Jin Di ,Xin-hong Ho ,Qing Liu ,Xio-peng Yn ,*,Ping Li

a Science and Technology on Electromechanical Dynamic Control Laboratory,School of Mechatronical Engineering,Beijing Institute of Technology,Beijing 100081,China

b Ordnance Science Institute of China,Beijing 100089,China

Keywords:Pulse Doppler fuze ID Chaotic binary code Encryption Repeater jamming

ABSTRACT Pulse Doppler(PD)fuze is widely used in current battlefield.However,with the threat of repeater jamming,especially digital radio frequency memory technology,the deficiency in the anti-repeater jamming of a traditional PD fuze increasingly emerges.Therefore,a repeater jamming suppression method for a PD fuze based on identity(ID)recognition and chaotic encryption is proposed.Every fuze has its own ID which is encrypted with different chaotic binary sequences in every pulse period of the transmitted signal.The thumbtack-shaped ambiguity function shows a good resolution and distance cutoff characteristic.The ability of anti-repeater jamming is emphatically analyzed,and the results at different signal-to-noise ratio(SNR)show a strong anti-repeater jamming ability and range resolution that the proposed method possesses.Furthermore,the anti-repeater jamming ability is influenced by processing gain,bit error rate(BER)and correlation function.The simulation result validates the theoretical analysis,it shows the proposed method can significantly improve the anti-repeater jamming ability of a PD fuze.

1.Introduction

A Pulse Doppler(PD)fuze has high resolution in range and speed.It is widely used for detecting target and generating starting signal.The received target echo is processed in the correlator,the PD fuze will generate starting signal when the output signal of correlator meets the preset requirements of range and speed.However,with the development of digital jammers,the threat of repeater jamming,which is based on digital radio frequency memory(DRFM),is becoming increasingly serious to fuzes[1,2].One traditional solution is using a pseudo-random sequence to encode the transmitted signal of a PD fuze,such as m-sequence and gold sequence.However,the quantity and confidentiality of these sequences are both limited,which means it is easily for an enemy to detect and interfere.Liu et al.[3]reconstructed the transmitted pseudo random code using a third-order auto-correlation function,and the corresponding forward jamming was generated.Experimental results have verified the method can efficiently interfere with the PD fuze.Reference[4]studied the effect of various types of repeater jamming on a pseudo random coded PD fuze,the results shown that all kinds of repeater jamming can deceive and interfere with the PD fuze.Another traditional solution is feature extraction.Reference[5,6]analyzed the performance of a PD fuze on antiperiod modulation jamming,anti-sweep jamming,and anti-noise jamming,the corresponding anti-jamming methods were also proposed.Reference[7,8]extracted the multi-dimensional characteristics of the received echo,and then distinguished the target and jamming using pattern recognition methods,which resulted in an improvement on the PD fuze performance in anti-noise jamming and anti-period modulation jamming.However,these studies neglected methods for anti-repeater jamming,and these methods do not work in anti-repeater jamming.MIMO with beamforming to enhance the directionality of antennas[9,10]are used for antijamming,but the beamforming will increase the computational complexity which makes it difficult to meet the real-time requirements of PD fuze.Reference[11]proposed a MIMO multichannel signal detection and jamming-aware decision fusion for anti-jamming.It is suitable for a wireless sensor network,so far a cooperative PD fuze network and decision fusion have not been equipped due to the particularity of fuze.Once a distributed and cooperative fuze systems are full equipped,the proposed method with decision fusion may work well.

Aperiodic pseudo-random phase modulation code is an effective method for resisting repeater jamming.Among them,the statistical characteristics of chaotic signals are similar to noise,and they are difficult to predict for the long-term,which means they are good at confidentiality and anti-jamming.Moreover,there are large number of chaotic sequences which are easy to generate,so they are increasingly used in fuze and radar anti-jamming design[12-19].Reference[12]proposed the application of chaotic sequences in fuze transmission signals,and the research results show that the signals generated by this method have ideal ranging,speed and anti-jamming performance.Chen et al.[13,14]utilize the characteristics of the non-periodic and initial sensitivity of the chaotic signal.They designed a frequency modulation(FM)signal with chaotic binary sequence,and it effectively improved the antirepeater jamming ability of a FM fuze.Reference[15]uses a chaotic sampling sequence as the FM signal.The excellent performance was analyzed by simulation and theoretical analyses.Reference[16]proposed a wideband radar transmission signal based on chaotic frequency hopping and phase modulation,which solved the problem of distance-speed coupling,reduced the interception probability,and improved the radar resistance.Lin et al.[17]used nonlinear dynamics to generate a large-bandwidth chaotic radar signal with high range resolution and no fuzzy distance.Reference[18]proposed a phase modulation signal based on simple chaotic sequence,the method was easy to implement and improved the anti-jamming ability of PD radar.These applications on fuze and radar proved the feasibility of using chaotic sequences for PD fuze.Esmaeili-Najafabadi et al.[19]applied a Bernoulli chaotic system with minimum peak side-lobe level(PSL)in radar waveform design.Numerical experiments validated the superiority in detection performance and anti-jamming ability.However,the anti-repeater jamming performance of these methods is limited by their auto-correlation and cross-correlation coefficients.When the jamming power increases,its anti-jamming effect decreases significantly.Therefore,additional features with higher stability and uniqueness is urgently needed.

Recently,research on the specific emitter identification(SEI)has provided new ideas for anti-repeater jamming of PD fuze.Part of the research focusses on the non-linear devices of pulsed radiation sources,the fuze signals are sorted and identified to achieve antijamming using the differences of the devices[20,21].Another part of the research analyzes the subtle characteristics of the unintentional modulation of the pulse signal from the perspective of the time-frequency characteristics.Correspondingly,the effect of sorting and identifying the pulse signal can be achieved.Reference[22]used empirical mode decomposition(EMD)to analyze the time-frequency characteristics of non-steady-state signals,and obtained a better radiation source identification effect than wavelet decomposition.Reference[23]applied the quadratic timefrequency analysis method on radiation sources identification.The quadratic time-frequency characteristics of the radiation source signal are extracted and updated online to achieve the effects of suppressing jamming and emitter identification.Reference[24]proposed a SEI method based on information fusion in the space-time domain.It can achieve the identification of the uncertain emitter and achieve a higher recognition accuracy.However,these methods are based on device differences;the extraction of subtle features has high requirements on the sampling rate and accuracy of the system,and is severely affected by noise,making their applications more limited.

Based on the analyses mentioned above,this paper proposes an anti-jamming method for a PD fuze based on identity recognition and chaotic encryption.Each fuze has a unique ID,which is encrypted with different chaotic binary sequences in every ID period.The received signal is used for fixed distance and decryption.The fuze ID can be obtained through decryption.The PD fuze can distinguish the target echo from repeater jamming by its own ID.Different from the periodical pseudo-random modulation and other traditional method mentioned above,the proposed antirepeater jamming method can recognize the fuze by its ID and are not influenced by the JSR.Consequently,the anti-repeater jamming ability of PD fuze is significantly improved.

The rest of the paper is organized as follows:the design of fuze ID,the chaotic-encrypted sequences and the encrypted transmitted fuze signal in Section 1.Section 3 indicates the performance on fixed-distance of the proposed chaotic-encrypted transmitted signal through the analyses of ambiguity function.The ID recognition and anti-repeater jamming mechanism are emphatically introduced,and the robustness are also analyzed in Section 3.In Section 4,the simulation and analysis of the proposed method is presented with a wide range of parameters to verify the effectiveness of the method.The conclusion in Section 5 presents the main innovation of the proposed method and some further work.

2.Transmitted signal design

2.1.Fuze ID

In order to distinguish the target echo and the jamming signal,the characteristics of a fuze transmitted signal can be used.However,the unintended subtle characteristics of the fuze transmitted signal have imposed high requirements on the system sampling accuracy and calculation complexity,and are greatly affected by the signal-to-noise ratio(SNR).Therefore,it is necessary to add an intentional unique identity to the fuze signal.

A 7 bit ASCII code is used to identify a specific fuze,each fuze has a unique ASCII code,which is the fuze ID.There are 27Lkinds of different fuze ID,Lis the number of ASCII code that the fuze ID has.The fuze ID is converted to periodical non-return-to-zero(NRZ)code.

WherePτMis a pulse,the pulse amplitude is 1 and the pulse width is τM,Kis the ordinal number of the fuze ID period,andym∈｛0，1｝.The conversion is shown in Fig.1.

2.2.Chaotic-encrypted sequence

The Henon map is one of the simplest two-dimensional chaotic maps.It is easy to generate and calculate.Compared with commonly used logistic maps,its parameter distribution is wider and chaotic bifurcation behavior is more complicated[25,26].Thus the Henon map is used to generate chaotic sequences there.Henon map is defined as

Wherea∈[0，1.4],β∈[0.1，0.3],aare the bifurcation parameters of the Henon map.The bifurcation diagram ofβ=0.3 is shown in Fig.2.

Fig.1.Pulse code modulation of PD fuze ID.

Fig.2.Bifurcation diagram of Henon map whileα∈[0，1.4].

According to Fig.2,the bifurcation diagram is obvious when α＞1.1,it means that the Henon system generates chaos whenα＞1.1,so the range of the value is set asα∈[1.1，1.4].The value ofxnis in the real number domain,while the cipher operation is in the integer domain.Therefore,it is necessary to convertxnto the integer domain.Reference[27]proposed an algorithm of extracting binary sequence from chaotic sequence.The threshold function is defined as

Where vis the threshold value,usually expressed by the average value of a sequence.The chaotic sequence can be converted to binary code through the threshold function

WhereNis the length of the chaotic encryption sequence,τZis the width of the chaotic-encrypted sequence,andτZ=7LτM/N,is the value ofZ(t)in the nth pulse.zn∈｛0，1｝.

2.3.Encryption of fuze transmitted signal

Then the fuze ID is encrypted by the obtained chaotic-binary code,and the obtained binary cipher text sequence can be expressed as

WhereEKis the encryption algorithm,that is,each ID period takes differentaandβto generate chaotic encryption sequences.⊕is mod 2 plus,zn(K)is the chaotic encryption sequence generated by the key to the No.Kfuze ID period,the Henon map parametersaandβare used as keys in this paper.Cn∈｛0，1｝.The fuze encryption transmitted signal is shown in Fig.3.

The fuze transmitted signal based on chaotic encryption can be expressed as

WhereAtis the transmitting pulse amplitude,ω0is the carrier angular frequency,Tpis the transmitting pulse width,?is the convolution,δ(*)is the unit impulse function,Tris the pulse repetition period,andTr=τZ.The function of the random key is to generate different chaotic encryption sequences in each different period of the fuze ID.Within each period of fuze ID,the fuze ID is encrypted with the chaotic encryption sequence.The encrypted binary sequence is used for binary phase shift keying(BPSK)on the radio frequency carrier directly,and finally radiates through the antenna after pulse modulation.

Fig.3.Encryption block diagram of PD fuze transmitted signal.

3.Analysis on performance of fixed-distance of PD fuze signal based on chaotic encryption

3.1.Principle of fixed-distance

The fixed-distance process of the PD fuze signal based on chaotic encryption is shown in Fig.4.

According to the equation,the target echo signal can be expressed as

WhereAris echo signal amplitude,τis the delay of target echo,ωdis Doppler angular frequency,φ0is initial phase of echo,here,settingφ0=0 for convenient.

The echo signal is mixed with the local oscillator,and the output signal isUrm(t)is divided into two channels,and one signal is used for fixeddistance determination.Urm(t)is processed by the correlator.The reference signal is obtained by the transmitting signalC(t)with a certain delay,then the output signal of the correlator is

Whereτpis delay set by local reference signal.It can be seen from Eq.(9)that the output signal of the correlator contains the delay and Doppler frequency signal.Therefore,the range and speed of the target echo can be obtained by Doppler filtering and envelope detection.

3.2.Ambiguity functions and resolution

The complex envelope of the fuze signal based on chaotic encryption can be expressed as

The ambiguity function is widely used to measure the resolution performance of radar signal.The ambiguity function of fuze signal based on chaotic encryption can be deduced asχ(τ，ξ).

Whereξrefers to frequency shift.SetL=1N=35τZ=1μs,then the ambiguity function of PD fuze signal based on chaotic encryption can be obtained,as shown in Fig.4.

As shown in Fig.5,the center of the ambiguity function has an obvious peak.After leaving the center,there are small side lobes scattered around,and the ambiguity function distributes in the shape of a‘thumbtack’.

As shown in Fig.6,whenξ=0,Fig.6 is equal to the range autocorrelation function.The range correlation main lobe is obvious,which indicates that the range determination accuracy is higher and the range resolution isHowever,whenξ=0.03/35μs andξ=0.06/35μs,the range main lobe drops and side lobe rises obviously,which affects the range cutoff characteristics of the fuze.It can be seen that the existence of the Doppler frequency affects the range determination performance of the chaotic encryption fuze,its Doppler tolerance is 1/14LτMand requiresξ?1/14LτMin practice.

As seen from Fig.7,the ambiguity function of single-period velocity presents a Sinc-shaped envelope when it is under a certain time delay.It has an obvious velocity autocorrelation main lobe whenτ=0.Whenτ=0.2τZandτ=0.4τZ,the main lobe drops and the side lobe rises rapidly,showing that the ability to extract the velocity of range targets of chaotic encryption fuze is weak.In conclusion,the chaotic encryption fuze is suitable for detecting low-speed targets at short range.

4.Anti-repeater jamming analysis of PD fuze chaotic encryption signal based on ID recognition

4.1.ID recognition of PD fuze target echo

The other signal ofUrm(t)enters the fuze ID channel and uses the local key as a reference signal for decryption,as shown in Fig.8.

Using keyKgenerates a chaotic encryption sequenceZK(t-τp).Then,Urm(t)is decrypted byZK(t-τp),after correlation detector and binary maximum likelihood decision,the obtained decryption sequence is WhereDis decryption algorithm,S(*)is unipolar code conversion function,S(*)∈｛0，1｝.Λi｛*｝is the binary maximum likelihood decision function,andKτandKτpare two different keys.

Fig.4.Block diagram of fixed-distance.

Fig.5.Ambiguity function of the chaotic-encrypted signal of the PD fuze.

Arhas no effect on signal polarity,thus,whenωd?π/7LτM,Eq.(11)can be simplified to.

The obtained decryption sequence can be converted into 7-bit ASCII codeYRthrough the code translator,and the identification of fuze can be completed by comparingYRwith the fuze IDY.Whenτ=τpzn(Kτ)=zn(Kτp),it means that the encryption sequence is consistent with the decryption sequence,thusYR=Y.Thus it can be recognized as the fuze echo signal,and the fuze identity recognition is completed.

4.2.Analysis on anti-repeater jamming

When the repeater jammer intercepts the transmitted signal of a PD fuze,the jammer will save the received signal and retransmit it after time and frequency modulation.The repeater jamming will deceive the PD fuze in range and velocity,which may result in a fake target to PD fuze.The received repeater jamming signal can be expressed as

WhereJmis the number of the fake target that generated form the repeater jammer,Axjis the amplitude of the repeater jamming,Δωxjis the modulation frequency shift of the jammer.Δτxjis the jamming delay,which is composed of the delay caused by space propagation and the modulation delay of jammer.φxjis the initial phase of jamming signal,and settingφxj=0.

The received repeater jamming signal is mixed with the local oscillator frequency,and the output signal is

After the frequency mixing,the signalSjm(t)is decrypted under the control of local keys,then the decrypted sequence is

According to Eq.(13),whenΔωxj?π/7LτM,the single-period form of Eq.(16)can be simplified as

YJ(t)can be converted into ASCII codeYJthrough the code translator,according to Eq.(17),YJis related toΔτxj,AxjandJm.WhenJm=1,simulating a single point target echo,YJis unrelated toAxjaccording to Eq.(13).The result shows that increasing the power of the jammer has no effect on the PD fuze,only whenΔτxj=τpzn(KΔτj)=zn(Kτp),andYJ=Ycan the fuze be interfered with.

Fig.6.Range ambiguity function at different Doppler frequency.

Fig.7.Doppler ambiguity function at different delay.

Fig.8.Block diagram of fuze ID recognition.

However,for the repeater jamming,because ofΔτxj＞τp,it can be considered that the repeater jamming cannot complete the interference on the PD fuze in one ID period,it means the effective jamming delay isΔτxj=7KLτM+τp，K=1，2，….Correspondingly,the chaotic encryption sequencezn(KΔτxj)≠zn(Kτp),YJ≠Y.It means that the encryption sequence and the decryption sequence do not match,and it cannot interfere with the PD fuze.

That is,even if all encrypted transmitted signal are intercepted by an repeater jammer,it cannot interfere the fuze based on chaotic encryption and ID recognition because it does not have an right decryption sequence and thus the PD fuze will not get the right ID.

WhenJm＞1,the repeater jamming simulates a multi-point echo.Only if the following conditions apply

4.3.Robustness analysis

4.3.1.Robustness against frequency shift

According to Eq.(13),the success rate of fuze ID recognition of a chaotic encryption PD fuze can be affected by additional frequency shiftωd.The change of the success rate of ID recognition rateParat different frequency shift are shown in Fig.9.

According to Fig.9,within the frequency shift of 80 kHz,the ID recognition success rate of the chaotic encryption PD fuze is still more than 90%,showing its good robustness to the Doppler frequency shift.However,it can be found that high Doppler frequency shift(more than 80 kHz)will influence the decryption process of the fuze ID obviously.The reason is that the intensely change of amplitude envelope affects the results of correlation detector and binary maximum likelihood decision,and results in the increase of BER,finally lead to the failure of fuze ID recognition.It also shows that the proposed method is more suitable for low Doppler frequency at low speed scenario.

Fig.9.The fitting line of ID recognition success rate of PD fuze at different Doppler frequency shift.

4.3.2.Robustness against noise

In addition,it should be noticed that the fuze ID recognition accuracy and anti-repeater jamming performances will be affected by the BER under different signal-noise ratio(SNR),because the fuze ID needs to be decoded in the process of anti-repeater jamming.If the BER is too high,the anti-repeater jamming method of PD fuze based on fuze identity recognition will fail.Therefore,it is necessary to discuss the BER of chaotic encryption fuze decoding under different SNR.

Before calculating the BER,the processing gain needs to be calculated.Due to the spread spectrum of chaotic code and the correlation detector,the processing gain can be expressed as

WhereWzis the spread spectrum signal(here,this is the width of chaotic binary code);Rmis the code transfer rate(here,this is the fuze ID transfer rateThe BER under the correlation detection is

WhereQ(·)is the complementary error function[28],Ebis the minimum energy required per bit,is the power spectral density of the interfering noise signal,Njmis the average power of noise signal reaching the front end of the fuze receiver.Lets=ag+N0，g=1，2,a1、a2are the amplitude of two equal-energy polar signals received by the receiver under BPSK modulation,can be expressed as

The BER at different processing gains and SNR is shown in Fig.10.

Fig.10.BER at different processing gain and SNR.

According to Fig.10,with the increase of SNR,the BER decreases rapidly.At the same SNR,the higher the processing gain is,the lower the BER will be.When SNR is-10dB,the BER can still be maintained at a low level(less than 10%).Therefore,the antirepeater jamming method using fuze ID and chaotic encryption has a strong robustness to noise.

4.3.3.Real-time analysis

In the real work scenario of PD fuze,the high speed of bullet-tofuze meeting puts forward higher requirements for the real-time signal processing.The chaotic encryption and decryption code are generated in advance for real work,thus the increased signal processing time are only about binary stream encryption and binary stream decryption.

Defined the complexity of one XOR operation asΟ(1),then the complexity ofNtimes XOR operation forNpoints encryption are Ο(N)as well as theNpoints decryption.SetN=70 for practical consideration.Assume the oscillator frequency of FPGA is 100 MHz,then the time consuming of 70 points encryption and decryption is 1.4μs.For a high speed meeting scenario for PD fuze at 1000m/s,the deviation is only about 1.4 mm.Therefore,the computational complexity fully meet the requirements of real-time for PD fuze.

In conclusion,the PD fuze chaotic encryption signal based on identity recognition has strong robustness to frequency shift and noise,and the real-time performance can fully meet therequirements of high speed meeting for PD fuze.The performance of the anti-repeater jamming mainly depends on the length of chaotic encryption sequence and the SNR of environment.The performance of the anti-repeater jamming under low SNR can be further enhanced by improving the length of chaotic encryption sequence and SNR.And the success rate of anti-jamming of PD fuze is unaffected by increasing the number of simulated echo points and jamming power.

Table 1Simulation parameters.

Fig.11.Range envelope from the correlator of the PD fuze based on chaotic encryption at different SNR.

5.Simulation and analysis

To validate the performance of the proposed PD fuze on antirepeater jamming and target recognition,the simulation for a wide range of conditions with various parameters are made.Simulation parameters are shown in Table 1.

Fig.12.(a)Fuze ID and repeater jamming recognition output of PD fuze based on chaotic encryption and fuze ID at-8dB SNR,20 kHz Doppler frequency shift;(b)Fuze ID and repeater jamming recognition output of PD fuze based on chaotic encryption and fuze ID at-10 dB SNR,80 kHz Doppler frequency shift.

Fig.13.(a)Success rate of anti-repeater jamming by different ways at 20 kHz frequency shift,-8 dB SNR.;(b)Success rate of anti-repeater jamming by different ways at 80 kHz frequency shift,-10 dB SNR.

Adding Gaussian white noise to the simulation process to make the simulation proceed at-10dB～0 dB SNR.The range envelope of PD fuze based on identity recognition is shown in Fig.11.

According to Fig.11,the output range envelope of the chaotic encryption PD fuze is obvious at different SNR.The lower the SNR,the higher the side lobe of the range envelope.In Fig.11,the width of the target envelope is about 3 m,it shows that the simulation range resolution is consistent with the theoretical resolutionThe range envelope in Fig.11 verifies the feasibility and resolution of the proposed fixed-distance method of PD fuze based on chaotic encryption.

To verify the anti-repeater jamming performance of PD fuze based on fuze ID recognition and chaotic encryption under different frequency shift.The ID recognition results under different Doppler frequency shiftωd/2πand SNR are compared.As shown in Fig.12.

In Fig.12(a)and Fig.12(b),it can be seen that only when the target echo is received,can the obtained decryption ID be consistent with the fuze ID.For repeater jamming,the correct fuze ID cannot be obtained correctly because the decryption sequence is inconsistent with the encrypted sequence.Therefore,the fuze can effectively recognize its own echo and repeater jamming signals by its own ID,the PD fuze based on identity identification and chaotic encryption has a strong anti-repeater jamming performance.But in Fig.12(b),a higher Doppler frequency shift and lower SNR will result in an increase of BER,thus the decryption result is not as ideal as it in Fig.13(a).This will finally influence the fuze ID recognition accuracy.Thus,the proposed repeater jamming suppression method for PD fuze based on ID recognition and chaotic encryption are more suitable for low Doppler frequency shift(no more than 80 kHz)in low speed condition and relatively high SNR(higher than-10 dB).

Furthermore,Fig.13(a)and(b)compares the anti-repeater jamming performance under different jamming-to-signal ratios(JSR)at certain SNR and frequency shift of three cases:the PD fuze based on identity recognition and chaotic encryption,traditional m-sequence phase modulation PD fuze,and the method of chaotic sequence proposed in reference[15].Psis the anti-jamming success rate.Here,JSR refers to the ratios of repeater jamming to target echo.

According to Fig.13,the decryption process of fuze ID is not affected by the jamming energy when the frequency shift and SNR are constant.But the anti-jamming success rate of the other two methods reduces rapidly with increasing JSR.The result shows that the proposed method can effectively suppress repeater jamming at different JSR and performs much better than the two other ways due to the fuze ID and chaotic encryption.As shown in Fig.13(a)and(b),higher Doppler frequency shift and lower SNR will result in lower success rate of anti-repeater jamming.Therefore,for practical engineering application,the method is more suitable for a relatively low Doppler frequency(less than 80 kHz)and relatively high SNR(higher than-10dB)to reach a high anti-jamming rate(more than 90%).

6.Conclusion

In this paper,an anti-repeater jamming method of PD fuze based on chaotic encryption and identity recognition is proposed.Each fuze has a unique fuze ID which is encrypted with a different chaotic-binary code during the ID period.The theoretical and simulation results show that the ambiguity function distributes in the shape of a“thumbtack”,which indicates that the ambiguity function has good range cut-off characteristics and resolution.The principle of fuze echo recognition and anti-repeater jamming robustness are systematically analyzed.The analysis results show that it has strong anti-repeater jamming ability and robustness.Different from the periodical pseudo-random modulation and other traditional method for anti-jamming,the proposed antirepeater jamming method can recognize the fuze by its ID and are not influenced by the JSR.Its anti-jamming performance is mainly affected by the Doppler frequency shift and SNR.The result of simulation validates the excellent performance of the proposed PD fuze based on chaotic encryption and fuze ID recognition on fixed-distance and anti-repeater jamming.

We have to concede that the correlation performance of the selected chaotic map and the anti-repeater jamming performance at lowSNRare still to be improved.The further work will be concentrated on the optimization of the chaotic sequences to improve their correlation performance.The adaptive antenna array pattern method is also considered to further improve the antijamming performance in the space domain[29].

Declaration of competing interest

There is no conflict of interest.

Acknowledgements

Foundation:National Natural Science Foundation of China under Grant No.61973037 and No.61673066.