ISAR active jamming method based on sinusoidalmodulation

Yu Zhang,Congfeng Liu,and Yan Zhu

Key Laboratory of Electronic Information Countermeasure and Simulation Technology,Ministry of Education, Xidian University,Xi’an 710071,China

ISAR active jamming method based on sinusoidalmodulation

Yu Zhang*,Congfeng Liu,and Yan Zhu

Key Laboratory of Electronic Information Countermeasure and Simulation Technology,Ministry of Education, Xidian University,Xi’an 710071,China

It is potentially useful to perform deception or cover jamming using the rotating angular reflectors since they can form deception echoes along range and azimuth.Inspired by the coherentjamming and micro-motion modulation,a novelactive method is proposed for inverse synthetic aperture radar(ISAR).Radar pulses are sampled and frequency-modulated along azimuth by sinusoidalsignal,and then the jamming signals are retransmitted to the radarand the jamming images are induced after ISAR imaging. Therein,the jamming principle,key parameters and the jamming effect are discussed.The simulated data verify the effectiveness ofthe jamming method.

inverse synthetic aperture radar(ISAR),deception jamming,cover jamming,micro-motion modulation,sinusoidal modulation.

1.Introduction

Inverse synthetic aperture radar(ISAR)is a high resolution microwave imaging system[1–4].It has great prospects in many military applications such as features extraction, targetclassification,recognition and identification of noncooperative targets[5–8].The ISAR image is characterized by the high resolution along both the down-range and cross-range directions.The IASR imaging technique has been rapidly developed to accommodate to the increasingly complicated electromagnetic environment,consequently to challenge the ISARcountermeasure field.The research on jamming methods against ISAR is urgentand important[9].

The ISAR imaging is a course of two-dimensional signals processing.Thus,ISARhas the advantage ofhigh processing gain received signals which brings difficulties to the jamming technique.The traditional active radio frequency noise jamming can be easily suppressed by the radar signal processor.The noise frequency modulated jamming is effective butrequires high fidelity of the radar signal[10].The traditional passive jamming such as corner reflector or chaff can also be suppressed easily.Reference[11]broughtforward a method based on rotating angular reflectors,which was effective on the condition that the angular reflectors were well arranged and their rotate speeds were suitable.However,when the angular reflectors are fixed,the arrangement mode,the reflection coefficients and the rotating speeds are determined,and then the radar can remove the jamming signal by some digital signalprocessing methods like echo correlation.Using the idea of micro-motion modulation,a jamming method was proposed for SARwhich can produce multiple false targets in the azimuth direction[12].Another method named coherent jamming was also proposed in which the weighted frequency modulation can be in both fast and slow time domains which can produce both cover jamming and false targetdeceptive jamming[13].

Inspired by the micro-motion modulation and the coherent jamming,a novel jamming method for ISAR imaging is proposed.In this method,the radar pulses are sampled first,and then are frequency-modulated in the fast time and micro-motion modulated in the slow time.The resulting signals are retransmitted as the jamming signals which can produce cover or deceptive jamming on the radar image.The jamming method is potentially useful against radar in three aspects:first,the barrage jamming can cover the radar image;second,the false-target information is revealed and utilized to deceive the target identification;third,barrage jamming and false-target images can increase the cost burden and waste the finite resource of radar.

In this paper,we introduce and analyze the novel ISAR active jamming method based on micro-motion modulation.The remainder of this paper is organized as follows. The signalmodelofthe jamming signaland the image formation of the jamming signals are derived in Section 2. Section 3 analyzes the characteristics of the barrage jamming and the deceptive false-targetimages.The simulationresults are shown and discussed in Section 4 to prove the validity of this method.Finally,in Section 5,some conclusions are presented.

2.Signalmodel

Consider an ISAR thattransmits a linear frequency modulated(LFM)pulse.The waveform ofthe transmitted signal in the fasttime and the slow time domains can be expressed asfcis the carrier frequency,T is the pulse width,μis the chirp rate,t is the full time,tmis the slow time satisfying tm=mT in which T is the pulse repetition interval(PRI),and?t is the fast time satisfying?t=t?tm.

Suppose that the jammer is set on the moving target, which is known as the self-screening jamming.The geometry of the radar,the moving target and the jammer are shown in Fig.1.The coordinate xoy located on the target is established with the axis x being the lightofsight(LOS) and origin O being the image center.

Fig.1 Geometry of radar,moving target and jammer

The radar target and the jammer are both rigid bodies.Suppose the jammer is located on point OP.Then the micro-motion modulation jamming signals will produce the deceptive high-speed rotating parts around the jammer.Thus,OPcan be regarded as the rotating center of the high-speed rotating point P.Now choose another rigid body scattering point Q and the high-speed rotating scattering point P as our research objects.

As shown in Fig.1,R0,RPand RQare the distances from O,OPand Q to the radar respectively.And the distances from Q and P to the image center O are R1and R2respectively.The rotational angular velocity of the flying target is indicated asω,and that of the rotating point P isωP,they are both counterclockwise.The initial angles of Q,P and OPareθ1,θPandθ2,and after the image time,the angles ofthem are(ωtm+θ1),(ωPtm+θP)and (ωtm+θ2).

We analyze the echoes of the rigid bodies first.Suppose the range from the radar transmitter to a rigid body scattering point Q at the m th PRI is RQ(tm),then the time consumed for propagation is,where c is the propagation velocity of the electromagnetic wave. The return signalof the point Q can be written as

Fora wideband LFMsignal,dechirping processing is an acceptable method to achieve a high resolution range profile[14].Let the reference range be Rref=R0,then the return signalafter dechirping can be expressed as

The 1D down-range profile of the point Q can be constructed by the Fourier transform as

Assume thatno range migration occurs during the imaging time.Aftera standard motion compensation algorithm, we have

Using the small accumulation angle assumption,the Doppler frequency of the pointscatterer Q is given as

Equation(7)shows that there are correspondences between the Doppler frequency of the echoes and the crossrange coordinate of the point Q.

Nextwe willtake the assumed high-speed rotating scattering point P as our study object.A 1D down-range profile can be given on the basis of(5)as

During the image accumulation,we have

The Dopplerfrequency of the pointscatterer P is given as

where yO'is the ordinate value of the rotation center ofthe micro-motion target.By comparing(7)and(10),we can obtain a conclusion as follows.Underthe smallaccumulation angle condition,the Doppler frequency of the echoes of the rigid body scatterer is constant;while the Doppler frequency of the echoes of the high-speed rotating body

scatterer is a sine curve withas the center.

Consequently the micro-motion jamming signal can be represented as

where tj(tm)is the range from the radar transmitter to the jammer.This shows that the jamming signal is a cosine weighted frequency modulation signal and it is modulated in the slow time domain.The relative parameters and the characteristic of this jamming willbe discussed as follows.

3.Analysis and discussions

From(11),the parameters rP,ωPandθPare all related to the characteristic of our simulated false micro-motion target,where rPis the distance from that to the rotating center namely the jammer,ωPis the rotating speed of that, andθPis its initialphase.As the constantphase almosthas notinfluenced ISAR,we can ignoreθPin ouranalysis.

Suppose that

where mfis the coefficient of frequency mo-dulation.Since n(tm)=?mfcos(ωPtm)which is used for modulation is a periodic signal,we can use the Bessel function to expand(12)as the following series form:

where Jk(mf)]dτ.This shows that p(tm)consists of a lot of single-frequency signals whose frequency intervals are allωP,and each amplitude is decided by Jk(mf).

Therefore,the micro-motion modulation jamming can be seen as the results of frequency shifting of the radar echoes by 0,±ωP,±2ωP,±3ωP,etc.This is similar with the coherentjamming in the down-range domain[13,15]. According to(7),there is a linear relationship between Dopplerfrequency and the cross-range coordinate.In other words,the frequency shiftwillcause the shiftof the crossrange coordinate.Thus,after the jamming signal is processed by the radarreceiver,its outputshould be expressed as a series of discrete sinc functions which are symmetric aboutthe jammer.And according to the distance between each sinc function peak,the jamming effect can be cover or deception.

Combined with the coherent jamming in down-range such as sinusoidal weighted frequency modulation jamming,we can obtain two-dimensional simulated target image.The related parameters are discussed as follows.

3.1 Rotating speed of micro-motion target

According to the analysis of the preceding context,the jamming outputs in cross-range are a series of discrete sinc functions which are symmetric aboutthe jammer.The amplitude of each pulse is decided by the Bessel function Jk(mf).And the frequency intervalisωPwhich is the angular frequency of the cosine function.

Using the small accumulation angle assumption,it is known that the Doppler frequency of some point remains aboutthe same during the imaging time.Thus,the echoes of that point approximate to a single frequency signal whose time width is T and frequency is fd.A sinc function whose bandwidth is 1/T and center frequency is fdcan be obtained by taking fast Fourier transform(FFT)tothe echoes.Ifwe wantto distinguish differentpoints,every sinc functions must notoverlap each other.Therefore,the distance between every two sinc functions cannot be less than 1/T.

Consequently,we can draw a conclusion thatwhen

there will appear the false target deception jamming,otherwise,there willappear the cover jamming.

According to(13),the frequency spectrum interval is ωP.And as is wellknown,there is one-to-one mapping between the azimuth coordinate and Doppler frequency shift justas(7).Thus,the range separation along the cross-range between every two jamming pulses is

which means that the range separation is proportional to the rotating speed of the micro-motion target.

3.2 Turning radius of micro-motion target

According to the theory of frequency modulation,there is no modulation when mf=0.And the frequency of modulated signalnearly remains unaffected when mf＜＜1, this jamming is unqualified and ruled out.

For the Bessel function Jk(mf),the harmonics are small when mf=1 and k＞2;The higher the value of mf,the larger the amplitude of higher order harmonics,as shown in Fig.2.For some certain mf,when k＞mf+1,we have Jk(mf)≈0[16]as shown in Fig.3.

Fig.2 Relationship between Jk(mf)and mf

Fig.3 Relationship between Jk(mf)and k

For the wider disturbance range,mfshould be as large as possible.However,if mfis too large,the interference peak will be reduced.Thus,we can choose a suitable effective jamming pulse numberwhich is

It can be seen that the jamming number is proportionalto the rotationalradius.

The jamming numberis 2mf,so the corresponding jamming coverage along the cross-range is

It can be seen that the jamming coverage is decided by the productof the rotating speed and the radius of the micro-motion target.

4.Simulations

To furtheranalyze the effectofthe proposed jamming idea, a computer simulation is presented in this part.The main radar parameters are listed in Table 1 and the scattering parameters ofthe targetare listed in Table 2.The range between the targetand the radar is 10 km and the rotational angularvelocity of the targetis 0.8π/s.

Table 1 Simulation parameters

As shown in Table 2,the target is a plane with about 1 m in wingspan and 2.2 m in length.The ISAR image of the plane is illustrated in Fig.4.Itwillbe used as the target simulation modelin the following simulations.

Table 2 Scattering parameters of the target

Fig.4 ISAR image

4.1 Micro-motion jamming with differentωP

Suppose that the jammer is located in the center of the plane,and the rotational radius of the simulated micromotion point is rP=0.03 m,based on(15),we can calculate that the jamming pulse number is about 4.According to the above analysis in Section 3.1,the jamming effectwillbe false targets whenωP＞2π/T as shown in Fig.5(a);When rP=0.12 m andωP=2π/T,the jamming pulse number is about 16 and turns to be cover jamming as shown in Fig.5(b).

Fig.5 Jamming effects with differentωP

4.2 Micro-motion jamming with differentturning radii

According to(17),the jamming coverage is decided by the product of the rotating speed and the radius of the simulated micro-motion point.Once the rotating speed is determined,different rotating radii of the micro-motion target willcause differentjamming coverages.Forexample,supposeωP=2π/T,Rjis 3.58 m when rP=0.12 m as shown in Fig.5(b),Rjis 2.24 m when rP=0.075 m as shown in Fig.6(a)and Rjis 5.37 m when rP=0.18 m as shown in Fig.6(b).

Itcan be seen thatin Fig.5(a),the jamming coverage is smaller than the other two figures,but its jamming power is stronger.This can be explained by the analysis in Section 3.2.Thus,we should choose a suited rPwhich is not too large thatthe jamming power is weakened and not too smallthatthe jamming coverage is insufficient.

Fig.6 Jamming effects with different turning radii

4.3 Micro-motion jamming in two-dimensionalimageCombined with the coherent jamming methods in downrange,we can obtain the two-dimensional jamming effects.Many methods are available such as noise weighed frequency modulation jamming,pulse weighted frequency modulation jamming,and sawtooth weighted frequency modulation jamming.No matter which method is chosen, it plays a role thatit moves our micro-motion jamming to different down-range.Thus the jamming effects will turn from one-dimensional in cross-range of above figures to the two-dimensionalones in Fig.7.

As we can see from Fig.7,both false-target jamming and cover jamming have been obtained.From the analysis in Section 3,we can control the jamming type,the jamming number and the jamming coverage area by setting differentωP,rPand their product.

Fig.7 Jamming effects in two-dimension image

5.Conclusions

A new method for countering ISAR is proposed in this paper.Based on the theory of micro-motion modulation, radar signals are sampled and frequency-modulated by sinusoidalsignals along azimuth,then retransmitted as jamming signals and collected by ISAR.According to differentrotating speeds ofthe assumed micro-motion scattering point,the deception or cover jamming can be produced. The number of false points is decided by the rotating radius,and the jamming coverage is decided by the product of the rotating speed and the radius of the micro-motion target.The work of this papercan be developed to provide a noveltransponderjamming which can replace the conditionalcorner reflector.

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Biographies

Yu Zhangwas born in 1979.She received her B.S., M.S.and Ph.D.degrees from Xidian University,in 2001,2004 and 2009,respectively.She is currently an associate professor at Xidian University.Her research interests focus on the radarimaging and jamming methods againstimaging radar.

E-mail:zhangyu@mail.xidian.edu.cn

Congfeng Liuwas born in 1973.He received his B.S.and M.S.degrees from Electronic Engineering University,in 1996 and 1999 respectively,and received the Ph.D.degree from Xidian University in 2008.He is currently an associate professor at Xidian University.His research interests focus on the applications of the signal processing on radar, communication and microphone speech processing.

E-mail:cfliu@mail.xidian.edu.cn

YanZhuwas born in 1980.She received her B.S., M.S.and Ph.D.degrees from Xidian University,in 2002,2005 and 2012,respectively.She is currently a lecturer at Xidian University.Her research interests are the applications of the signal processing on radar and communication.

E-mail:yzhu@mail.xidian.edu.cn

10.1109/JSEE.2015.00079

Manuscript received April 10,2014.

*Corresponding author.

This work was supported by the Fundamental Research Funds for the Central Universities(K50511020024).