Security information factor based airborne radar RF stealth

1.College of Electronic and Information Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China; 2.Schoolof Electronics,Electrical Engineering and Computer Science,Queen’s University Belfast,Belfast BT7 1NN,UK

Security information factor based airborne radar RF stealth

FeiWang1,2,*,MathiniSellathurai2,Weigang Liu2,and Jiangjiang Zhou1

1.College of Electronic and Information Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China; 2.Schoolof Electronics,Electrical Engineering and Computer Science,Queen’s University Belfast,Belfast BT7 1NN,UK

Radar radio frequency(RF)stealth is very important in electronic war(EW),and waveform design and selection.Existing evaluation rules of radar RF stealth include too many parameters of radar and interceptors,such as Schleher interception factor, which makes it dif fi cult to evaluate radar RF stealth technologies ifinterceptor parameters are unknown.In communication,security capacity has been presented to describe the possible ability to communicate in complete security.Since the essentialofthe security capacity is to have the interceptor getnone valued information from the emitter,this paper is proposed to study security information factors taking advantage of mutual information to evaluate radar RF stealth undersome conditions.Through analyzing mutual information obtained by the radar and the interceptor,this paper de fi nes the security information factor with and withoutcooperative jamming.Furthermore,this paper deduces the ratio of the match fi lter to the match incoherent fi lter and discuss mutualinformation received by the interceptor.Numerical simulations illustrate radar RF stealth effects based on the security information factor concept under different conditions.

mutualinformation,radar signal,stealth.

1.Introduction

The stealth technology is used to avoid being detected by a variety of detection devices.As radar cross section(RCS) and acoustic stealth are against active radar and passive acoustic detection,radar radio frequency(RF)stealth is againstpassive radar detection[1,2].Radar RF stealth not only depends on transmitpower,butalso relies on realparameters of the passive radar detector which is probably driven by economics and operationalfactors.

To survive the more and more serious challenge of advanced interceptors,many complicated low probability interception(LPI)signals are presented[3-5].However,the quick appearance of high performance interceptors has made many LPI signals unfashionable.For example,the channelized receiver could improve the sensitivity to about 20 dB by dividing the instantaneous frequency bandwidth of 2 GHz into a great number of narrow channels of 10 MHz.In any practicalscenario,the common wide band radarsignalhas no valuable advantage when itis facing the instantaneous channelized receiver even though the channelized receiver needs to put data from adjacent channels togetherif they are from a single radarsignal.On the other hand,the super heterodyne receiver is a high gain narrowband interceptor which is suitable for emitter identi fi cation,and often used to search for speci fi c radar type.With enormous parallel processors,the matched incoherentreceivercould yield abouta sensitivity of 10 d B on the channelized receiver,which would carry out matched fi ltering in a number of channels to combat a number of potential threats simultaneously[6].

Evaluation ofradar RF stealth has drawn much attention for several decades[7].The basic standard is to compare the maximum detection range of the radar and the interceptor,which is the principle of the intercept factor.If the radar signal detection range is larger than that of the interceptor,we tend to think that the radar signal has good RF stealth performance.Wu and Dishman studied signal power stealth performance in the special battle scenario, which relied on the average radius of beam-forming technology[8,9].And Fancey proposed a complicated metrication through comparing peak values,bandwidth and shrewdness of a great many LPI signals,which depended on the prior experience knowledge of the RF stealth strategy[10].

The information theory is the base stone of communication and radar.In communication,security capacity only considers the channel information without any relation with hardware and software technologies[11].Similarly,we propose a security information factor coming from mutualinformation to describe radar RF stealth without knowing the detail of the interceptor.Bell established the relationship between mutualinformation and radarsig-nals using the differential entropy theory[12],which has been generally applied to radar waveform design[13-15]. To develop Bell’s theory,under different conditions,such as in incoherent pulses,coherent pulses and cooperative jamming states,we presenta security information factor to evaluate radar RF stealth through comparing mutualinformation got by the radar and the interceptor,respectively. Meanwhile,we analyze mutualinformation loss of the interceptor with the match incoherent fi lter.

The rest of the paper is organized as follows.Section 2 introduces mutualinformation and presents security information factors with and withoutcooperative jamming,and deduces the ratio of the match fi lter to the match incoherent fi lter.Section 3 illustrates our opinions with numerical simulations.

2.Security information factor for radar RF stealth

The system modelto be discussed is shown in Fig.1,where the targetand the interceptor are all within the radar main beam.The co-operatormain beam points to the interceptor and its leakage power is neglected.

Fig.1 Classicalcooperative jamming scene for radar RF stealth

We de fi ne the Fourier transform(FT)of radar transmission signal x(t)by X(f)and the target RCS byσf,the radarreceive signalby y(t)and the interceptorreceive signal by z(t).We next discuss mutual information between (i)radar transmission antennas and receiver antennas;(ii) radartransmission antennas and interceptorantennas,with and withoutco-operatorjamming.

With Bell’s information theory,we have the following assumptions:

Assumption 1The noise is additive Gaussian white noise.

Assumption 2

where xk(t)are random variables with zero mean and Gaussian distribution.Frequency components of xk(t)are con fi ned to Fk=[fk,fk+Δf],and FT of xk(t)is approximately constant.xk(t)and xj(t)are uncorrelated if k/=j.Itis the same for y(t)and z(t).x(t),y(t)and z(t) use the same sampling interval.

Assumption 3Allantenna loss and path loss are negligible,and only the noise fl ooris considered.Radarreceiver and interceptor receiver noises are expressed as nr(t)and ni(t)respectively,and they have the same properties of Assumption 1.

According to the mutual information equation,mutual information of xk(t)and zk(t)is

where h denotes entropy.Since the variance of xk(t)and

Because the conditional probability density function f[zk(t)|xk(t)]=f[nik(t)],we have

Then,the mutualinformation in(1)can be formulated as

Δf is the length of the frequency bin.Hence,of each sample is expressed as:

where Tris the signal duration time.Similarly,the noise power would be

where Tiis the process time ofthe interceptor.Substituting (6)and(7)into(4)yields

For there are 2Δf Tistatistically independentsamples, then,

If the antenna gain is taken into consideration,mutual information Iintbetween radartransmission antennas and interceptor antennas is over the frequency bandωi,thatis,

Similarly,we have mutualinformation Irecbetween the radartransmission antenna and the receiverantenna as

where Wrand Wiare effective bandwidths of the radar receiver and the interceptor respectively,pnnr(f)and Pnni(f)are radar receiver and interceptornoise power,Trand Tiare effective process time of the radar receiver and the interceptor,Gtis the radar transmission gain,Gris the radarreceiver gain,Gtiis the gain from the radartransmitter to the interceptor,Giis the interceptor antenna gain, Lr(Rri)is the attenuation from the radar to the interceptor and Lr(2Rr)is the attenuation from the radar emitter to the targetand then to the radar receiver.Equations(10) and(11)represent mutual information at the antenna port without any signal processing procedure.Meanwhile,as post-processing cannot increase mutual information with the data processing inequality principle,(10)and(11)are the maximum mutual information obtained by the interceptor and the radar receiver in fullidealconditions while Wr=Wi.

From(10)and(11),it is easy to take some Trand Wrto make(11)larger than(10),which shows thatthe larger the time bandwidth product,the more the mutualinformation.Traditional fi ghter pulse Doppler radar usually transmits many short pulses whose widths are often from 1μs to 3μs,to get the information gain and measure the target speed.As the fi ghteris a greatthreat,the warning interceptoris always designed to pay attention to this type ofsignal so thatwe could assume that Tr≈Tiand Wr≈Wi.

What’s more,in a modern battle fi eld,an electronic jammeris indispensable to keep the fi ghterin radar RF stealth. With Tr=Tiand Wr=Wi,if there is cooperative jamming,we could modify(10)and(11)as

where Pnncis the cooperative jamming power,Gcrand Gciare the antenna gain from the co-operator to the radar receiver and the interceptor.Gicis the antenna gain from the interceptor to the co-operator.Lc(Rci)is the cooperative path loss to the interceptor and Lc(Rct+Rr)is the pass loss to targetplus targetto the radar receiver.

Now,we have expressions from(10)to(13)to express the maximum mutual information of radar transmission antennas and receiver antennas,radar transmission antennas and interceptorantennas,with and withoutco-operator jamming.We de fi ne security information factor Isas

whereρrandρirepresent the minimum mutual information needed by the radar receiver and the interceptor to trigger their following signal processing procedure.And ρrΔ=TrWrln(1+SNRr/Wr),ifρr=ρi,we could rewrite(14)as which is similar to the de fi nition of security capacity in communication.The difference is that(15)takes radartask ρrinto consideration because the radarmust fi nish the task in limited time.And Is≥1 means that radar RF is in a completely safe state while fi nishing the task.In communication,if the security capacity is greater than zero,then there is a maximum transmission rate for the current scenario.Meanwhile,an eavesdroppercannotgetthe information more than the source entropy.Similarly,under specifi ed airborne radar detection probability and false alarm probability,if Is≥1,then in the current scenario,with powercontrolorlarge bandwidth waveform design,the detection probability ofthe interceptorcould be less than 0.5. If the limit of the detection probability of the interceptor can be relaxed,(15)may also be relaxed.

In a realscenario,the radar receivercould obtain mutual information presented in(10)and(13)through the match fi lter and the interceptor has less opportunity to have a match fi lterprocess.So we would discuss the mutualinformation loss resulted from the match incoherent fi lter pro-cess and then modify Iint.

For the match incoherent fi lter,we assume that the frequency spectrum of zk(t)intercepted by the interceptor is

where zk(t),xk(t)and nik(t)are de fi ned in(1),(2)and (3).The output of the match incoherent fi lter of the frequency bin fkwould be

Then,the signalto noise ratio(SNR)of(17)is

As the output SNR of the match fi lter of frequency bin fkis|X(fk)|2/|Ni(fk)|2,we could modify(10)and(12) from the match fi lter to the match incoherent fi lter,which become

Usually,the radar receiver could accumulate target information through the incoherentintegration of echoes of multiple pulses,but the interceptor has little chance to accumulate radar RF information because itshould fi rstly tell if any two pulses are from the same radar.That is,if the radar transmits Npincoherent pulses,the radar receiver could improve targetinformation by accumulating Npmutualinformation and the interceptor never can.Then,with Npincoherentpulses shown in Fig.2(a),we could rewrite (15)as

Fig.2 Accumulation gain of incoherent and coherent pulse train

Fig.2(b)also shows the equivalent pulse of coherent pulse train[16],and A=|X(f)|so thatwe could rewrite (11),(13)and(21)as

This paper just pays attention to discussing the security information factor on ideal antennas with match fi lters or incoherent match fi lters.And the information loss caused by signal processing arithmetic will be studied in the future.

3.Numericalsimulations

With(10)to(15),(19)to(24),we would discuss radar RF stealth with changing parameters,such as bandwidths, match fi lters,coherent integration and co-operative jamming power.

(i)We de fi ne typicalradar parameters as follows:

Antenna gain:Gt=Gr=Gti=30 dB;required detection SNR:SNRr=101.5,ρrΔ=TrWrln(1+ SNRr/Wr);pulse width:Tr=1μs;number of pulses: Np={64 1 024 2 048 4 096};bandwidth:Wr= {1 10 100 200}MHz;noise fl oor:Pnnr(f)= Wr·10?17.4 W.

(ii)We de fi ne typicalinterceptor parameters as follows:

Antenna gain:0-60 dB;instantfrequency bandwidth:

WIF=2 GHz;noise fl oor:Pnni(f)=WIF·103· 10?17.4W;effective bandwidth:Wi≤200 MHz;process pulse width:Tr=Ti=1μs.

(iii)Other parameters are de fi ned as follows:

Target RCS:σf=1 m2,Gcr=0 dB,Gci=10 dB, Gic=-30 dB,Δf=1 MHz.Lcand Lrhave the same attenuation and the attenuation factor is 0.012 6 dB/km when the carrier frequency is 10 GHz.

In simulation fi gures,the common terms‘suboptimal’and‘optimal’represent the interceptors taking the match incoherent fi lter and the match fi lter,respectively.Vertical coordinate of Fig.3 to Fig.6 is the value of Is.

In Fig.3,with(10),(11),(15)and(19),we set Np=1 and the interceptor gain as 0 dB,which are common in some radar warning receiver.The target and the interceptorare atthe same place.Both the radarand the interceptor have the same effective bandwidth.Fig.3 shows thatradar RF could be stealth in alldistances if the radar only offers the minimum information required by the radar receiver. This is because the sensitivity of the interceptor is lower than that of the radar by 30 dB,and the receive antenna gain of the interceptor is also lower than that of the radar by 30 dB.

Fig.3 Radar RF security information factor when Np=1 and interceptor gain is 0 dB

In Fig.4,with(10),(11),(19),(21),(22)and(24),we set Np=64 and the interceptor gain as 60 dB,which are common in some electronic signalintelligence system. Both the radar and the interceptor have the same effective bandwidth.The target is at 80 km and the interceptor is gradually away from 80 km to 500 km.Fig.4 shows that a large bandwidth is not always bene fi cialif the interceptor has the same effective processor bandwidth.The left graphics of Fig.3 are from(21)and the rightfrom(24).

Fig.4 Security information factor when Np=64 and interceptor gain is 60 dB

In Fig.5,the target and interceptor parameters are the same as in Fig.4.Fig.5 shows that incoherent integration ofnarrow band pulses is an available method to realize radar RF stealth.

Fig.5 Security information factor with different incoherent integration lengths of the interceptor

In Fig.6,with(10),(11),(19),(21),(22)and(24),we setthe interceptorgain as 60 dBand its effective bandwidth as 20 MHz,which are common in some super heterodyne receiver.The targetand interceptor distances are the same as those in Fig.4(a).Fig.6 shows that radar RF stealth contributed by large bandwidths depends on the processor bandwidth of the interceptor.

Fig.6 Security information factor with fixed interceptor bandwidth

Fig.7 shows cooperative jamming power Pnncto full ideal interceptor with(20),(22)and(23)when the target is at80 km and the interceptor is gradually away from 100 km to 520 km.As Gcr=0 dB,Rci=Rri,and other parameters are the same as those in Fig.4(a),cooperative jamming is abouta constantfor differentsignal bandwidths.This fi gure also shows that the narrow bandwidth signalis better if the radar is facing the bestinterceptor.

Fig.7 Cooperative jamming power for signalstealth

From Fig.3 to Fig.7,we could get some important information:

(i)Radar power control is the fi rst key for radar RF stealth.All fi gures from Fig.3 to Fig.7 have radar power controlled.

(ii)Coherent integration of the pulse train has greater gain than thatof incoherentintegration,as Fig.5 shows.

(iii)Using wideband radar to cope with the narrow interceptoris feasible,as Fig.6 shows.

(iv)Using wideband radar to cope with the intelligent wideband interceptor should be prudent,as Fig.4 shows. An alternative way to cope with the wideband interceptor could be with cooperative jamming,as Fig.7 shows.

(v)A feasible approach for RF stealth is to make thebandwidth of electronic support measurement as large as possible while let the bandwidth of radar signal bandwidth be as smallas possible.For example,radar may emit agile hopping narrowband coherentpulse signals while the hopping range of the carrier frequency should be as large as possible.

(vi)Taking an interference waveform which is orthogonal to the radar signal.The narrower the bandwidth of the interference waveform,the less energy emitted by the jammer.The interference waveform also should be designed with the same carrier frequency and the same band as the radarsignal.

4.Conclusions

With the proposed security information factor,this paper shows thata large radarbandwidth sometimesmay be awkward if the intelligentinterceptorhas enough bandwidth to cope with radar RF signals.Strictly radar power control and mutualinformation integration of large sums ofpulses mightbe two ofthe bestways for radar RF stealth with low cost.And cooperative jamming is also a feasible method to cope with specialexpensive intelligentinterceptors.

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Biographies

Fei Wang was born in 1976.He received his B.S. degree in power engineering from Hohai University,Nanjing,China,in 1998.He received his M.S. degree and Ph.D degree in signal processing from Jilin University,Changchun,China,in 2003 and 2006,respectively.His research interests include fundamental signal processing and airborne radar signalprocessing.

E-mail:wangxiaoxian@nuaa.edu.cn

MathiniSellathurai was born in 1973.She received her Licentiate degree from Royal Institute of Technology(KTH),Stockholm,Sweden in 1997 and Ph.D.degree from McMaster University,Hamilton, Canada in 2001.Herresearch interests include array and adaptive signal processing applied to radar and wireless communications.

E-mail:M.Sellathurai@hw.ac.uk

Weigang Liu was born in 1985.He received his B.S.degree in engineering from Wuhan University of Technology,Wuhan,China,in 2008,and M.S. degree in engineering from Chongqing University, Chongqing,China,in 2011.He is currently working toward his Ph.D degree in the Institute of Digital Communication(IDCOM),University of Edinburgh,Edinburgh,UK.His research interests include cooperative communication,convex optimization,stochastic geometry,and physicallayer security in wireless communications.

E-mail:W.Liu@ed.ac.uk

Jianjiang Zhou was born in 1962.He received his B.S.degree in radar engineering from Aeronautics College of Nanjing in 1985,and M.S.and Ph.D. degrees in communication and information system from Nanjing University of Aeronautics,Nanjing in 1988 and 2001.He is a professor in the Departmentof Electronic Engineering,Nanjing University of Aeronautics and Astronautics.His research interests include radar signal processing and radar automatic target recognition.

E-mail:zjjee@nuaa.edu.cn

10.1109/JSEE.2015.00031

Manuscriptreceived October 27,2013.

*Corresponding author.

This work was supported by the National Natural Science Foundation of China(61371170)and the Priority Academic Program Development of Jiangsu Higher Education Institutions.