Simulation oftwo-dimensionalISAR decoys on a moving platform

State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System, National University of Defense Technology,Changsha 410073,China

Simulation oftwo-dimensionalISAR decoys on a moving platform

XiaoyiPan*,WeiWang,Qixiang Fu,Dejun Feng,and Guoyu Wang

State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System, National University of Defense Technology,Changsha 410073,China

It is potentially useful to perform deception jamming using the digital image synthesizer(DIS)since it can form a two-dimensional(2D)decoy but suffers from multiple decoys generation.Inspired by the intermittent sampling repeater jamming (ISRJ),the generation of inverse synthetic aperture radar(ISAR) decoys is addressed,associated with the DIS and the ISRJ.Radar pulses are sampled intermittently and modulated by the scattering model of a false target by mounting the jammer on a moving platform,and then the jamming signals are retransmitted to the radar and a train of decoys are induced after ISAR imaging.A scattering model of Yak-42 is adopted as the false-target modulation model to verify the effectiveness of the jamming method based on the standard ISAR motion compensation and image formation procedure.

inverse synthetic aperture radar(ISAR),digitalimage synthesizer(DIS),intermittentsampling,decoys.

1.Introduction

The inverse synthetic aperture radar(ISAR)imaging can yield a high-resolution intensity image of moving targets such as aircraftand ships[1-4].ISAR imaging plays an important role in many military applications,such as feature extraction,target classi fi cation,and recognition and identi fi cation of noncooperative targets[5-9].Surveillance systems such as the ALCOR radar[10],the ground based radar(GBR)[11]and the AN/APS-137B(V)radar [12]possess the capability of detecting and classifying by coherently processing the received echoes of transmitted pulses in the ISAR imaging mode.The ISAR image is characterized by high resolution along both the downrange and cross-range directions which can also be applied to launch weapon systems[12].

The need for generating one-dimensional(1D)or twodimensional(2D)imaging decoys to counter wideband imaging radars(ISAR/SAR)remains a high priority for many electronic warfare systems[13-16].Decoys can be produced by using the acoustic charge transport(ACT) tapped delay lines which are no longer commercially available and also with a limited bandwidth.Anothertechnique to form decoys is based on the fi bre-optic which is also bulky and costly[17].The digitalradio frequency memory(DRFM)is widely used in the radar active coherent jamming[18-22].With the capability of high speed sampling,the DRFM reduces production costs and achieves a wide bandwidth.Based on the DRFM technique and the digitalimage synthesizer(DIS),Pace et al.provides a solution to forming a false-targetimage ora two-dimensional (2D)decoy by digitalmodulation on the phase samples in both amplitude and phase[12,23,24].But the chirp phase samples in the synthesizerare processed on the assumption thatthe platform with a jammer is static.In the real-world scenario,the platform with a jammer which is the common self-screening jamming(SSJ)geometry,is frequently moving.Furthermore,the DIS modulation suffers from the complexity of generating multiple decoys[25].Multiple decoys are potentially useful against the radar in two aspects.First,the scattering information is revealed and utilized to deceive the target identi fi cation;second,multiple decoys can increase the cost burden and waste the fi nite resource of the radar for recognizing the realone.

The theory of Shannon sampling theorem has indicated thata signalcan be recovered exactly from measurements uniformly and totally sampled by an analog-to-digitalconverter(ADC)whose sampling frequency is no less than twice of the bandwidth of the signal[26].Thus,a high quality ADC is extremely needed to achieve the optimal reconstruction of the broad-band radar signal which may become practically infeasible.Another problem is thatthe jamming signals are at least lagged one pulse-width than the target echoes in the SSJ scenario[27].Actually,thereis no need for a jammer to sample the radar signalat such a high rate since the purpose of the jammer is not to reconstruct it but to interfere it.Inspired by this characteristic of sampling,the intermittent sampling repeater jamming(ISRJ)is presented and developed based on a receivetransmit time-sharing antenna[27-29].The ISRJ reduces the time delay of retransmitting so that the preceded false point scatterers can be induced.The high isolation of the two receive-transmit antennas is also conquered since the IRSJ is based on a receive-transmittime-sharing antenna. The transmitted pulses are sampled intermittently by the jammer and among each intermittentsampling intervalthe samples are retransmitted to the radar.A setof pointscatterers are induced after the de-chirping or matched fi ltering.However,the ISRJ can only introduce false pointscatterers but notfalse-target images where each point spread function(PSF)is a scaled sinc function[29].Since the ISAR is a technique of reconstructing a 2D intensity image of moving targets,a jamming method that can imitate 2D decoys is extremely needed.

In this paper,the generation of 2D decoys from a series ofintercepted ISARchirp pulses based on the DIS and the ISRJ is concerned.There are two basic questions to be answered when the jamming signals are collected by the radar:fi rstly,whathappens after the motion compensation and;secondly whathappens after the imaging.The restof this paper is organized as follows.The signalmodelof the jamming signalis derived in Section 2.Section 3 is dedicated to the image formations of the jamming signals.Section 4 analyses the characteristics of the induced decoys. The simulation results based on a pointscatterer modelare shown in Section 5,in which the high resolution range profi le(HRRP)after motion compensation and the generated decoys are demonstrated.Finally,in Section 6,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 as

Assume thatthe intermittentsampling signalis a rectangular envelope pulse train with pulse durationτand pulse repetition interval(PRI)Ts,as illustrated in Fig.1.The sampling signalhas a form as[26]

whereδ(.)is the impulse function and?denotes the convolution processing.

Fig.1 Intermittent sampling pulse series

Suppose thatthe jammeris mounted on the moving platform,which is commonly known as the SSJ scenario.The geometry ofthe radar,the moving platform and the jammer are shown in Fig.2.The radarcoordinate system is denoted as UOV.The platform coordinate system xoy is embedded on the moving platform,its origin is at the geometric center o,and its x-axis is the heading direction of the platform.To describe the rotation motion of the platform,new reference coordinates XoY,which are transformed from the radar coordinates UOV and with the origin atthe geometric centerof the platform,are introduced.

Fig.2 Geometry ofthe radar and the moving platform

Suppose thatthe platform,e.g.a pilotless aircraft,fl ights with a velocity v and the radialvelocity is vy.Attime t,the electromagnetic wave from the radar goes through the distance Rloswhich is the distance from the radar to the jammeron the lightofsight(LOS),and then arrives atthe jammer which locates at(X0,Y0)in XoY coordinates when t=0.Then according to the‘stop-go’motion model,Rlossatis fi eswhere R0indicates the initial position of o,d0=is the distance of the jammer from the geometric center of the platform andθ0=arctan(Y0/X0)is the initialrotation angle of the jammer.

Once the jammer receives the ISAR transmitted signal, itsamples the pulse intermittently.Take the radartransmitting signal’s time as the starting time,and then the unit amplitude intermittently sampled signalcan be written as

where c is the propagation velocity of the electromagnetic wave,anddenotes the time consumed for propagation.

After the radar signal is intermittently sampled by the jammer,a false-target model is utilized to modulate the samples.The point-scatterermodelis usually used in radar imaging to modelthe radarsignalscattered by a man-made target.Assume thatthe false-targetmodelincludes N point scatters located atdifferent(xi,yi)in the xoy coordinates with complex scattering coef fi cientσi(i=1,2,...,N). The modulated jamming signalcan be represented as a sum of point-scatterers responses

where rilosrepresents the range between the projection on LOS ofthe pointscatterer i and the imaging center o.After the standard motion compensation,we have

Then the platform motion can be described by the circularmotion with angularvelocityω(rad/s)around the imaging center o.In orderto getthe same cross-range resolution of the real targetimage,the false-targetmodelis assumed static with respect to the platform which means that rilosin the slow time should satisfy

in a smallaccumulation angle.So after motion compensation,(5)can be represented as From(8),the modulated jamming signal is obtained.An analysis of the jamming effects after ISAR imaging follows.

3.ISAR image formations

For a wideband LFM signal,dechirping processing is an acceptable method to achieve a high resolution range profi le(HRRP)[30].Letthe reference range be Rref,then the jamming signals after dechirping and omitted the residue video phase(RVP)can be expressed asis the intermittent sampling rate and D=τfsdenotes the duty ratio of the intermittent sampling pulse.According to the principles of intermittent sampling and retransmitting,itis obvious that D∈(0,0.5] [26,27].The 1D down-range pro fi le can be constructed by Fouriertransforming as

where B is the bandwidth of the LFM signaland r‖is the down-range cell.Using the small accumulation angle assumption,the Doppler frequency of the pointscatterer i is given as

Suppose that no migration through range cell(MTRC) occurs during the imaging time,and then the false-target image in the RD plane of the ISAR can be obtained by taking the 2D FFT

where TMis the imaging time.

It means that after the intermittently sampled and modulated jamming signal is retransmitted to ISAR,a set of false-target images(i.e.2D decoys)are induced along the down-range direction.Each n represents a decoy and is de fi ned as the n th decoy.Alldecoys are multiple copies of the false-target model in the DIS and distributed in differentrange cells.The false-targetimages hold the information of the false-targetmodel such as civil targets,so that the ISAR may recognize each decoy as a realtargetbutbe militarily insensitive or cost a huge calculation burden to distinguish the realtargetimage from multiple false-target images.At last,the decision to engage the target may be hard or delayed to make.

4.Analyses and discussions

4.1 Amplitude modulation coefficient

The amplitude modulation coef fi cient of the n th falsetargetimage is

which can be extracted from(13)directly.Note that sinc(nD)=0 when

For a de fi nite D,the amplitude of the n th false-target image is zero when n satis fi es sinc(nD)=0.Thus,the n th decoy is notvisualin the ISARimage plane.Forexample,when D=0.2,sinc(nD)is zero when n=5l,(l/= 0,l∈Z)and when D=0.5,then sinc(nD)is zero when n=2l,(l/=0,l∈Z)as shown in Fig.3.Usually,the bigger value of D,the bigger amplitude of D sinc(nD)at the same n exceptfor nD=l,(l/=0,l∈Z).

Fig.3 sinc(nD)of different D s

4.2 Position and number of false targets

According to(13),the distance of the two adjacent falsetargetimages in the down-range direction is given as

Itmeans thatΔr is directly proportionalto the intermittent sampling rate fsand inversely proportional to the chirp rate k.Consider a target taking up L‖in the down-range direction,then for a good discrimination of the two adjacentfalse-targetimages,Δr should satisfy

which means that

Ifthe imaging scene is L‖maxalong the down-range direction and neglecting the effect of invisible decoys,then the maximum number of false-targetimages is

5.Simulations

To furtherdemonstrate the effectofthe proposed jamming idea,simulations based on a realplane model(Yak-42)are presented in this section.Since Yak-42 is a civilplane and itcan be used as a militarily insensitive false-targetmodel to deceive the radar identi fi cation.Similarly,when militarily sensitive decoys are needed,other models such as Mig-25 can be also utilized as the modulation model.

Ablock diagram ofthe simulation is illustrated in Fig.4. The simulation mainly consists of three parts:the transmitted radarsignal,the intermittentsampling and the falsetargetmodulation,and the received signal.In summary,the procedure of the simulations is the following:

(i)Select radar parameters,i.e.carrier frequency,bandwidth,pulse width and pulse repetition frequency(PRF), etc.

(ii)Select platform motion parameters,i.e.initial location(X0,Y0),velocity vxand circular velocityω,and a false-targetmodulation model.

(iii)Transmit signalrepeatedly to the moving platform, update the platform location,sample the signal intermittently,modulate the samples with the false-target model and calculate received signals.

(iv)Arrange the received raw data into a two dimensional(range×pulse)matrix.

(v)Perform the standard motion compensation and image formation procedure and generate ISAR decoys in the range againstthe cross-range domain.

Fig.4 Block diagram of simulation

The main simulation parameters are listed in Table 1. The X-band radar is operating at10 GHz and transmitting an LFM waveform with a bandwidth of 1 000 MHz.A total of 512 pulses are transmitted,which provides a coherent image integration time of 0.512 s and the cross-range resolution of 0.16 m.The ISAR image consists of 1 024 range-cells and 512 Doppler frequencies.The range resolution is 0.15 m,so that L‖max=0.15?1 024≈154 m. The velocity of the platform is vx=200 m/s.

Table 1 Simulation parameters

As shown in Fig.5(a),the Yak-42 pointscatterer model with 35 m in wingspan and 37 m in length is utilized as the false-target modulation model in the following simulations.The ISAR decoy generated by the conventional technique of the DIS is illustrated in Fig.5(b)and L‖≈37 m.Itcan be seen thatthe decoy retains the information of the target but only one decoy can be obtained by the conventionalDIS technique.

Fig.5 False-target scattering modeland ISAR decoy based on DIS

5.1 Decoys of differentTs

In order to get a good discrimination of the two adjacent decoys,the intermittent sampling period should satisfy Ts≤0.41μs according to(18).

For the purpose of comparison,two different values of Ts=0.2μs,0.5μs and D=0.5 are adopted in the following simulation.Before the imaging procedure,a standard motion compensation including range alignmentand phase correction is applied to the signals[31].The HRRP before and afterthe standard motion compensation of Ts= 0.2μs are illustrated in Fig.6(a)and Fig.6(b),respectively. It can be seen that after the motion compensation,the signals are keptin its range cells.

Similarly,HRRP before and after the standard motion compensation of Ts=0.5μs are illustrated in Fig.7(a) and Fig.7(b),respectively.

Then perform the imaging procedure and ISAR decoys of Ts=0.2μs and 0.5μs are illustrated in Fig.6(c)and Fig.7(c),respectively.

The maximum number of decoys satis fi es Nmax=3 when Ts=0.2 s,and allthe false-targetimages are visual in the image plane as shown in Fig.6(c)since D=0.5. When Ts=0.5μs,Nmax=6 and the intensity of±2th decoys are relatively smallin the image plane as shown in Fig.7(c).For Ts=0.5μs＞0.41μs,the two adjacent false-target images are superposed in the down-range as depicted in Fig.7(c).

5.2 Decoys of differentDs

For the purpose of illustrating the amplitude of the falsetargetimages,we take two different D s into the simulation when Ts=0.2μs:i)D=0.25;ii)D=0.1.Simulation results are illustrated in Fig.8(a)and Fig.8(b),respectively.

Fig.7 Procedures of Ts=0.5μs

According to(14),when D=0.25,the false-target images of n=4l,(l/=0,l∈Z)in the image plane are not visual for their amplitude modulation coef fi cient is zero. When D=0.1,the false-targetimages of n=10l are not visualcorrespondingly.Since the values of Tsare the same in the two simulations,the maximum number of decoys satis fi es Nmax=3.Allfalse-targetimages can be seen in the simulations.Note thatalthough the maximum numbers of false-target images in the two simulations are equivalent,butthe intensity of the false-targetimages are notthe same as shown in Fig.8(a)and Fig.8(b).The smaller the value of D is,the smaller the intensity is as indicated by the decoys in Fig.8,which is in accordance with the theoreticalanalysis in Section 4.1.

Fig.8 Decoys ofdifferent D s

5.3 Decoys of different JNRs

In a more realistic scenario,the noise will also be received by the ISAR.To characterize the performance ofthe jamming idea,we add the Gaussian distributed complex noise with different jamming-to-noise ratios(JNRs)into the jamming signal.The simulation results with three different JNRs(2 dB,0 dB,and-2 dB)are depicted in Fig.9 while Ts=0.2μs and D=0.5.

Fig.9 Decoys of different JNRs

Itcan be noted thatarti fi cialpoints increase and scattering centers of the false-target images are missing with the decrease of the JNR,as shown in Fig.9.The simulation results qualitatively imply that the false-target images induced by the jamming signals are similar to the realtarget image.

6.Conclusions

A method to generate 2D decoys on a moving platform for countering the ISAR is proposed in this paper.Based on the intermittent sampling,multiple false-targetimages (i.e.2D decoys)are formed after the radar signal samples modulated by a false-target model are retransmitted and collected by the ISAR.The duty ratio in fl uences the intensity of the decoys while the intermittent sampling period affects the position.In orderto keep the two adjacentfalsetarget images distinguished,the intermittentsampling period should be chosen properly.The work ofthis papercan be developed to provide a novel RF decoy capability.

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Biographies

Xiaoyi Pan was born in 1986.He received his M.S.and Ph.D.degrees in information and communication engineering from the National University of Defense Technology,Changsha,China,in 2009 and 2014,respectively.Currently,he is a lecturer with the National University of Defense Technology.His fi elds of interest include inverse synthetic aperture radar imaging and electromagnetic environment effects.

E-mail:pan xiao yi@hotmail.com

WeiWang was born in 1970.He received his Ph.D. degree in information and communication engineering from the National University of Defense Technology,Changsha,China,in 2003.Currently,he is a professor with the National University of Defense Technology.His fi elds of interest include radar target detection,signal processing,target recognition and electromagnetic environment effects.

E-mail:13807319968@139.com

Qixiang Fu was born in 1980.He received his M.S. degree in information and communication engineering from the National University of Defense Technology,Changsha,China,in 2003,where he is currently working towards his Ph.D.degree.He is also a lecturer with the National University of Defense Technology.His fi elds of interest include radar system,radar engineering,and signalprocessing.

E-mail:kdfuqixiang@126.com

Dejun Feng was born in 1972.He received his Ph.D.degree from the National University of Defense Technology,Changsha,China,in 2006.Currently,he is an associate professor with the National University of Defense Technology.His fi elds of interest include radar signal processing,radar system simulation and inverse synthetic aperture radar.

E-mail:fdj117@sina.com

Guoyu Wang was born in 1962.He received his Ph.D.degree in information and communication engineering from the National University of Defense Technology,Changsha,China,in 1999.Currently, he is serving as a professor at the National University of Defense Technology.His fi elds ofinterestinclude signalprocessing,radarsystem simulation and electromagnetic environmenteffects.

E-mail:nudtgzs@gmail.com

10.1109/JSEE.2015.00030

Manuscriptreceived June 01,2013.

*Corresponding author.

This work was supported by the National Natural Science Foundation of China(61372170;61401491).