a deception jamming method countering bi- and multistatic
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Research ArticleA Deception Jamming Method Countering Bi- andMultistatic ISAR Based on Micro-Doppler Effect
Zheng-Zhao Tang, Yang-Yang Dong , Chun-Xi Dong, Xin Chang, and Guo-Qing Zhao
School of Electronic Engineering, Xidian University, Xiβan 710071, China
Correspondence should be addressed to Yang-Yang Dong; dongyangyang2104@126.com
Received 15 May 2018; Accepted 28 August 2018; Published 18 September 2018
Academic Editor: Nazrul Islam
Copyright Β© 2018 Zheng-Zhao Tang et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.
Bi- and multistatic inverse synthetic aperture radar (ISAR) operate with spatially separated transmitting and receiving antennas.A deception jamming method countering bi- and multistatic ISAR is proposed in this paper based on the study of micro-Dopplereffect. The jammer modulates the intercepted ISAR signals with added micro-Doppler information and retransmits them to thereal target, which scatters the jamming signals to the radar receivers. Deceptive false-target images with interference bands in thecross-range direction will be induced by the jamming signals through the imaging process of radar receivers. Additionally, real-time movement features of the false-targets can be flexibly adjusted by changing the modulation parameters, which improves thefidelity of the false-targets. The equivalent number of looks (ENL) index is used to evaluate the jamming effects. Simulation resultsvalidate our theoretical analysis and show the effectiveness and practicability of our method.
1. Introduction
ISAR has been widely used in many military fields suchas target classification, enemy recognition, and precisionweapon guidance because of its all-day and all-weathersurveillance and high-resolution imaging on the target. In thecomplex electromagnetic environment of modern warfare,bi- andmultistatic ISARhave drawnmore andmore attentiondue to their advantages in target information acquisition[1], identification, antijamming, and concealment. Bi- andmultistatic ISAR can generate high-resolution images ofhigh-speed moving targets with one transmitter and severalreceivers that are spatially separated. The characteristics ofpseudobistatic ISAR system are analyzed by Palmer et al in[2]. Y.Huang et al. discussed the imaging resolution of bistaticISAR system in [3, 4]. Afterwards, Z.Z. Gao et al. discussedthe variation regulations of bistatic angle and equivalent line-of-sight azimuths in the wave-number domain [5]. Bi- andmultistatic ISAR show great potential to be widely applied inmany military applications.
In recent years, the micro-Doppler effect introducedfrom laser radar has been developed and utilized in severalapplications such as feature extraction [6] and the accurate
identification of targets [7, 8]. Meanwhile, with the develop-ment of high-resolution time-frequency analysis algorithm[7], the feature extraction algorithm [9] of ISAR targets basedon micro-Doppler effect shows great potential [10] in theapplication of target identification [11]. Micro-Doppler effectalso has an impact on the countermeasures to ISAR [12,13]. The study of bi- and multistatic ISAR countermeasuresis scarce according to the literature available [14]. Shi etal. proposed an ISAR jamming idea based on the micro-Doppler effect capable of inducing a train of false-targetsin the ISAR images [15]. A method capable of generatingdeceptive images in the downrange direction of bistatic ISARbased on sub-Nyquist sampling is proposed in [16]. However,this method cannot interfere with the cross-range directionand the features of the false-targets are fixed.
Based on the previous study, a method capable of gen-erating deceptive false-target images with interference bandsin the cross-range direction was proposed in this paper. Thejammer modulates the intercepted ISAR transmitting sig-nals with added micro-Doppler information and retransmitsthem to the target, which then scatters the jamming signalsto the radar receivers. Deceptive false-target images will beinduced near the real target images, as well as interference
HindawiMathematical Problems in EngineeringVolume 2018, Article ID 3689382, 6 pageshttps://doi.org/10.1155/2018/3689382
2 Mathematical Problems in Engineering
TargetP
x
y
OM
N
Radar receiver N
Radar receiver
Radar transmitter Radar receiver
Radar receiver
Tx
RT RR1
RR2
RR3
RP
R1x
R2x
R3x
οΌ
Figure 1: Geometry of the multistatic ISAR and a target withrotating motion.
bands in the cross-range direction, through the motion com-pensation and two-dimensional pulse compression imagingprocess of the radar receivers. The features of the false-targetimages can be flexibly adjusted to improve the fidelity of thefalse-targets, so that the decision to engage the target may bedelayed even impractically to make without accurate targetrecognition. Althoughmost of the analyses are directed basedon the principle of bistatic ISAR, it can easily be extendedto the applications in countering multistatic ISAR for thejamming signals are theoretically scattered in all directionsand in all angles.
This remainder of this paper is organized as follows.Section 2 introduces the principle ofmultistatic ISAR system.Section 3 presents the jamming signal analysis on the basisof the bistatic configuration. Section 4 shows the simulationresults together with some performance and key parameterdiscussion. And the ENL index is utilized to evaluate thejamming effect. Finally, some conclusions are presented inSection 5.
2. Multistatic ISAR System Model andMathematical Analysis
We show the whole signal processing steps from coherentprocessing to final image forming in a certain given multi-static system setup. For the purpose of simplicity, supposethat the radar transmitter, receivers, and the jammer are allstationary. The target of multistatic ISAR can be equivalentto a rotating platform model with an angular velocity πafter ideal motion compensation, as in Figure 1. The radartransmitter and receivers are located at Tx, R1x, R2x, and R3xand the instantaneous slant ranges between the target and theradar transmitter and receivers are RT, RR1, RR2, and RR3,respectively. The bistatic angle of Tx, R1x, and the target isdenoted as π½. The 2D coordinate xOy is embedded on thetarget and the origin O is the centre of the moving target. They-axis is the bisector of angleπ½ and the x-axis is perpendicularto the y-axis. RP is the range between point scatterer P(x0, y0)andO, and πP is the included angle betweenRP and the x-axis.
M and N are the projection of P in the line of sight of radartransmitter and receiver, respectively.
The LFM signal is widely used as the transmitting signaldue to its advantage of enhancing transmit power andwidening the bandwidth. Suppose that the transmitting signalof the ISAR transmitter is a linear frequency modulated(LFM) pulse whose central frequency is defined as f0 and thechirp rate is defined as k. The waveform of the transmittingsignal in the fast time and the slow-time domain can beexpressed as
π (t, tπ) = ππππ‘ ( π‘π)
β exp [π2π (π0π + 12ππ2)]
Where ππππ‘ ( π‘π) ={{{1 |π‘| β€ 0.5π0 |π‘| > 0.5π ,
(1)
π‘ = π β π β ππ πΌ is the fast time, π‘π = π β ππ πΌ is the slowtime,π is the pulse width, m is an integral number, and T ispulse repetition period.
Since π π βͺ π π, π ππ, and π π 1π can be equivalent to π ππand π π 1π, respectively. Suppose that the sum of ranges fromthe point O to the radar transmitter and receiver (bistaticrange) is R0 and the bistatic range of point scatterer P is
π π (π‘π) β π ππ + π π 1π = π π + π π 1 + ππ(tπ)β ππ(tπ) = π π + ππ(cos(π2 β
π½2 β (π + πtπ))
β cos(π2 βπ½2 + (π + πtπ)))
(2)
The rotation angle of target is negligible during the processingtime of radar imaging, therefore has sin(ππ‘π) β ππ‘π andcos(ππ‘π) β 1, and then (2) can be expressed as
π π (π‘π) = π π + 2ππ β sin (ππ + πtπ) cos π½2= π π + 2ππβ (sin ππ cos (πtπ) + cos ππ sin (πtπ)) cos π½2
= π π + π¦π cos π½2 + π₯ππtπ cosπ½2
(3)
and thus the echo signals of point scatterer P collected byradar receiver R1x are
ππ (π‘π) = ππ β ππππ‘ ( π‘π) β exp(βπ2ππ0π
β (π π + 2π¦π cos π½2 + 2π₯ππtπ cosπ½2))
(4)
Mathematical Problems in Engineering 3
ππ is the scattering coefficient of P. Carrying out the Fouriertransform (FT) in the slow-time domain, then the Dopplerfrequency of point scatterer P has a form as
ππ· = 4πππ0π₯0π cos
π½2 (5)
It can be seen from (5) that the Doppler frequency of eachpoint scatterer of the target is proportional to its position inthe range direction. The use of spectrum analysis methodssuch as FT can separate different point scatterer in each rangeresolution cell. Thus the range-Doppler image of the targetcan be obtained.
The imaging principle of other radar receivers is same asR1x.
3. Jamming Signal Analysis
Without loss of generality, a bistatic configuration is usedto analyze the jamming signal, as in Figure 2. Denote theradar transmitter, receiver, and the jammer Tx, Rx, and Jx,respectively. The jammer modulates the intercepted ISARtransmitting signals with added micro-Doppler informationand retransmits them to the target. Therefore the jammer andthe radar receiver can be equivalent to a bistatic ISAR systemwith a bistatic angle denoted as π½. The 2D coordinate xOy isembedded on the target and the origin O is the centre of thetarget. The y-axis is the bisector of π½ and the x-axis is perpen-dicular to the y-axis. Denote the false rotating point scatterer
as P(xP, yP) and it is rotating centre as O1. P has both thesame translational movement as point O1 and the rotationalmovement with a radius denoted as RP in the xOy plane.Additionally, the initial phase and the angular velocity of P aredenoted as πP and πP, respectively. M and N are the projec-tions of P in the line of sight of the jammer and radar receiver.Denote the initial angle included in RP and the x-axis as π.
The jammer generates deception jamming signalsthrough three steps: intercepting, modulating, and retrans-mitting. Suppose that the radar transmitting signal is sameas Section 2.
The bistatic range of P can be written as
π π (π‘π) β π π½π + π π 1π = π π½ + π π 1 + ππ(π‘π)β ππ(π‘π) + π π cos (πππ‘π + ππ) β π πβ sin (πππ‘π + ππ) = π π+ π ππ1 (cos(π2 β
π½2 β (π + ππ‘π))
β cos(π2 βπ½2 + (π + ππ‘π)))
+ π π (cos (πππ‘π + ππ) β sin (πππ‘π + ππ))
(6)
π‘π is the slow time. Then the jamming signal modulatedby the jammer can be expressed as
ππ (π‘π) = ππ β ππππ‘ ( π‘π) β exp(βπ2ππ
β (π π + π ππ1 (cos(π2 βπ½2 β (π + πtπ)) β cos(π2 β
π½2 + (π + πtπ)) + π π (cos (ππtπ + ππ) β sin (ππtπ + ππ)))))
(7)
Carrying out the FT in the slow-time domain, then theDoppler frequency of P has a form as
πππ· = 4πππ ππ₯1π cos
π½2 sin (πππ‘π + ππ) (8)
It can be seen from (8) that when the target scatters thejamming signals to the radar receiver, false-target imageswithmicro-Doppler features are induced in the ISAR images.The false-target images rotate at an additional angle whichequalsπ½/2 comparedwith the real target images. And the falsemicro-motion points will induce interfere bands in the cross-range direction.
4. Simulations and Image Result Analysis
4.1. Simulation Description. A plane model of 74 pointscatterers is adopted to demonstrate the effect of the jammingidea which takes up to 20m (downrange) Γ 20m (cross-range). The simulation process is described in Figure 3.
Simulation parameters are listed in Table 1. The radar isassumed operating at 10GHz (f0) and transmitting a LFM
waveform with 1GHz bandwidth (B). The pulse width (π) is10πs and the pulse repetition frequency (PRF) is 200Hz. Atotal of 512 pulses are transmitted. Values of RT0, RJ0, andRR10 are set as 50km, 60km, and 70km, respectively, whichsatisfy the approximation of far-field back scattered field.The bistatic angle (π½) is 120β. The transmitting power (PJ)of the jammer is 140W and the antenna gain (GJ) is 30dB.The rotating angular velocity (π) of the target is 0.02rad/s.
4.2. Image Result. Figure 4(a) shows the range-Dopplerimage of the plane model. The single and multiple false-target images of ordinary deception jamming method areillustrated in Figures 4(b) and 4(c), respectively. It can be seenthat the false-target images are distributed in different rangecells but the Doppler frequency of each false-target is thesame.
Figure 4(d) depicted a single false-target image with tworotating micro-motion points, whose rotation radius is 3mand the angular velocity is 20rad/s. The false-target imagerotates an additional angle of 60β (π½/2) compared with
4 Mathematical Problems in Engineering
TargetP
x
y
OM
N
Radar Transmitter Radar
Receiver
Jammer
Tx
RT
RR1
RJ
RP
R1x
O
οΌ1
οΌ
οΌx
Figure 2: Geometry of the Jamming Scenes.
radar transmitting signals
Jammer modulates and retransmitters
Target scatters jamming signals
Radar receiver imaging process
Figure 3: Simulation process.
Table 1: Simulation parameters.
f0/GHz 10 RR10/km 70B/GHz 1 RJ0/km 60π/πs 10 PJ/W 140PRF/Hz 200 GJ/dB 20N 512 π/radβ sβ1 0.02RT0/km 50 π½/β 120
Figure 4(b) and has two interference bands in the cross-rangedirection, which verifies the conclusions in Section 3.
In order to flexibly control the image features andmotioninformation of the false-target, we further studied the jam-ming effect with the changing of certain parameters com-pared to Figure 4(d), and the simulation results are shown inFigures 4(e)β4(h). In Figure 4(e) the equivalent bistatic angleis reduced to 60β and as a result the false-target image rotates30β. In Figure 4(f) the rotation radius of the micro-motionpoints has increased to 5m; it can be seen that the widthof the interference bands has broaden. Figure 4(g) illustratesthe false-target image when the jammerβs retransmitting timedelay reduced to 60ns. And Figure 4(h) illustrates the false-target images with the angular velocity of micro-motionpoints reducing to 10rad/s. It can be seen that the sparsedegree of interference bands has decreased.
Compared to Figure 4(c), the image of multiple false-target and micro-motion points was depicted in Figure 4(i).It can be seen that the real target image was hidden withinthe false-targets images and interference bands, making itdifficult for ISAR to distinguish.
Through the above simulation, we can arbitrarily set theposition, number, and movement information of the false-target and the micro-motion point scatterers according tothe operational needs, which greatly improves the fidelity ofdeception jamming.
4.3. Analyses of Jamming Effect. The equivalent number oflooks (ENL), which is an indicator of the grayscale of animageβs pixels, is used to analyze the jamming effect. It is themost commonly used standard for image evaluation and isdefined as the ratio of the mean of the image to the standarddeviation of the image:
πΈππΏ = πβπ2 (9)
Themean value of the image reflects the average gray levelof the image. The standard deviation of the image representsthe degree of deviation of all points in the image area from theaverage, which reflects the nonuniformity of the image.Therewill be big changes of the mean and standard deviation of theISAR images when they are jammed. The bigger the changesare, the more significant the jamming effect is. The ENLs ofthe images in Figure 4 are listed in Table 2.
It can be seen that the jamming method proposed in thispaper has a more significant effect on ISAR images in bothcases of single and multiple false-target deception jammingthan ordinary deception jamming method.
5. Conclusions
The novelties of this paper are that multiple false-targetimages with additional micro-Doppler information will beinduced by the jamming signals. Additionally, the real-timemovement features of the false-target images can be flexiblyadjusted as needed. Multiple false-target images which aresimilar to the real target can increase the cost burden andwaste the finite resource of radar for identifying the real one.The deceptive jamming method could have a negative impacton the ISAR target recognition applied to aircrafts, ships, andmissiles.
Data Availability
Data is obtained by computer simulation.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was supported by the China Postdoctoral ScienceFoundation under Grant 2017M623123.
Mathematical Problems in Engineering 5
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Table 2: ENLs of the image results in Figure 4.
Image number ENL mean value standard deviationFigure 4(a) 3.6537 23.1853 6.3457Figure 4(b) 4.8865 39.8606 8.1573Figure 4(c) 6.0223 59.5701 9.8916Figure 4(d) 5.3407 45.3751 8.4961Figure 4(e) 5.3227 45.1859 8.4893Figure 4(f) 6.1563 64.9237 10.5458Figure 4(g) 5.3078 45.1247 8.5016Figure 4(h) 5.5369 46.9147 8.4731Figure 4(i) 8.5110 125.9509 14.7986
6 Mathematical Problems in Engineering
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