc functions in different bins, with its sidebands equally spaced at multiples of [omega]'/2[pi] in the cross-range. In addition, the bandwidth of the m-D is about 2Z, which is a function of wave length and rotation radius. Therefore, the jamming may contaminate the image of the main body in both the range and Doppler domain, particularly when it is emphatic.
3. TWO STEPS TO DETERMINE THE KEY PARAMETERS
Each sinc in (14) would be identified as a fake "point" target or a point-scatterer in radar, and according to the principle of time-frequency conversion, the distance in the down-range and the distance in the cross-range among scatterers are given by 
[d.sub.r] = [c[f.sub.s]/2k] and [d.sub.a] = [[lambda]/4[pi]] [[omega]'/[omega]] (15)
For the sake of covering a target which takes up of [d.sub.[parallel]] (downrange) x [d.sub.[perpendicular to]] (cross-range) [m.sub.2], there are two conditions that need to be met: a, the distance array ([d.sub.r],[d.sub.a]) should not be too sparse; b, the available jamming area [[DELTA].sub.[parallel]] (down-range) x [[DELTA].sub.[perpendicular to]] (cross-range) should be large enough. In order to satisfy the condition a, values of [f.sub.s] and [omega]' should be chosen properly taking no account of the peak amplitude of each fake scatterer first [22,29]. Usually, we need that
[d.sub.r] [member of] (2 - 10) [[sigma].sub.r] and (da [member of] (2 - 10) [[sigma].sub.a] (16)
where [[sigma].sub.r] = [c/2B] and [[sigma].sub.a] = [[lambda]/2[omega][T.sub.M]] are the resolution in the down-range and cross-range. So it can be obtained that
[f.sub.s] [member of] (2 - 10) x [1/[T.sub.p]] and [omega]' = (2 - 10) x 2[pi]/[T.sub.M] (17)
The next step is to fulfill condition b. As the available jamming area is determined by the down-range bins indexed by N and cross-range bins indexed by L, the amplitude of the fake scatterer indexed by (n, Z) is
A (n, l) = [tau][f.sub.s][T.sub.p][T.sub.M] sinc (n[tau][f.sub.s]) [J.sub.l] (Z) (18)
Then condition b means that A (n, l) should be no less than the amplitude of the scatterers of the target. The amplitude of the target echo is [T.sub.p][T.sub.M] as can be known from (14). So if the amplitude of a fake scatterer is equal to that of the true one, the amplitude ratio of the fake scatterer to the true one, namely the amplitude modulation coefficient, should be
[M.sub.J] = [[T.sub.p][T.sub.M]]/[[tau][f.sub.s][T.sub.p][T.sub.M]sinc (n[tau][f.sub.s])[J.sub.l](Z)]] = [1/[[tau][f.sub.s]sinc (n[tau][f.sub.s])[J.sub.l](Z)]] (19)
So condition b can be expressed by 
[M.sup.2.sub.J] [less than or equal to] [[P.sub.J]/[P.sub.T]] x [4[pi][gamma][R.sup.2]/G[sigma]] (20)
with [P.sub.J] denoting the jamming equivalent radiated power, G the radar antenna gain, [P.sub.T] the radar peak power, [sigma] the maximum radar cross section of the target, [gamma] (usually supposed to be 0.5) the mismatch loss of polarizatio, and R the slant range.
The amplitude of [J.sub.l] (Z) and the spread of Z along with Z are illustrated in Fig. 3. It is already known that L [approximately equal to] Z+1 and l [member of] (-L, L) for Z [much greater than] 1 . The cover area [[DELTA].sub.[perpendicular to]] equals (2L + 1) x [d.sub.a], and r' can be computed by
(2Z + 3) x [d.sub.a] [greater than or equal to] [d.sub.[perpendicular to]] [??] r' [greater than or equal to] [[lambda]/8[pi]] ([[d.sub.[perpendicular to]]/[d.sub.a]] - 3) (21)
Usually, r' will be very small referring to (21) for a radar in X band, and then [[DELTA].sub.[perpendicular to]] will be large enough to cover the ISAR imaging scene in cross-range. Then according (20), the value of [tau] can be decided at last. The flow chart of the parameter decision is shown in Fig. 4.
Generally, when [P.sub.J] is enough, there will be many choices of [tau] maintaining (20). However, with the permission of realization, the smaller value of [tau] is, the more rapid response and more uniform of fake scatterers in amplitude will be generated . Uniform amplitude of fake scatterers will generate a better contaminated ISAR image than that some nail-like peak value of amplitude near the imaging centre.
4. SIMULATIONS AND ANALYSIS
To further analyze the effect of the jamming, an ISAR imaging simulation of target with a jammer is presented in this part. The flow chart of the simulation is given in Fig. 5.
The main simulation parameters are listed in Table 1. The range from the centre of the target and the radar is chosen as 40 km for the approximation of far-field backscattered field condition. The reference distance is also assumed to be 40 km which means that the target is rotating with its centre.
The target model with a finite number of perfect point scatterers is assumed to be located as shown in Fig. 6(a) and takes up 12 x 4 [m.sup.2], and the imaging center and the jammer are all located at (0, 0). For the purpose of simplicity, the point scatterers are assumed to scatter the electromagnetic energy in all directions and in all angles with [sigma] = 0.1[m.sup.2] which is good enough for modeling as mentioned in . Without loss of generality, this paper considers the imaging model of targets on the 2-D imaging plane.
According to (17), let [T.sub.S] = 20[micro]s and [omega]' = 8[pi]rad/s. r' should be no less than 0.02 m according to (21). We take four groups of parameters into the simulation: 1) r' = 0.02 m, [tau] = 10 [micro]s; 2) r' = 0.02 m, [tau] = 5 [micro]s; 3) r' = 0.2 m, [tau] = 10 [micro]s; 4) r' = 0.2 m, [tau] = 5 [micro]s.
ISAR imaging of the target without jamming is shown in Fig. 6(b). Comparing Figs. 6(c) and (d), Fig. 6(e) and Fig. 6(f), it can be seen that the target's image is all covered and smeared in these four figures, but more totally in Figs. 6(d) and (f) for the amplitude of fake scatterers are more uniform with a smaller [tau] (= 5 [micro]s) as mentioned above. When [omega]' = 8[pi]rad/s and r' = 0.02 m, we have that Z [approximately equal to] 8 and [[DELTA].sub.[perpendicular to]] [approximately equal to] 9m as shown in Fig. 6(c) and Fig. 6(d). If r' = 0.2 m, then we have Z [approximately equal to] 83 and [[DELTA].sub.[perpendicular to]] [approximately equal to] 79 m as shown in Fig. 6(e) and Fig. 6(f) which has already exceeded the imaging scene in the cross-range. Comparing Fig. 6(c) and Fig. 6(e), Fig. 6(d) and Fig. 6(f), it can be figured out that [[DELTA].sub.[perpendicular to]] has been spread with the increment of r'. The strength of the scatterers in Fig. 6(e) and Fig. 6(f) indicated by the corresponding colorbar is smaller than that in Fig. 6(c) and Fig. 6(d) as the increment of r'. On the other hand, when r' is the same, the strength of the scatterers reduces as the decrement of [tau].
5. SIMULATIONS BASED ON MEASURED DATA
In this section, the jamming method is applied to the measured data of a real target. The measured data is obtained by a radar with the bandwidth of 400 MHz, pulse duration of 125 [micro]s, and PRF of 400 Hz. The simulated jamming data is obtained based on the measured data. The flow chart of the jamming simulations based on the real data is illustrated in Fig. 7. From Fig. 5 and Fig. 7, it can be seen that the difference between the numeric simulations and the simulations based on measured data is that the intermittent sampling and the micro-motions modulation processing is after the radar receiver. According to the theory of the linear signal and system, the two simulations are equivalent in the flow.
As shown in Fig. 8(a), the real data are from a plane with 34.88meter in wingspan and 36.8-meter in length. Take 256 echoes for ISAR imaging, then the coherent time [T.sub.M] = 0.64 s. The ISAR image of the plane is illustrated in Fig. 8(b). Let [T.sub.S] = 25 [micro]s and [omega]' = 6[pi] rad/s according to (17). r' should be no less than 0.06 m referring to (21). Take four groups of parameters into the experiments: 1) r' = 0.06 m, [tau] = 12.5 [micro]s; 2) r' = 0.06 m, [tau] = 5 [micro]s; 3) r' = 0.2 m, [tau] = 12.5 [micro]s; 4) r' = 0.2 m, [tau] = 5 [micro]s.
In experiments 1) and 2), when r' = 0.06m, [[DELTA].sub.[perpendicular to]] is approaching 40 m as shown in Fig. 8(c) and Fig. 8(d). In experiments 3) and 4), when r' = 0.2 m, [[DELTA].sub.[perpendicular to]] equals 123 m as shown in Fig. 8(e) and Fig. 8(f) which has exceeded the imaging scene in the cross-range. The simulation results based on the measured data also illustrate that the strength of point-scatterers decreases with the increment of r' and decrement of [tau] which is similar to the results depicted in the numeric simulations.
This paper proposes a new ISAR countermeasure based on the ISRJ and micro-motion modulation. Numeric simulations are performed to test the performance of the jamming. Furthermore, jamming experiments based on measured data are provided to validate the effectiveness of the jamming method. The results show that the proposed jamming method smears the ISAR image of a target in the RD imaging plane. One of the main challenges of this jamming method is that the jamming energy actually spreads out into the 2-D intensity image. The selection criteria of jamming parameters is important. The essential requirement for the jamming energy will be addressed in the further work.
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Xiaoyi Pan *, Wei Wang, Dejun Feng, Jing Huang, Qixiang Fu, and Guoyu Wang
School of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China
Received 20 September 2012, Accepted 28 December 2012, Scheduled 4 January 2013
Xiaoyi Pan, Corresponding author: Xiaoyi Pan (firstname.lastname@example.org).
Table 1. Simulation parameters. [f.sub.0] 10 GHz [T.sub.P] 100 [micro]s PRF 1000 Hz R 40 km [sigma] 0.1 [m.sup.2] [P.sub.J] 10 w B 300 MHz [P.sub.T] 1 kW G 30 dB [omega] 0.04[pi] rad/s [T.sub.M] 0.512 s [gamma] 0.5
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|Title Annotation:||intermittent sampling repeater jammingA|
|Author:||Pan, Xiaoyi; Wang, Wei; Feng, Dejun; Huang, Jing; Fu, Qixiang; Wang, Guoyu|
|Publication:||Progress In Electromagnetics Research C|
|Date:||Mar 1, 2013|
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