RESEARCH Open Access

Efficient filter design against interruptedsampling repeater jamming for widebandradarWei Xiong1,2, Gong Zhang1* and Wenbo Liu3

Abstract

Interrupted sampling repeater jamming (ISRJ) is an effective coherent jamming, which can induce false high-resolutionrange profile (HRRP) and image to greatly complicate the target detection and recognition of wideband radar. To counterISRJ, an efficient filter is designed based on the time-frequency (TF) characteristic differences between target echo andISRJ. Meanwhile, a feasible jamming suppression scheme is proposed, which not only could eliminate ISRJ but also couldreserve the target echo. The main emphasis is that the received echo suppressed by our scheme is similar with the truetarget’s HRRP on the basis of high correlation coefficient (CC) and large signal-jamming-to-noise ratio (SJNR)improvement factor. Simulation results are covered to illustrate the feasibility and validness of jamming suppression.

Keywords: Interrupted sampling repeater jamming (ISRJ), Wideband radar, Jamming suppression, Time-frequencycharacteristics

1 IntroductionConsiderable attention has been paid to the electromag-netic jamming and anti-jamming for radar system in theelectronic countermeasure (ECM) community over thepast two decades [1–5]. To prevent or complicate theradar target detection and recognition, much work hasbeen done on the jamming techniques, especially somenew jamming tricks that appear to counter the widebandradar system, such as the interrupted sampling repeaterjamming (ISRJ) [1–9], false-target digital image synthesizer(DIS) [10–12], and scatter wave jamming (SWJ) [13–15].As a coherent repeater jamming, ISRJ firstly proposed byWang et al. [1] can induce a train of false targets after thepulse compression (PC) without completely sampling andstoring the whole radar pulse. The method can be used bya digital radio frequency memory (DRFM)-based repeaterjammer and has received growing attention from ECMcommunity for its excellent jamming performances and ad-vantages. Wang et al. [1] analyzed the relationship betweenISRJ’s parameters and jamming effects. Besides, the time-

domain, frequency-domain, and amplitude characteristicsof ISRJ-based false targets were described in [2]. The in-duced false targets make it more difficult to detect andrecognize the true target. Moreover, the jamming signalcould cancel the echo of true target. Feng et al. [4] exploredthe three conditions that should be met for the cancelationof target echo, including the repeater power, delayed time,and repeater frequency. Moreover, since the false targets in-duced by ISRJ always contain the phase variation informa-tion for cross-range resolution, the jamming trick also hasbeen employed to generate two-dimensional false imageand has showed its potential against radar imaging [5–9].Wang and Cai [5] proposed the intermittent sampling jam-ming to counter the bi- and multistatic synthetic apertureradars (SARs). To counter the inverse SAR (ISAR), a sub-Nyquist sampling jamming was proposed with the com-pressive sensing (CS)-based reconstruction algorithm [6].Meanwhile, Pan et al. [7] investigated a CS-based matchedfiltering algorithm and applied it to the high-resolutionrange profile (HRRP) reconstruction of sub-Nyquist sam-pling jamming. In view of the induced false HRRP andimage, ISRJ provides a complex countermeasure against thewideband radar to detect and recognize target.Fortunately, several anti-jamming techniques have been

well studied to counter the repeater jamming [15–18].

* Correspondence: gzhang@nuaa.edu.cn1Key Laboratory of Radar Imaging and Microwave Photonics, Ministry ofEducation, Nanjing University of Aeronautics and Astronautics, Nanjing211106, People’s Republic of ChinaFull list of author information is available at the end of the article

EURASIP Journal on Advancesin Signal Processing

© The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, andreproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link tothe Creative Commons license, and indicate if changes were made.

Xiong et al. EURASIP Journal on Advances in Signal Processing (2017) 2017:9 DOI 10.1186/s13634-017-0446-3

The very effective electronic counter-countermeasure(ECCM) for radar system is pulse diversity [16, 17], whichis often adopted to combat the DRFM-based repeater jam-mer. However, to the best of our knowledge, most strat-egies are designed for the whole pulse sampling jammingincluding the pulse diversity, while the schemes for ISRJmight be fewer. Gong et al. [18] proposed an ECCMscheme to suppress the ISRJ for de-chirping ISAR and in-vestigated the suppression effects for single point target.However, the strategy was only based on the ISRJ modelof single point target, and the interrupted pulse sampleswere repeated once. The jamming suppression effects ondifferent orders, delayed time, jamming-to-signal ratio(JSR), and signal-to-noise ratio (SNR) were not consid-ered. Besides, suppression results were depicted but notevaluated. Moreover, the jamming suppression effect ofapproach I relies on the time width selection of frequencysmoothing window. Some jamming residue affects thesuppression performances.It is noticed that the target for wideband radar, which

is also called as extended target, is represented as aseries of scatterers instead of a single point. Comparedwith the ISRJ of single point target, the ISRJ of extendedtarget is more complicated followed with the target scat-tering. It is also essential to generate the false HRRP orimage against the wideband radar. In this work, we focuson the ISRJ against wideband de-chirping linear fre-quency modulation (LFM) radar, put forward an efficientfilter for the extended target on the principles of time-frequency (TF) characteristic differences via short-timeFourier transform (STFT). Compared with the previouscontributions [18], our work is proved to have the fol-lowing improvements. (1) The proposed filter expandsthe jamming suppression approach for the extended tar-get and is more suitable for the ISRJ against widebandradar. (2) The TF characteristic differences between tar-get echo and ISRJ are summarized and analyzed in de-tail. (3) We expand the analysis of jamming suppressioneffects on ISRJ with different orders, delayed time, dutyratio, JSR, and SNR. (4) Correlation coefficient (CC) andsignal-jamming-to-noise ratio (SJNR) improvement fac-tor are adopted to evaluate the jamming suppressionperformances. (5) The overall jamming suppressionscheme is depicted further. The designed filter not onlycould suppress the jamming and noise but also wouldreserve the target echo. Besides, the suppressed returnshave high HRRP similarity with the target echo. It isbeneficial for the target detection and recognition ofwideband radar.The remainder of our paper is structured as follows.

In Section 2, the principles of ISRJ are first introduced.Then, we describe the signal model of extended targetwith ISRJ in Section 3. Section 4 addresses the designedfilter. Meanwhile, two assessment factors of jamming

suppression are depicted and the overall suppressionscheme is proposed further. In Section 5, numerous sim-ulations have been carried out and simulation results arepresented, whereas conclusion is given in Section 6.

2 Principles of ISRJISRJ is apt to be carried out, and the jamming styleis feasible. The trick of ISRJ has been employed toconfuse the wideband radar and protect the importantmilitary target, such as the fighter, seeker, and otherair vehicles.As shown in Fig. 1, it is assumed that the radar and

escorted jammer are relatively stationary, the radar is lo-cated at O, the target is located at G decided by the vec-tor Rt , and the escorted jammer is located at J decidedby the vector Rj. The vector from the protected target tothe jammer is Rtj, and the included angle is denoted asα. Herein, the point-scatter model is usually employed tomodel a man-made target. Suppose that the target con-sists of Nt scatterers, and each scatterer is with the pos-ition (xi, yi), complex scattering coefficient βi, and vectorri, which is relative to the reference point of target. Thedashed arrow lines represent the paths of electromag-netic propagation. When the target is irradiated with thewideband radar wave, the target echo after scattering isfirstly intercepted, interrupted, and stored by a prepos-ition jammer. Then, the interrupted samples are re-peated once or several times and transmitted to theradar. Besides, the amplitude modulation is sometimesnecessary. Finally, the ISRJ and true target’s echo is allreceived by the radar receiver along the radar line-of-sight (RLOS).Let Nr denote the repeater times, which is also

called orders [2, 4]. Generally, there are three typesof repeater. They are direct repeater jamming, repeti-tive repeater jamming, and circular repeater jamming.As depicted in Fig. 2, the interrupted sampling func-tion of DRFM-based repeater jammer can be depictedas a rectangle envelope pulse train p(t) with the dur-ation τ and interval Ts [1]

Fig. 1 Typical scene of escorted jamming for the wideband radar

Xiong et al. EURASIP Journal on Advances in Signal Processing (2017) 2017:9 Page 2 of 12

p tð Þ ¼ rect0tτ

� ��X∞n¼−∞

δ t−nTsð Þ; ð1Þ

where rect0(t/τ) is a rectangle envelope pulse, which is 1for 0 ≤ t ≤ τ and 0 otherwise; * stands for the convolutionoperation; and δ(⋅) refers to the delta function. The dutyratio is defined as Dr = τ/Ts. The direct repeater jammingimmediately modulates and repeats the interrupted sam-ples only once, whereas for the repetitive repeater jam-ming, the repeaters take place in the current interval Ts

i

several times. With regard to the circular repeater jam-ming, the interrupted samples in the current Ts

i and theones in the last Ts

j (j = 1,2,⋯,i) are all restored, modu-lated, and repeated with a fixed circular order in theinterval Ts

i − τ. Compared with the first two types ofISRJ, the circular one has some extra requirements, suchas more restored space and more random repeaterorder. It makes the DRFM-based repeater jammer morecomplicated. The direct repeater jamming and repetitiveone are more common, and their suppression perfor-mances have been investigated in this paper.

3 Signal modelWithout loss of generality, a de-chirping LFM radaris considered and the transmitted signal s t̂ ; tm

� �is

defined by

s t̂ ; tm� � ¼ rect

t̂Tp

� �exp j2π f 0t þ

12Kt̂

2� �� �

; ð2Þ

where rect t̂=Tp� �

represents a rectangle envelope pulse,

which is 1 for t̂�� ��≤Tp=2 and 0 otherwise; Tp is the pulse

width; f0 refers to the radar carrier frequency; and K isthe chirp rate. Let TPRI denote the pulse repeat interval(PRI). tm =mTPRI and t̂ ¼ t−tm stand for the slow time

and fast time, respectively [19]. When the bandwidth ofradar signal B is large, the target echo is always consid-ered as the coherent summation of complex timereturns from target scatterers and is expressed as

sT t̂ ; tm� � ¼XNt

i¼1

βirectt̂−2Ri

t=cTp

� �

exp j2π f 0 t−2Rit=c

� �þ 12K t̂−2Ri

t=c� �2 � �

;

ð3Þwhere Rt

i = Rt + ri is the radical distance between target’sith scatterer and radar antenna. Then, the interruptedsamples Is t̂ ; tm

� �of the radar transmitted signal can be

regarded as [1]

Is t̂ ; tm� � ¼ p tð ÞsT t̂ ; tm

� �: ð4Þ

Without consideration of the jammer system’s inher-ent delay (about tens of nanosecond), the ISRJ signal forrepeater can be written as

s0J t̂ ; tm� � ¼ ηJSR

XNj‐1

n¼0

XNt

i¼1

βirectt̂−τiΔJ−nTs−τnd

τ

� �

exp j2π f 0 t−τiΔJ−nTs−τnd� �þ 1

2K t̂−τiΔJ−nTs−τnd� �2 � �

;

ð5Þ

where ηJSR is the JSR-based coefficient, τiΔJ ¼ Rj þ Ritjþ

�RitÞ=c is the jamming propagation delay for the ith scat-

terer, Rtji = Rtj + ri denotes the radical distance between

jammer’s receiver and target’s ith scatterer, Nj = ⌊Tp/Ts⌋refers to the generated integer of a radar pulse by inter-mittent sampling, ⌊ ⋅ ⌋ means the rounding operation to-ward negative infinity, and the time delay τd

n of the nth

Fig. 2 An illustration of the three types of ISRJ

Xiong et al. EURASIP Journal on Advances in Signal Processing (2017) 2017:9 Page 3 of 12

(n = 0,1,⋯,Nj − 1) interrupted sampling is considered assame, i.e., τd

i = τdj = τdk (i ≠ j). Followed with Nr times of

repeaters, the ISRJ arrives at

sJ t̂ ; tm� � ¼ XNr−1

k¼0

s0J t̂‐kτ; tm� �

: ð6Þ

It is seen that ISRJ also repeats the phase and azimuthdirection information of the target echo, which makesthe induced false targets would have the similar struc-ture and attitude with the true target.Furthermore, let N0 denote the additive noise in the

range cells, then the total received echo is given as

secho t̂ ; tm� � ¼ sT t̂ ; tm

� �þ sJ t̂ ; tm� �þN0: ð7Þ

For the de-chirping radar, the stretch trick is alwaysemployed to process the LFM waveform with largebandwidth and obtain the PC result. It loosens the re-quirement for sampling frequency and can obtain high-range resolution by mixing the echo with the radar refer-ence signal. Herein, the reference signal sr t̂ ; tm

� �can be

expressed as Eq. (8):

sr t̂ ; tm� � ¼ s t̂−tref ; tm

� �¼ rect

t̂−trefT ref

� �exp j2π f 0 t−trefð Þ þ 1

2K t̂−tref� �2� �� �

;

ð8Þ

where tref = 2Rr/c, Rr are the reference time and range,respectively. Then, the mixed target echo and ISRJ signalfor the repeater arrive at the formulas as

~sT t̂ ; tm� � ¼XNt

i¼1

βirectt̂−2Ri

t=cTp

� �

exp−j4πKRΔt

i

ct̂−

2Rit

c

� �−j4πf 0R

iΔt

cþ jπK

2RiΔt

c

� �2" #

;

ð9Þ

~s0J t̂ ; tm� � ¼ ηJSR

XNj‐1

n¼0

XNt

i¼1

βirectt̂−2Ri

j nð Þ=cτ

!

⋅ exp −j4πKRi

Δj nð Þc

t̂−2Rr

c

� �−j4πf 0R

iΔj nð Þ

cþ jπK

2RiΔj nð Þc

!2" #;

ð10Þ

where RiΔt ¼ Ri

t−Rr , RiΔj nð Þ ¼ Ri

j nð Þ−Rr , and Rji(n) = (Rj +

Rtji + Rt

i)/2 + c(nTs + τdn)/2. Further, the mixed ISRJ with Nr

times of repeaters is given as

~sJ t̂ ; tm� � ¼ ηJSR

XNr−1

k¼0

XNj‐1

n¼0

XNt

i¼1

βirectt̂−2Ri

j nð Þ=c−kττ

!

⋅ exp−j2πK

2RiΔj nð Þc

þ kτ

!t̂−

2Rr

c

� �

−j2πf 02Ri

Δj nð Þc

þ kτ

!þ jπK

2RiΔj nð Þc

þ kτ

!2:

ð11Þ

The stretch processing result of total echo in Eq. (7) isexpressed as

~secho t̂ ; tm� � ¼ ~sT t̂ ; tm

� �þ ~sJ t̂ ; tm� �þ ~N0: ð12Þ

Followed with the Fourier transform (FT), we canget the HRRP of received echo from Eq. (13), whereFT(⋅) denotes the FT and Ñ0 and N̂0 refer to thestretch and FT results of additive noise N0.

~Pecho f ; tmð Þ ¼ FT ~secho t̂ ; tm� �� �

¼Zt̂~secho t̂ ; tm

� �exp −j2πf t̂� �

dt̂

¼Zt̂~sT t̂ ; tm� �

exp −j2πf t̂� �

dt̂

þZt̂~sJ t̂ ; tm� �

exp −j2πf t̂� �

dt̂ þ N̂0

¼ ~PT f ; tmð Þ þ ~PJ f ; tmð Þ þ N̂0:

ð13ÞIt can be seen that the HRRP of each order false

target contains the phase variation information forcross-range resolution and would further inducethe false two-dimensional image. It was also ana-lyzed in [5–9].

4 Jamming suppression4.1 TF characteristics analysisFrom Eqs. (9) and (11), it is seen that there is greatsimilarity between the mixed true target echo andmixed ISRJ in the time domain; meanwhile, it hasbeen analyzed that the frequency spectrum of ISRJ isa superposition of shifted replicas of the echo’s fre-quency spectrum [1]. The traditional FT-basedspectrum analysis algorithms are failed to discriminateand suppress ISRJ. However, instantaneous frequency(IF) is more suitable for characterizing the time-varying features of the signal. It provides an alterna-tive approach to depict the characteristics of theabove signal. The IF of mixed true target echo ~sTt̂ ; tm� �

is given as

Xiong et al. EURASIP Journal on Advances in Signal Processing (2017) 2017:9 Page 4 of 12

fT t̂� � ¼XNt

i¼1

rectt̂−2Ri

t=cTp

� �d

dt̂−2KRi

Δt

ct̂−

2Rit

c

� �−2f 0R

iΔt

cþ 2K

RΔti

c

� �2

¼XNt

i¼1

rectt̂−2Ri

t=cTp

� �−K

2RiΔt

c

� �:

ð14ÞAnd the IF of mixed ISRJ ~sJ t̂ ; tm

� �is written as

f J t̂� � ¼ XNr−1

k¼0

XNj‐1

n¼0

XNt

i¼1

rectt̂−2Ri

j nð Þ=c−kττ

!

⋅d

dt̂

−K

2RiΔj nð Þc

þ kτ

!t̂−

2Rr

c

� �−f 0

2RiΔj nð Þc

þ kτ

!

þK2

2RiΔj nð Þc

þ kτ

!2

¼XNr−1

k¼0

XNj‐1

n¼0

XNt

i¼1

rectt̂−2Ri

j nð Þ=c−kττ

!−K

2RiΔj nð Þc

þ kτ

! !:

ð15ÞIt can be analyzed that some characteristic differences

as follows make it feasible to design a filter to suppressISRJ, especially on the time points when the jammer re-ceives and samples the radar signal.

(1)For the kth repeater and the ith scatterer, the IF ofISRJ in the pulse duration is not continuous due to2[Rj

i(n + 1) − Rji(n)]/c = Ts > τ, while the one of true

target echo is continuous [18].(2)For the kth repeater and the ith scatterer, the relative

delayed time 2Rji(n)/c + kτ = (Rj + Rtj

i + Rti)/c + (nTs +

τdn) + kτ of ISRJ in Eq. (15) is different from the

delayed time 2Rti/c of true target echo in Eq. (14). It

contributes to make the TF energy distribution ofeach order ISRJ shift from the one of true target echo.

(3)From Fig. 2, we can draw out that the time forinterrupted sampling and repeated transmitting isdivisional in the pulse duration, i.e., the receive-transmit antenna of jammer works asynchronously.

4.2 Filter designOn the premise of ensuring the target echo to be re-served and jamming to be suppressed, the ideal weightsof filter for the range bins of target should be 1, whilethe ones for the other range bins should be 0. In thesubsection, an effective filter is designed to suppress ISRJbased on the analyzed TF characteristic differences.From Eqs. (14) and (15), it is obvious that the calcu-

lated IF of mixed target echo and jamming returns areall stationary and linear. It means that the conventionalliner time-frequency analysis (TFA) methods are

qualified to analyze their TF characteristics, such asSTFT [20] and wavelet transform (WT) [21]. In thispaper, STFT is employed to extract the TF characteris-tics, which is established on the assumption that theconsidered signal is piece-wisely stationary in a shorttime. By performing STFT on the mixed target echo andmixed jamming returns, the energy distribution of TFrepresentation can be described as

TFT t̂ ; f� � ¼ STFT ~sT t̂ ; tm

� �� ��� ��2¼ jZ

~sT t̂ ; tm� �

ω t̂−t� �

exp −j2πf t̂� �

dt̂ j2

;

ð16Þ

TFJ t̂ ; f� � ¼ STFT ~sJ t̂ ; tm

� �� ��� ��2¼ jZ

~sJ t̂ ; tm� �

ω t̂−t� �

exp −j2πf t̂� �

dt̂ j2

;

ð17Þwhere STFT(⋅) represents the STFT and ω t̂

� �means the

frequency smoothing window. Moreover, the TF energydistribution of total received echo arrives at

TFTJ t̂ ; f� � ¼ STFT ~secho t̂ ; tm

� �� ��� ��2¼ TFT t̂ ; f

� �þ TFJ t̂ ; f� �þN1; ð18Þ

where N1 = |STFT(Ñ0)|2 represents noise energy

followed with STFT.In the time domain, we employ the same trick in [18]

to find the time points with great TF characteristic dif-ferences when the jammer samples the radar signal andfirst sum TFTJ t̂ ; f

� �along the frequency direction and

define the result as

Φ t̂� � ¼ Z

fTFTJ t̂ ; f

� �df : ð19Þ

It is assumed that the energy concentrated domain ofEq. (19) is [t1, t2] in the pulse duration, the time pointsof which satisfy that Φ(t1) > ζ,Φ(t2) > ζ and Φ t̂

� �< ζ; t̂∉

t1; t2½ � , and ζ is the energy threshold. Then, we dividethe domain [t1, t2] into L segments and select the time

point t̂minl with the minimum value of Φ t̂

� �in each seg-

ment [tl1, tl2] as follows:

t̂minl ¼ arg

t̂minΦ t̂

� �l ¼ 1; 2;⋯; L

s:t:t̂∈ tl1; tl2½ �tl1 ¼ t1 þ l−1ð ÞTwtl2 ¼ t1 þ lTw;

( ð20Þ

where Tw = (t2 − t1)/L is the width of each segment. The

selected time points t̂minl

n oL

l¼1with great TF characteris-

tic differences are considered for the interrupted sam-pling of jammer, i.e., the ISRJ might be absent at these

Xiong et al. EURASIP Journal on Advances in Signal Processing (2017) 2017:9 Page 5 of 12

points in the mixed returns. In addition, the receivedecho after stretch processing near these time pointscould be regarded as the mixed target echo. It is ex-tracted and represented as

se t̂� � ¼XL

l¼1

rectt̂−t̂min

l

Twin

!~secho t̂ ; tm

� �: ð21Þ

Subsequently, we have the normalized filter H(f ) andexpress it as

H fð Þ ¼ FT se t̂� �� ��� ��2=κ ¼ j

Zt̂se t̂� �

exp −j2πf t̂� �

dt̂ j2

=κ;

ð22Þ

where κ is the maximum of FT se t̂� �� ��� ��2 . It can be

seen that the designed weights of H(f ) for the target

range bins are larger and even be 1, while the ones forthe other range bins are much smaller and even be 0. Fi-nally, the jamming and noise are suppressed after multi-plying the HRRP of the received returns by the designedfilter function. It can be formulated as

P f ; tmð Þ ¼ H fð Þ⋅~Pecho f ; tmð Þ ¼ H fð Þ⋅ ~PJ f ; tmð Þ þ ~PT f ; tmð Þ þ N̂0� �

:

ð23Þ

4.3 Suppression performance assessmentHerein, the CC and SJNR improvement factor areadopted to evaluate the jamming suppression perfor-mances of our proposed algorithm.In general, the CC between the ideal HRRP of target

~PT f ; tmð Þ and the filtered result P(f, tm) can be taken toevaluate the jamming suppression performances forwideband radar. It is always hoped that the expected CCwould satisfy

E ρ P f ; tmð Þ; ~PT f ; tmð Þ� �� �≥ρ0; ð24Þ

where

E ρ P f ; tmð Þ; ~PT f ; tmð Þ� �� � ¼EXNn¼1

P f n; tmð Þ~PT f n; tmð Þ !

E P f ; tmð Þk k2 ~PT f ; tmð Þ 2

� � :ð25Þ

ρ0∊ [0, 1] refers to the lower bound of CC (LBCC).The other performance assessment is indicated by the

SJNR improvement factor. For the wideband radar, thepower of target and jamming extends some range bins.We have the improvement factor of SJNR represented as

δsjnr ¼ 20 log10AmpSmax

p

AmpJmaxp þ AmpN ave

p

!

−20 log10AmpSmax

~pecho

AmpJmax~pecho

þ AmpNave~pecho

!;

ð26Þ

where AmpSmaxp ;AmpJmax

p

� �and AmpSmax

~pecho;AmpJmax

~pecho

� �de-

note the maximum amplitudes of target and jamming inP(f, tm) and ~Pecho f ; tmð Þ , respectively. AmpNave

p and

Receive the echo of awideband radar

Estimate the time pointswith great differences ofTF energy distribution

Judge if ISRJ exists? Target detection

Construct the proposedfilter

N

Y

Identify the jammingmode further

Adopt other anti-jammingmeasures

Judge if ISRJ is suppressedsuccessfully?

N

Y

True target information

False target information

Filter the received echowith the above filter

Fig. 3 Working flowchart of a wideband radar against ISRJ with ourproposed filter

Table 1 Parameter description of the ISAR, target, and jammer

Radar parameters Carrier frequency f0 10 GHz Pulse width Tp 128 μs

Band width B 1 GHz PRI 1 ms

Width of ω t̂� �

4.2 μs Location of O (0 m, 0 m)

Target parameters SNR 25 dB Location of G (0 m, 100,005 m)

Jammer parameters Repeat sampling interval Ts 20 μs Sampling duration τ 5/10 μs

Delayed time τdn 5.45/5.11 μs Order Nr 1 and 3

JSR 20 dB Location of J (0 m, 10,000 m)

Xiong et al. EURASIP Journal on Advances in Signal Processing (2017) 2017:9 Page 6 of 12

AmpNave~pecho

refer to the average noise amplitudes before

and after the jamming suppression.

4.4 Jamming suppression working flowThe working flowchart of wideband radar for ISRJ sup-pression is given in Fig. 3. When the protected targetecho and ISRJ are received simultaneously, the widebandradar system will primarily judge whether ISRJ exists. Itcould be identified based on the representation charac-teristics of HRRP and SAR/ISAR image. If the ISRJ is de-tected and confirmed, the radar system has to extractthe time points with great differences of TF energy dis-tribution. Then, the proposed filter is constructed andthe PC result of received returns will be fed to the filter.Finally, the jamming suppression performances will beevaluated. If the suppression result has high CC andlarge SJNR improvement factor, the target could be de-tected and recognized. If some ISRJ residue still retainswith low CC and small SJNR improvement factor, the

jamming mode will be identified with other characteris-tics and another corresponding anti-jamming measureswill be adopted further, such as the trick of complicatedradar waveform and some measures of low probability ofinterception.

5 Simulation results and analysisIn this work, the simulated radar system is a widebandLFM ISAR, whose parameters and target and jammerare all listed in Table 1. These parameters are also citedin [2, 18]. It is pointed out that the hamming window isemployed as the frequency smoothing window ω t̂

� �in

Eqs. (16), (17), and (18), and the energy threshold ζ inEq. (20) is set as 0.1 after the normalization of Φ t̂

� �.

The simulated seeker, as shown in Fig. 4a, is regarded asthe extended target, which is consisted of 16 scattererswith each reflection coefficient βi = 0.4. The location ofG in Table 1 and Fig. 1 means the position of the seekerhead scatterer, which is also denoted as the reference

(a)

(b) Fig. 5 HRRP of the received echo, where τdn = 5.45 μs. a Oncerepeater. b Thrice repeater

(a)

(b)Fig. 4 An illustration of the seeker’s scatterers and its HRRP. a Asketch of seeker’s scatterers. b HRRP

Xiong et al. EURASIP Journal on Advances in Signal Processing (2017) 2017:9 Page 7 of 12

origin of coordinate in Fig. 4a. At the beginning, Fig. 4billustrates the ideal target’s HRRP without jamming andnoise. Then, some simulations of jamming suppressionhave been carried out, and suppression results are ana-lyzed in detail.

5.1 ISRJ effectsIn the subsection, ISRJ is first investigated against theseeker detection and recognition. When SNR = 25 dBand JSR = 20 dB, Fig. 5 shows the jamming effects forradar system with the delayed time τd

n = 5.45 μs and dif-ferent order (Nr = 1, 3). Besides, the ones with delayedtime τd

n = 5.11 μs are depicted in Fig. 6.The generated HRRP of false targets also demonstrate

that the number of false targets is related to the order[1–4]. In addition, it is seen that ISRJ can induce falsetargets or barrage jamming, especially the prepositionfalse target, which would greatly complicate the targetdetection and recognition of radar system.

5.2 Jamming suppression performancesHerein, the jamming suppression performances of theproposed filter are presented. In view of the unknownsampling duration time of DRFM-based jammer, we just

Fig. 7 Energy distribution of TF, where τdn = 5.45 μs. a Target echo. bReceived returns in Fig. 5a. c Received returns in Fig. 5b

(a)

(b)Fig. 6 HRRP of the received echo, where τdn = 5.11 μs. a Oncerepeater. b Thrice repeater

Xiong et al. EURASIP Journal on Advances in Signal Processing (2017) 2017:9 Page 8 of 12

(a)

(b)

(c)Fig. 9 Simulation results of received returns in Fig. 5b. a Selectedtime points. b Filter function. c Suppression result

(a)

(b)

(c)Fig. 8 Simulation results of received returns in Fig. 5a.a Selected time points. b Filter function. c Suppressionresult

Xiong et al. EURASIP Journal on Advances in Signal Processing (2017) 2017:9 Page 9 of 12

select single time point t̂minl in each segment [tl1, tl2] in

Eq. (21). Four different cases are discussed in detail.

5.2.1 Performances versus orderAs a representation, Fig. 7a shows the energy distributionTFT t̂ ; f

� �of the protected target echo via STFT, while the

energy distribution TFTJ t̂ ; f� �

for Fig. 5 is depicted inFig. 7b, c. When the interrupted samples are repeatedonce (Nr = 1), the selected time points in Eq. (20) are sym-bolized by the notation “Δ” in Fig. 8a, where the segmentnumber is M = 5. The filter function is shown in Fig. 8b,and the jamming suppression result of our proposed filteris further illustrated in Fig. 8c. Similarly, when the inter-rupted samples are repeated thrice (Nr = 3), the simulationresults are presented in Fig. 9. We can find that not onlythe jamming and noise are suppressed but also the targetecho is reserved effectively.

5.2.2 Performances versus delayed timeAs shown in Figs. 5 and 6, it is concluded that differentdelayed times would induce different effects of false tar-get, which might be preposition, postposition, or barragejamming. Different from case 1, the jamming suppres-sion performances for Fig. 6a with the delayed time τd

n =5.11 μs are investigated. As a comparison, the jammingsuppression result of approach I in [18] is shown inFig. 10a, while that of our proposed filter is shown inFig. 10b. Since the time width of ω t̂

� �is smaller than

the sampling duration τ, the spectrum of the target sig-nal spreads by the windowing. Then, the ISRJ near thetarget, especially the barrage jamming, is hardly to besuppressed by the approach I and some jamming resi-dues are still reserved in Fig. 10a. From Fig. 10b, it im-plies that our proposed jamming suppression schemealso can obtain desired suppression performances on the

(a)

(b)Fig. 11 Performances of jamming suppression with different JSRsand SNRs, where τdn = 5.45 μs and Nr = 1. a Curves of CC. b Curves ofSJNR improvement factor

(a)

(b)Fig. 10 Jamming suppression result comparison of the receivedreturns in Fig. 6a. a Approach I in [18]. b Our proposed filter

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barrage jamming in Fig. 6a, although a little of the jam-ming residue exists around the target range bins.

5.2.3 Performances versus SNR and JSRIn this case, the effects of different SNR and JSR on jam-ming suppression are shown. The number of MonteCarlo trials is 200 for each of the different SNR or JSR.For the case of Fig. 8, the curves of CC are shown inFig. 11a, and the curves of SJNR improvement factor arepresented in Fig. 11b. Analogously, Fig. 12 depicts thejamming suppression performances with different SNRsand JSRs for the case of Fig. 9. From Figs. 11 and 12, wecan summarize the observations as follows:

1. The curves of CC climb observably when SNR <25 dB and increase slightly when SNR > 25 dB. InFig. 11a, the CC for each JSR is larger than 0.8

when SNR > 25 dB. In Fig. 12a, when SNR >25 dB, the CCs for JSR = 15 and 20 dB arrive at0.9, while the ones for JSR = 25 and 30 dB arelarger than 0.8. Without generality, the LBCC ρ0is set as 0.8. It is indicated that when SNR >25 dB, the received echo suppressed by ourproposed scheme is similar with the HRRP ofideal target echo, which is helpful for the targetdetection and recognition of wideband radar.

2. The SJNR improvement factor grows incollaboration with SNR increasing and largerSJNR improvement factor can be obtained inthe case of larger JSR. It means that ourproposed scheme can distinctly improve theSJNR and is also beneficial to increase theeffectual range of radar target detection in thecomplicated electromagnetic environment.

(a)

(b)Fig. 13 Jamming suppression results, where τdn = 5.45 μs and Dr = 50%.a HRRP of the received returns. b Suppression result

(a)

(b)Fig. 12 Performances of jamming suppression with different JSRsand SNRs, where τdn = 5.45 μs and Nr = 3. a Curves of CC. b Curves ofSJNR improvement factor

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5.2.4 Performances versus duty ratioIn the above three cases, the duty ratio Dr all is 25%. Inthe case of Fig. 8, when the duration τ is set as 10 μsand Dr = 50%, the jamming effect and suppression resultare shown as Fig. 13a, b, respectively. It is demonstratedthat the duty ratio mainly affects the amplitude of falsetarget [1, 2]. Our proposed method is also suitable forthe case of large duty ratio.

6 ConclusionsIncreasing attention has been paid to the ISRJ, whichcan greatly complicate the target detection and recogni-tion of wideband radar. The novelty of this paper is thatan efficient filter is designed and expanded to counterISRJ based on the TF characteristic differences betweentarget echo and ISRJ in the domain of TF spectrum,where the energy concentrates. Meanwhile, a feasiblejamming suppression scheme is proposed. The jammingsuppression effects on ISRJ are also analyzed with differ-ent orders, delayed time, SNR, JSR, and duty ratio. Nu-merous results demonstrate that the designed filter caneffectively suppress the jamming and noise. Moreover,the received echo suppressed by our scheme is similarwith the target’s HRRP on the basis of high CC and largeSJNR improvement factor. It is beneficial for the targetdetection and recognition of wideband radar.

AcknowledgementsThe authors thank the associate editor Guolong Cui and the anonymousreviewers for their beneficial comments and suggestions that improve thequality of this paper.

FundingThis work was supported by the National Natural Science Foundation ofChina under grants 61471191 and 61501233, the Aeronautical ScienceFoundation of China under grant 20152052026, the Funding of JiangsuInnovation Program for Graduate Education under grant KYZZ16_0169, andthe Fundamental Research Funds for the Central Universities and this ispartly funded by China Scholarship Council.

Authors’ contributionsWX and GZ designed the jamming suppression scheme and experiments.WX and WBL performed the experiments and analyzed the experimentresults. WX and GZ contributed to the manuscript drafting and criticalrevision. All authors read and approved the final manuscript.

Competing interestsThe authors declare that they have no competing interests.

Author details1Key Laboratory of Radar Imaging and Microwave Photonics, Ministry ofEducation, Nanjing University of Aeronautics and Astronautics, Nanjing211106, People’s Republic of China. 2Leihua Electronic Technology ResearchInstitute, Aviation Industry Corporation of China, Wuxi 214063, People’sRepublic of China. 3College of Automation Engineering, Nanjing University ofAeronautics and Astronautics, Nanjing 211106, People’s Republic of China.

Received: 7 July 2016 Accepted: 13 January 2017

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