An Adaptive Transmitting Scheme for Interrupted

sensors Article

An Adaptive Transmitting Scheme for Interrupted Sampling Repeater Jamming Suppression Chao Zhou 1,2 , Feifeng Liu 1,2, * and Quanhua Liu 1,2 1 2

*

Radar Research Laboratory, School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China; [email protected] (C.Z.); [email protected] (Q.L.) Key Laboratory of Electronic and Information Technology in Satellite Navigation (Beijing Institute of Technology), Ministry of Education, Beijing 100081, China Correspondence: [email protected]; Tel.: +86-10-6891-8043

Received: 12 August 2017; Accepted: 23 October 2017; Published: 29 October 2017

Abstract: The interrupted sampling repeater jamming (ISRJ) based on a digital radio frequency memory (DRFM) device is a new type of coherent jamming. This kind of jamming usually occurs as main-lobe jamming and has the advantages of low power requirements and easy parameter adjustment, posing a serious threat to the modern radar systems. In order to suppress the ISRJ, this paper proposes an adaptive transmitting scheme based on a phase-coded signal. The scheme firstly performs jamming perception to estimate the jamming parameters, then, on this basis, optimizes the waveform with genetic algorithm. With the optimized waveform, the jamming signal is orthogonal to the target echo, thus it can be easily suppressed with pulse compression. Simulation experiments are performed to verify the effectiveness of the scheme and the results suggest that the peak-to-side-lobe ratio (PSR) and integrated side-lobe level (ISL) of the pulse compression can be improved by about 16 dB and 15 dB, respectively, for the case where the jamming-to-signal ratio (JSR) is 13 dB. Keywords: interrupted sampling repeater jamming; digital radio frequency memory; radar waveform design; jamming perception; adaptive transmitting

1. Introduction The application of digital radio frequency memory (DRFM) devices has greatly improved the performance and efficiency of radar electronic countermeasures (ECM) systems [1–3]. Based on the abilities of intercepting and storing radar transmitting signals, many new jamming strategies have been proposed [4–7]. Among them, interrupted sampling repeater jamming (ISRJ) has attracted extensive attention [8–14]. There are two main intercepting modes for DRFM devices, i.e., full-pulse sampling mode and interrupted sampling mode. Based on the latter, an ISRJ jammer intercepts parts of the radar signal and retransmits them for several times at a current pulse repeat interval (PRI). Therefore, the jamming signal is coherent with the radar transmission and partial processing gain can be obtained from signal processing such as pulse compression and coherent integration, greatly reducing the requirements on transmitting power. Thus the jammer can be more easily installed in small platforms such as unmanned aerial vehicles (UAVs) to form a main-lobe jamming, which increases the difficulty of radar antijamming [8]. Meanwhile, because of the digital processing capability of a DRFM system, the jammer can easily adjust the jamming parameters (such as the intercepting positions and intercepting durations, etc.) to change the distribution of the grating lobes of pulse compression, by which different jamming effects can be achieved. ISRJ was first proposed by [9,10] in 2006, respectively (it was named as Chopping & Interleaving (C&I) jamming in [9]). According to these references, the jammer intercepts a slice of the radar transmission and retransmits it multiple times. This process will be conducted for several cycles until the falling edge of the signal is detected. After pulse compression, the jamming will appear Sensors 2017, 17, 2480; doi:10.3390/s17112480

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as multiple false target groups and each of them consists of a main false target and several symmetrically distributed secondary false targets. By changing the intercepting duration and number of retransmitting times, the jamming can achieve effects of both deception and suppression. A modified strategy named interrupted sampling direct jamming (ISDJ) was also proposed in [10]. For this kind of jamming, the intercepted slices were retransmitted for only one time, whereas more slices can be intercepted. Therefore, the jamming will have only one false target group (after pulse compression), which consists of a stronger main false target and more secondary false targets. Hereafter, more publications were involved in this topic and most of them focused on jamming performance analysis and jamming strategy optimization [11–13]. For instance, Wang et al discussed the mathematical principle of ISRJ [11]; Li et al derived the connection between the intercepting duration and the jamming power [12] and studied the operating distance of the jammer based on coherent jamming principle [13]. In contrast, the electronic counter-countermeasures (ECCM) methods for ISRJ have not been fully studied. Some modern signal processing methods were attempted to filter out the jamming. Among them, the time-frequency (TF) analysis has been widely used. Especially, an ISRJ suppression method for dechirping radar was proposed in [15]. By making use of the discontinuity of ISRJ in the time-frequency domain, a band-pass filter was designed to suppress the jamming. However, this method requires a clear separation between adjacent false targets of the ISRJ. While in [16], the jamming was first reconstructed with the estimated jamming parameters, and then an adaptive CLEAN algorithm was employed to cancel the jamming. Despite their effectiveness, almost all of these methods are passive schemes, which means, countermeasures are taken after jamming enter the receiver. However, in the changing battlefield environment, these passive schemes require quite a lot of system resources while achieve limited performances. For the above considerations, modern radar systems should have the ability of jamming perception [17–19], thus be able to choose the optimal antijamming method. Hence in this paper, an adaptive transmitting scheme based on a phase-coded signal was proposed. The scheme first carries out jamming perception to estimates the ISRJ parameters of jammer intercepting positions and intercepting durations, then performs waveform optimization with the estimated jamming information. With the optimized waveform, the intercepted jamming signal is orthogonal to the target echo, hence can be suppressed with pulse compression. Based on the iteration of jamming perception and waveform design, a dynamic active ISRJ suppression scheme can be formed. The structure of the paper is as follows: in Section 2, the mechanism of ISRJ is introduced and the operators of ISRJ are deduced. On this basis, the optimal antijamming waveform is given based on eigenvalue decomposition. In Section 3, the adaptive transmitting scheme for phase-coded signal is introduced, and the two key steps of jamming perception and waveform optimization are described in detail. In Section 4, simulation experiments are carried out to quantitatively evaluate the jamming suppression performances. Finally in Section 5, the main conclusions of the paper are summarized. The main notations used in this paper are defined in the following table (Table 1). Table 1. Main notations used in the paper. Symbols

Interpretation

s xI A τ0 F X τ T Y

Transmitted signal vector Intercepted signal vector Jammer sampling matrix Time delay Fourier transform coefficient matrix Spectrum of the intercepted signal Retransmitting delay Phase matrix corresponding to the retransmitting delay Phase shifted spectrum

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Symbols

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Table 1. Cont.

J 

FI M J u Γ  M K u  tk 1 , tk 2 k 1 λ K K Ω = ∪ (tk1 , tk2 ) tk1 , tk 2 k =1 K s1 , s2 tk1 , tk2 x s1 , s2 p x p CA CA F F





Jamming signal vector Interpretation Jamming operator Inverse Fouriertime transform Retransmitting of eachcoefficient jamming matrix slice Jamming signal Eigenvector of vector  Jamming operator Eigenvalueof  Retransmitting time of each jamming slice Eigenvector of Γ set Discontinuous positions Eigenvalueof Γ Number of discontinuous positions Discontinuous positions set Start time and end time of the k th discontinuous position Number of discontinuous positions Binary phase-coded Start time and end time of the kthsequence discontinuous position Time-discontinuous waveform Binary phase-coded sequence Time-discontinuous waveform Protection pulse vector Sampling matrix of Protection protectionpulse pulse,vector complementary to A Sampling matrix of protection pulse, complementary to A Cost function for waveform optimization Cost function for waveform optimization

2. The Mechanism of ISRJ 2. The Mechanism of ISRJ 2.1. The The Operator Operator Representation Representation of of Jamming Jamming Signal Signal 2.1. The mechanism mechanism of of ISRJ ISRJ is is shown shown in in Figure Figure 1.1. After rising edge edge of of the the radar radar The After detecting detecting the the rising transmitting signal, the jammer will intercept a slice based on the set strategy, and then delays and transmitting signal, the jammer will intercept a slice based on the set strategy, and then delays retransmits the slice for multiple times. The process of intercepting and retransmitting is repeated for and retransmits the slice for multiple times. The process of intercepting and retransmitting is repeated several times until thethe falling edge of of thethe signal is detected. Therefore, thethe ISRJ is is actually for several times until falling edge signal is detected. Therefore, ISRJ actuallyemitting emittinga partial sampled and delayed version of the radar transmitted signal. a partial sampled and delayed version of the radar transmitted signal.

Radar transmitting signal

1

Intercepted slices

1

Retransmitted slices

2

3

4

5

6

7

8

5

1-1

1-2

1-3

9

10

11

12

9-1

9-2

9-3

9

5-1

5-2

5-3

Figure 1. Mechanism of interrupted sampling repeater jamming (ISRJ). Figure 1.Mechanism of interrupted sampling repeater jamming (ISRJ).

h iT Assuming the transmitted signal vector is s = s1 s2 · · · T sn , where the subscript ‘n’ is sn  , where the subscript ‘n’ is the Assuming the transmitted signal vector is s  s1 s2 the number of signal samples. Then the intercepted signal x I can be expressed as: number of signal samples. Then the intercepted signal x I can be expressed as: x I = As xI  As i.e.,      i.e., s1 x1 a11 0 · · · 0      (1) 0 0a22 · 0· ·   s0  s2   x2 x1   a11 1  .  =     (1) , a ∈ 0, 1 . { } ii  . x   0.. a ..  ..  0   s2...    .  2   . 22 .    ，aii . 0,1 . 0 · · ·  ann sn xn    0  xn   0 0 ann   sn 

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where the sampling matrix A is a diagonal matrix and the values of the diagonal elements are ‘one’ or ‘zero’. The element ‘one’ corresponds to the intercepting period, while the element ‘zero’ corresponds to the retransmitting period. The specific structure of A (i.e., the pattern of zeros and ones) is related to the ISRJ strategy. Compared to the radar transmitting signal, the retransmitted signal has a time delay. By making use of the characteristics of Fourier transform, namely: fft[s(t − τ0 )] = fft[s(t)]e− j2π f τ0 .

(2)

where fft[·] means fast Fourier transform (FFT) and τ0 is the time delay. The retransmitting of the intercepted signal can be described by the process of ‘FFT-phase shift-IFFT (inverse fast Fourier transform)’, and each of the steps can be expressed as:

•

FFT to the intercepted signal: X = Fx I i.e.,      

•



e− j2π f1 t1 e− j2π f2 t1 .. . − j2π f n t1 e



    =    

e− j2π f1 t2 e− j2π f2 t2 .. . − j2π f n t2 e

··· ··· ···

e− j2π f1 tn e− j2π f2 tn .. . − j2π f n tn e

     



x1 x2 .. . xn

  .  

(3)

where F is the Fourier transform coefficient matrix and X is the spectrum of the intercepted signal. Multiply X by the phase factor (take ‘one retransmitting’ as an example):

     

•

X1 X2 .. . Xn

Y1 Y2 .. . Yn





    =    

e− j2π f1 τ 0 .. . 0

Y = TX i.e., 0 ··· − j2π f τ 2 e ··· .. . 0 ···



0 0 .. . e− j2π f n τ

    

X1 X2 .. . Xn

   .  

(4)

where T is the phase matrix corresponding to retransmitting delay τ and Y is the phase shifted spectrum. IFFT to the phase shifted spectrum: J = FI Y i.e.,      

J1 J2 .. . Jn





    =    

e j2π f1 t1 e j2π f1 t2 .. . j2π e f 1 tn

e j2π f2 t1 e j2π f2 t2 .. . j2π e f 2 tn

··· ··· ···

e j2π f n t1 e j2π f n t2 .. . j2π e f n tn

     

Y1 Y2 .. . Yn

   .  

(5)

where F I is the inverse Fourier transform coefficient matrix and J is the retransmitted jamming signal. In summary, the jamming signal can be expressed as: J = F I TFAs.

(6)

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where Γ = F I TFA is defined as the jamming operator. When considering the case of a slice is retransmitted for multiple times, the jamming operator can be expressed as: Γ = F I TFA + F I T2 FA · · · + F I T M FA.

(7)

where M is the number of retransmitting times of each jamming slice. 2.2. The Optimal Waveform for ISRJ Suppression According to previous analysis, the jamming signal is the output of jamming operator on radar transmitting signal. The process can be expressed as: J = Γs.

(8)

According to the matrix theory, we may have: Γu = λu.

(9)

where u is the eigenvector of Γ and λ is the corresponding eigenvalue. Therefore, in theory, the jamming signal can be suppressed by taking the eigenvector associated with some zero eigenvalue (or the linear combination of eigenvectors associated with multiple zero eigenvalues) as the transmitting signal. To analyze the characteristics of the eigenvectors associated with zero eigenvalues, we still take‘one retransmitting’ as an example. Then the jamming operator can be rewritten as follows according to Equation (6): Γ = F I TFA = EA   e11 e12 · · · e1N   (10)  e21 e22 · · · e2N    = . .. .. A. .. . . .   .. e N1

e N2

· · · e NN

N

where E = F I TF, eij = ∑ e j2π f k [(i− j)∆t−τ ] , ∆t is the time sampling interval, τ is the retransmitting k =1

delay and N is the total number of the signal samples. Assuming that the jammer intercepts L signal samples at a time, then the sampling matrix can be expressed as:   1   ( L)     ..   .     1     0     ( L)     . ..   A= (11) .   0       1     ( L)   ..   .       1   .. .

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Thus the operator matrix Γ can be expressed as:     Γ=  

e11 e21 .. . e N1

( L)

··· ··· ···

e1L e2L .. . e NL

0 0 .. . 0

( L)

· · · 0 e1(2L+1) · · · 0 e2(2L+1) .. .. . . · · · 0 e N (2L+1)

( L)

··· ··· ···

 e1(3L) e2(3L) .. . e N (3L)

··· ··· .. . ···

   .  

(12)

Let λ be the eigenvalues of Γ, then the following equation can be obtained [20]: det(Γ − λI) = (−λ)

N

α

∑e

! N −α − j2π f i τ

= 0.

(13)

i =1

where α > 1 is the total number of the intercepted samples by the jammer. Equation (13) shows that the operator matrix of the jamming have zero eigenvalues. Therefore, we will analyze the characteristics of eigenvectors associated with zero eigenvalues. Firstly, since both F and F I are reversible, they are full rank. Secondly, it is easy to test that the phase matrix T is full rank as well. Therefore, their product, that is, the matrix E is full rank, which means the column vectors of E are linearly independent. Then constitutes a new matrix B with the nonzero column vectors in Γ, and the new matrix is also full rank. Therefore, solving the matrix equation: Bx = 0.

(14)

we have the solution x = 0. The optimal waveform we want should meet: Γx = 0.

(15)

Substituting Equation (12) into Equation (15), we have the following equation group:   e11 x1 · · · + e1L x L + 0 · x L+1 · · · + 0 · x2L · · · + e1N x N = 0     e21 x1 · · · + e2L x L + 0 · x L+1 · · · + 0 · x2L · · · + e2N x N = 0 . ..   .    e x ···+e x +0·x NL L N1 1 L+1 · · · + 0 · x2L · · · + e NN x N = 0

(16)

It could be seen from Equation (16) that: 1. 2.

For thevariables whose coefficient are not zero, the equation holds only if the variables satisfy xi = 0. While for the variables whose coefficient are zero, the equation holds for any value of variables xi .

According to the above analysis, the optimal waveform should be zero during the intercepting durations of the jammer; in other words, the optimal waveform is time discontinuous. Therefore, for convenience, we call it the time-discontinuous waveform (TDW).

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For the case of multiple retransmitting, the difference lies only in the structure of the sampling matrix A:   1   ( L)     ..   .     1 Sensors 2017, 17, 2480 7 of 16     0     ( ML)   1    . .     L  . A= (17) .       0   1       1  0     ( L)  ML     A  . . (17)   .   .   0       1   1      L ..   .  

1

 

Which means the jammer intercepts  L signal samples at a time and retransmits them for M times. For thisWhich matrix, the the above analysis also applies, hence the conclusion canthem be drawn, means jammer intercepts at asame time and retransmits for M i.e., the L signal samples optimaltimes. radar waveform should transmit when the jammer is not sampling. For this matrix, the above analysis also applies, hence the same conclusion can be drawn, i.e., the optimal radar waveform should when the jammer is not sampling. 3. Adaptive Transmitting Scheme for transmit ISRJ Suppression

In this section,Transmitting an adaptive transmitting for ISRJ suppression is presented. The flowchart 3. Adaptive Scheme for ISRJ scheme Suppression of the scheme is shown in Figure 2. The scheme adaptively adjusts the transmitting waveform In this section, an adaptive transmitting scheme for ISRJ suppression is presented. The flowchart according to the dynamic jamming environment, thus realizing the dynamic game between the radar of the scheme is shown in Figure 2. The scheme adaptively adjusts the transmitting waveform and theaccording jammer. to the dynamic jamming environment, thus realizing the dynamic game between the radar and the jammer.

Jammer

Radar

Jamming Retransmitting

Jamming Perception

Signal Interception

Jamming Exists？

N Y Waveform Design

Radar Transmitting

Figure 2.Flowchart chartof of adaptive adaptive transmitting scheme. Figure 2. Flow transmitting scheme.

The detailed interpretations are as follows:

The detailed interpretations are as follows: 1. 2.

1. 2.

At the beginning, the radar transmits a predesigned waveform according to the mission; the ISRJ jammer starts to work, it intercepts and retransmits the radar signal according to At theWhen beginning, the radar transmits a predesigned waveform according to the mission; the set strategy; When the ISRJ jammer to work, it intercepts andwhether retransmits the radar 3. The radar carries outstarts jamming perception to determine the jamming exists:signal according to

3.

the set strategy; a. if there is no jamming, the radar maintains the transmitting waveform unchanged; The radar jamming to determine whether the is jamming exists: b. carries if there isout jamming in theperception echo, the jamming parameters estimation performed; radarisoptimizes the waveform with the jamming andwaveform transmits the optimized a. 4. The if there no jamming, the radar maintains the parameters transmitting unchanged; waveform in the next PRI. b. if there is jamming in the echo, the jamming parameters estimation is performed;

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The radar optimizes the waveform with the jamming parameters and transmits the optimized 8 of 16 the next PRI.

Sensorswaveform 2017, 17, 2480 in

According to the analysis of previous section, it is theoretically possible to achieve ISRJ suppression by transmitting TDW whose discontinuous positions are consistent with the jammer intercepting periods. However, However, a TDW may imply complex hardware and large radar operational bandwidth. Besides, the jammer will always detect the rising edge of the signal, so the simple TDW will cause the jammer to change the strategy, resulting in a failure of the jamming suppression ability of the designed waveform. Therefore, Therefore, we shall insert some protection pulses at the discontinuous discontinuous intervals of a TDW, TDW, making making the the whole whole waveform waveform continuous continuous in time. time. For the purposes of jamming suppression, suppression, the protection protection pulses should be orthogonal to the TDW. With this waveform, the jammer will sample and retransmit the protection pulses, thus the jamming signal can be easily suppressed with pulse compression. compression. The structure structure of of the the transmitting transmitting waveform waveform is is shown shown in in Figure Figure 3. 3. Transmitting signal = TDW + Protection pulses TDW

Protection pulses Figure 3. 3. Structure Structure of of transmitting transmitting waveform waveform for Figure for ISRJ ISRJ suppression. suppression.

3.1. JammingPerception In order to effectively jam the radar, the energy of the jamming jamming signal generally needs to be greater than the target echo. ISRJ can achieve some coherent processing gain, thereby reducing the requirement power. But But withwith respect to the to target theecho, processing gain achievable requirement for fortransmitting transmitting power. respect theecho, target the processing gain is small. This meansThis that means the jamming-to-noise ratio (JNR) ratio of ISRJ needs be needs significantly larger than achievable is small. that the jamming-to-noise (JNR) of to ISRJ to be significantly the signal-to-noise ratio (SNR) of the (SNR) target echo. example, if each jamming slicejamming is retransmitted larger than the signal-to-noise ratio of theFor target echo. For example, if each slice is once (in which case the jamming signal can achieve greatest processing gain), the peak amplitude of retransmitted once (in which case the jamming signal can achieve greatest processing gain), the peak the jamming after pulse compression be the same asbe that the target when thetarget JNR is two amplitude ofsignal the jamming signal after pulsewill compression will theofsame as that of the when times of is the SNR. To of achieve better jamming effect, the JNReffect, of ISRJ requires to berequires higher, the JNR two times the SNR. To achieve better jamming thegenerally JNR of ISRJ generally which provides favorable condition for condition jamming perception. to be higher, which provides favorable for jamming perception. The purpose purpose of of jamming jammingperception perceptionisistotoestimate estimatethe the intercepting positions and durations of intercepting positions and durations of an an ISRJ jammer, provide necessary prior knowledge forantijamming the antijamming waveform design. ISRJ jammer, andand provide the the necessary prior knowledge for the waveform design. This This is essentially a problem of target detection and parameter estimation in noise. Similar problems is essentially a problem of target detection and parameter estimation in noise. Similar problems have have been extensively studied the of fields of target detection edge detection and of been extensively studied in the in fields target detection [21,22],[21,22], edge detection and time oftime arrival arrival (TOA) estimation [23]. in this theispurpose is with achieved steps of wavelet (TOA) estimation[23]. While in While this paper, thepaper, purpose achieved steps with of wavelet denoising, denoising, difference and peak These detection. Thesehas methods has been widely used inareas different amplitude amplitude difference and peak detection. methods been widely used in different [24– areas [24–27], not be described in detail here. According to the subsequent simulations, the 27], hence willhence not bewill described in detail here. According to the subsequent simulations, the jamming jamming parameters can be accurately estimated when JNR is greater than 0dB.Besides, the JNR can parameters can be accurately estimated when JNR is greater than 0dB.Besides, the JNR can be further be further by increased by pulse accumulation if the conditions increased pulse accumulation if the conditions permit. permit. 3.2. Joint Design Design of of TDW TDW and 3.2. Joint and Protection Protection Pulse Pulse A has has the advantages of simple and good clutter suppression A phase-coded phase-codedsignal signal the advantages of implementation simple implementation and good clutter performance [28,29], therefore is widely used in radar transmission. In this section, the binary suppression performance [28,29], therefore is widely used in radar transmission. In this section, the phase-coded signal issignal takenisastaken an example to illustrate the joint design of TDW protection pulse. binary phase-coded as an example to illustrate the joint design ofand TDW and protection

pulse. Assume that the discontinuous positions of TDW are defined by: 

K k 1

t

k1

, tk 2  .

(18)

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Assume that the discontinuous positions of TDW are defined by: K

Ω = ∪ (tk1 , tk2 ).

(18)

k =1

where K is the number of discontinuous positions; tk1 and tk2 are the start time and end time of the kth discontinuous position. Then the TDW can be expressed as: x = As1 . (19) where s1 is a binary phase-coded sequence; x is the TDW; A is the sampling matrix, whose columns corresponding to the time defined in Ω are zero and the other elements are one. Similarly, the protection pulse can be expressed as: p = C A s2 .

(20)

where s2 is another binary phase-coded sequence; p is the protection pulse and C A is the sampling matrix of protection pulse which is complementary to A, i.e., the columns corresponding to the time defined in Ω are one and the other elements are zero. In waveform design research, the peak to side-lobe ratio (PSR) and integrated side-lobe level (ISL) of the autocorrelation function are usually used to evaluate the pulse compression performance of a waveform, while those of the cross-correlation function are usually used to evaluate the orthogonality of a pair of waveforms [30,31]. The two functions can be expressed as: The autocorrelation function of x: N −1

∑

γxx (m) =

x( k )x ∗ ( k + m ).

(21)

x( k )p ∗ ( k + m ).

(22)

k =0

The cross-correlation function of x and p: N −1

γxp (m) =

∑

k =0

However, for the situation considered in this paper, both the target echo and jamming signal are present in the received signal. Therefore, the autocorrelation characteristic of TDW alone cannot fully reflect the PSR and ISL of the signal after pulse compression. Considering that the jamming signal is essentially the retransmission of the protection pulse, therefore, it is necessary to consider the PSR and ISL characteristics of the summation of the autocorrelation and the cross-correlation functions. That is, the PSR of the sum function should be as large as possible while the ISL should be as small as possible. The summation of the autocorrelation and the cross-correlation functions is: χ(m) = γxx (m) + γxp (m).

(23)

Then the PSR and ISL can be defined as: PSR =

|χ(0)|2 . max|χ(k)|2

(24)

|k|>δ

2 ∑ |χ(k)|

ISL =

|k|>δ

2 ∑ |χ(k)|

.

|k|≤δ

where δ is the boundary of the main lobe of the autocorrelation function.

(25)

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F

 PSR

 1    ISL .

(22)

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where  is an adjusting factor. Many modern optimization methods (such as water-filling algorithm, simulated annealing The function can then be expressed as the weighted of have the two indicators: method, cost particle swarm optimization, compressed sensingsum etc.) been used to solve such problems [32–36]. In this paper, the genetic algorithm (GA) [36] is used to optimize the waveform. α + (1 − α) ISL. (26) F= PSR 4. Simulations where α is an adjusting factor. In order to verify the effectiveness the as proposed scheme, simulation experiments are Many modern optimization methods of (such water-filling algorithm, simulated annealing performed with the parameters shown incompressed Table 2. method, particle swarm optimization, sensing etc.) have been used to solve such problems [32–36]. In this paper, the genetic algorithm (GA) [36] is used to optimize the waveform. Table 2.Simulation parameters for ISRJ.

4. Simulations

Parameter Value Transmitting signal Binary phase-coded (m-sequence) In order to verify the effectiveness of the proposed scheme, simulation experiments are performed Carrier frequency 6 GHz with the parameters shown in Table 2. Code width 0.1 μs Code number 100 Table 2. Simulation parameters for ISRJ. Sampling rate 50 MHz Sampling points 2048 Parameter Value Intercepting duration 1 μs Transmitting signal Binary phase-coded (m-sequence) Retransmitting time 2 Carrier frequency 6 GHz Code width 0.1 µs The system uses an m-sequence-based binary phase-coded signal as the transmitting signal. The Code number 100 code number is 100 and Sampling the coderate width is 0.1 μs. The jammer switches to ‘intercepting and 50 MHz points retransmitting’ mode afterSampling detecting the rising edge of the radar 2048 signal. The intercepting duration is Intercepting duration µs set 1 μs and each of the intercepted slice is retransmitted for 1twice. Therefore, the jammer can Retransmitting time 2

intercept 4 jamming slices in the whole pulse duration. Assuming the jamming-to-signal ratio (JSR) is 15 dB, then the real part and pulse compression The system usessignals an m-sequence-based binary phase-coded signal theshows transmitting signal. result of the received are shown in Figure 4. In Figure 4a, the blackasline the real part of The code number is 100 and the code width is 0.1 µs. The jammer switches to ‘intercepting and the target echo, while the blue line shows the real part of the jamming signal. retransmitting’ after detecting risinginedge of the intercepting durationthe is The pulse mode compression result isthe shown Figure 4b.radar Withsignal. the setThe simulation parameters, set 1 µs and eachforms of the two intercepted slice is retransmitted for twice. Since Therefore, the jammer canisintercept jamming signal false targets after pulse compression. the jamming signal just the 4retransmission jamming slicesofinparts the whole of thepulse wholeduration. signal, the available processing gain is smaller than that of the Assuming the jamming-to-signal ratio (JSR) 15 dB, the real part and pulse compression target echo’s. Hence, the peak JSR is reduced byisabout 7 then dB after pulse compression, but the false result the still received signals are shown in Figure 4. In Figure 4a, the line shows real part of targetsofare strong enough to cause false alarms. Besides, theblack random peaks the caused by the the target echo,ofwhile the blue the real part the jamming superposition the side lobesline willshows seriously affect theofdetection of thesignal. real target, either.

(a)

(b)

Figure 4. Jamming effect of common binary phase-coded signal. (a) The real part of the received signals and (b) pulse compression of the received signals.

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The pulse compression result is shown in Figure 4b. With the set simulation parameters, the jamming signal forms two false targets after pulse compression. Since the jamming signal is just the retransmission of parts of the whole signal, the available processing gain is smaller than that of 17, 2480Hence, the peak JSR is reduced by about 7 dB after pulse compression, 11 of 16 the Sensors target2017, echo’s. but the 2017, 17, 2480 11 of 16 false Sensors targets are still strong enough to cause false alarms. Besides, the random peaks caused by the Figure 4. Jamming effect of common binary phase-coded signal. (a) The real part of the received superposition of4.the side lobes will seriously affect the detection of the real target, either. Figureand Jamming effect of common phase-coded signal. (a) The real part of the received signals (b) pulse compression of the binary received signals. The simulations of jamming perception are shown in Figure 5. With wavelet denoising, amplitude signals and (b) pulse compression of the received signals. difference peak detection, the typical results jamming parameters are shown in Theand simulations of jamming perception are of shown in Figure 5. With estimation wavelet denoising, simulations of peak jamming inrepresents Figure 5.parameters Withtrue wavelet denoising, amplitude difference detection, the typical results jamming estimation are Figure 5a,The in which theand JNR is set 0 perception dB and theare redshown curveof the jamming envelope, amplitude difference and peak the0 typical ofcurve jamming parameters estimation are each shown in Figure 5a,isinthe which thedetection, JNRjamming is set dB andresults the red represents the true jamming while the black curve estimated envelope. The discontinuous position between shown in Figure 5a, in which the JNR is set 0 dB and the red curve represents the true jamming envelope, while the black curve is the estimated jamming envelope. The discontinuous position segment of the jamming signal corresponds to the intercepting period of the jammer. With different envelope, while the black curve is the estimated jamming envelope. The discontinuous position each segment signal corresponds to the intercepting jammer. JNR,between the estimation error of ofthe thejamming intercepting duration is shown in Figure 5b.period It canofbethe seen that, when between eachJNR, segment of the jamming signal correspondsduration to the intercepting theIt jammer. With different the estimation error of the intercepting is shown inperiod Figureof5b. can be the JNR is 0 dB, the estimation error is about 0.054 µs (the value is the average of 100 Monte Carlo With different JNR, theisestimation error of theerror intercepting duration is shown Figure 5b. Itofcan seen that, when the JNR 0 dB, the estimation is about 0.054 μs (the value in is the average 100be simulations), which is equivalent 2 or 3 sampling points according to the sampling rate. The error is seen that, when the JNR iswhich 0 dB,tothe estimation 0.054points μs (the value is the average of 100 Monte Carlo simulations), is equivalent toerror 2 oris3 about sampling according to the sampling acceptable for subsequent waveform design. Monte which is equivalent to 2 or 3 sampling points according to the sampling rate. TheCarlo error simulations), is acceptable for subsequent waveform design. rate. The error is acceptable for subsequent waveform design.

(a) (b) (a) (b) Figure 5.Simulations of of jamming jamming perception results of jamming parameters with with Figure 5. Simulations perception(a)(a)estimation estimation results of jamming parameters Figure 5.Simulations of jamming perception (a) estimation results errors of jamming with jamming-to-noise ratio(JNR) (JNR) =0 dB dB (b) (b) jamming estimation VS. JNR. jamming-to-noise ratio =0 jammingparameters parameters estimation errors VS.parameters JNR. jamming-to-noise ratio (JNR) =0 dB (b) jamming parameters estimation errors VS. JNR.

With the estimated jamming parameters, the cost function can be given with Equations (21)–(26) With the estimated parameters, the function can given with Equations (21)–(26) With the estimated jamming parameters, the cost cost function can bebe given with (21)–(26) and solved with geneticjamming algorithm (GA). Performing 100 Monte Carlo simulations, theEquations average value of andthe solved with genetic algorithm (GA). Performing 100 Monte Carlo simulations, the average and solved with genetic algorithm (GA). Performing 100 Monte Carlo simulations, the average value cost function in each iteration step is shown in Figure 6. The iteration is stopped when the generationofvalue the costfunction function in each iteration stepstep is shown in Figure The iteration is stopped when the generation of the cost inand each iteration shown in 6.ofThe iteration is stopped when the number reaches 100 the cost function is is convergent to6.Figure the value about 13. numbernumber reaches reaches 100 and the is convergent the value ofto about generation 100cost andfunction the cost function istoconvergent the 13. value of about 13.

Figure 6.The convergence process of the waveform design algorithm. Figure 6.The convergence process of the waveform design algorithm.

Figure 6. The convergence process of the waveform design algorithm. For different jamming scenarios, the typical designed waveforms can be seen from the target For different jamming scenarios, typical designedblack waveforms can be target echo shown in Figure 7a, Figure 8a, andthe Figure 9awiththe line. Under theseen samefrom jamsthe shown echothe shown Figure 7a,In Figure 8a,7,and 9awiththe line. Under the in same jams8, shown with blue in dotted line. Figure eachFigure jamming slice isblack retransmitted once; Figure each with theslice blueisdotted line. In Figure eachinjamming slice retransmitted in Figure 8, each jamming retransmitted twice, 7, while Figure 9, theisjamming slices once; are retransmitted for jamming slice is retransmitted twice, while in Figure 9, the jamming slices are retransmitted for

so on. It should be noted that the figure only gives a typical result of the joint design process. Signals so on. It should be noted that the figure gives a typical result of the joint design process. Signals with different codes may be outputted in only the 100 simulations. with different codes may beresults outputted in the 100 simulations. The pulse compression of the received signal are shown in Figure 7b, Figure 8b and The pulse compression results of the received signal are shown in received Figure 7b, Figure 8b the and Figure 9b, where the black line shows the pulse compression result of the signal with Figure 9b, where the blackinline the pulse result of the of received signal with the designed waveform. While theshows same figure, the compression pulse compression result received signal with Sensors 2017, 17, 2480 12 of 16 designed waveform. While in the same figure, the pulse compression result of received signal with the conventional phase-coded signal is shown with the blue line for comparison. It can be seen that, the conventional is shown withbinary the blue line for comparison. canfalse be seen that, compared with thephase-coded conventionalsignal m-sequence based phase-coded waveform,Itthe targets compared with the conventional m-sequence based binary phase-coded waveform, the false targets are effectively suppressed the designed waveform the side can lobes also significantly For different jamming with scenarios, the typical designedand waveforms beare seen from the target are effectively suppressed with the designed waveform and the side lobes are also significantly reduced. echo shown in Figures 7a, 8a and 9awiththe black line. Under the same jams shown with the blue reduced. However, because the jamming protectionslice pulse in the designed waveform provide any dotted line. In Figure 7, each is retransmitted once; in Figure 8, cannot each jamming slice is However, because the protection the loss designed cannot provide any processing gain for the target is jamming apulse target in energy relativewaveform to thefor conventional waveform. retransmitted twice, while in echo, Figurethere 9, the slices are retransmitted different times, where processing gain for echo, there isWhen a target energy loss relative to conventional waveform. The loss is related to the the target jamming strategy. each slice is the retransmitted only one the first slice is retransmitted once, the second slice isintercepted retransmitted twice, and so on. for It should be The loss is related to the jamming strategy. When each intercepted slice is retransmitted for only one time, of the total intercepted bejoint half design of the transmitting pulse duration. this notedthe thatlength the figure only gives a typicalsignal result can of the process. Signals with differentAtcodes time, thetarget lengthenergy of the loss total intercepted can bei.e., half3 of point, reach thesignal maximum, dB.the transmitting pulse duration. At this may bethe outputted in the 100 will simulations. point, the target energy loss will reach the maximum, i.e., 3 dB.

(a) (a)

(b) (b)

Figure 7. Jamming suppression result of a typical designed waveform (the intercepting duration is 1 Figure 7.7.Jamming suppression result of of a typical designed waveform (the(the intercepting duration is 1 µs result aonce): typical waveform intercepting duration is 1 μsFigure and eachJamming jammingsuppression slice is retransmitted (a)designed the real part of the received signals with a typical and each jamming slice is retransmitted once): (a) the real part of the received signals with a typical μs and each jamming slice is retransmitted once): (a) the real part of the received signals with a typical designed waveform (b) pulse compression result of the received signal. designed designedwaveform waveform(b) (b)pulse pulsecompression compressionresult resultofofthe thereceived receivedsignal. signal.

(a) (a)

(b) (b)

Figure 8.Jamming suppression result of a typical designed waveform (the intercepting duration is 1 Figure suppression result atwice): typical waveform (the intercepting duration is 1 μs and each jamming slice is retransmitted (a)designed the real part of the received signalsduration with a typical Figure 8.8.Jamming Jamming suppression result ofof a typical designed waveform (the intercepting is 1 µs μs and each jamming slice is retransmitted twice): (a) the real part of the received signals with a typical and each waveform jamming slice is retransmitted twice): part of the received signals with a typical designed (b) pulse compression result(a) ofthe thereal received signal. designed waveform (b) pulse compression result of the received signal. designed waveform (b) pulse compression result of the received signal.

The pulse compression results of the received signal are shown in Figures 7b, 8b and 9b, where the black line shows the pulse compression result of the received signal with the designed waveform. While in the same figure, the pulse compression result of received signal with the conventional phase-coded signal is shown with the blue line for comparison. It can be seen that, compared with the conventional m-sequence based binary phase-coded waveform, the false targets are effectively suppressed with the designed waveform and the side lobes are also significantly reduced.

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(a)

(b)

(a) suppression result of a typical designed waveform (b) (each jamming slice is Figure 9. Jamming Figure 9. Jamming suppression result of a typical designed waveform (each jamming slice is retransmitted for different times): (a) the part of the received signals(each with jamming a typical designed Figure 9. Jamming suppression areal typical waveform slice is retransmitted for different times):result (a) theofreal part of designed the received signals with a typical designed waveform (b) pulse compression result of the received signal. retransmitted for different times): (a) the real part of the received signals with a typical designed waveform (b) pulse compression result of the received signal. waveform (b) pulse compression result of the received signal.

The average jamming suppression performance of the obtained 100 waveforms with different because the protection in 11. the In designed waveform cannot provide anyrespectively, processing JNRHowever, conditions shown in Figurespulse 10performance and Figure10a, the blue black lines, The average is jamming suppression of the obtained 100and waveforms with different gain for the target echo, there is a target energy loss relative to the conventional waveform. The loss present the PSR of the pulse compression results with the conventional waveforms, JNR conditions is shown in Figures 10 and 11. In Figure10a, the blue and and blackdesigned lines, respectively, isand related to theimprovement jamming strategy. When each slice is retransmitted only one time, the PSR different JSR intercepted is with shown Figure 10b. It candesigned befor seen that with the present the PSR of the pulse with compression results theinconventional and waveforms, the length of the total intercepted signal can be half of the transmitting pulse duration. At this point, increase of the JSR, the JSR improvement will increase first and then decrease. For the simulation and the PSR improvement with different JSR is shown in Figure 10b. It can be seen that with the the target energy losspaper, will reachoptimal the maximum, i.e., 3 dB. is about 15 dB, which can be obtained when parameters of JSR, this PSRwill improvement increase of the the JSRthe improvement increase first and then decrease. For the simulation The average jamming suppression performance of the obtained 100 waveforms with different the JSR is about 14 dB. parameters of this paper, the optimal PSR improvement is about 15 dB, which can be obtained when JNR conditions isthe shown inthe Figures and 11. In Figure the blue and black lines, ISL of pulse10compression result 10a, is shown in Figure 11 and therespectively, optimal ISL the JSRSimilarly, is about 14 dB. present the PSR of the pulse compression results with the conventional and designed waveforms, and improvement is about which is obtained at the JSR ofin12.8 dB 11 forand the the same simulation Similarly, the ISL of 16 thedB, pulse compression result is shown Figure optimal ISL the PSR improvement with different JSR is shown in Figure 10b. It can be seen that with the increase of parameters. is about 16 dB, which is obtained at the JSR of 12.8 dB for the same simulation improvement the JSR, the JSR improvement will increase first and then decrease. For the simulation parameters of The results suggest that the designed waveform has an obvious ISRJ suppression effect. parameters. this paper, the optimal PSR improvement is about 15 dB, which can be obtained when the JSR is about The results suggest that the designed waveform has an obvious ISRJ suppression effect. 14 dB.

(a)

(b)

(a) ratio (PSR) of the pulse compression result under (b) different jamming-toFigure 10.Peak-to-side-lobe signal ratio (JSR) (a) PSR of the pulse compression result with common and (b) Figure 10.Peak-to-side-lobe ratio (PSR) of the pulse compression result underdesigned different waveforms jamming-toFigure 10. Peak-to-side-lobe ratio (PSR) of the pulse compression result under different PSR improvement withof different JSR. signal ratio (JSR) (a) PSR the pulse compression result with common and designed waveforms (b) jamming-to-signal ratio (JSR) (a) PSR of the pulse compression result with common and designed PSR improvement with different JSR. waveforms (b) PSR improvement with different JSR. Similarly, the ISL of the pulse compression result is shown in Figure 11 and the optimal ISL improvement is about 16 dB, which is obtained at the JSR of 12.8 dB for the same simulation parameters.

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The2017, results suggest Sensors 17, 2480

that the designed waveform has an obvious ISRJ suppression effect.

(a)

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(b)

Figure 11.Integrated side-lobe level (ISL) of the pulse compression result under different JSR (a) ISL Figure 11. Integrated side-lobe level (ISL) of the pulse compression result under different JSR (a) ISL of the pulse compression result with common and designed waveforms (b) ISL improvement with of the pulse compression result with common and designed waveforms (b) ISL improvement with different JSR. different JSR.

5. Conclusions 5. Conclusions In order to suppress the ISRJ injected from the main lobe of the radar antenna, an adaptive In order to suppress the ISRJ injected from the main lobe of the radar antenna, an adaptive transmitting scheme is proposed in this paper. Based on an ordinary single-channel radar, the scheme transmitting scheme is proposed in this paper. Based on an ordinary single-channel radar, the scheme first estimates the intercepting positions and durations of the ISRJ with jamming perception first estimates the intercepting positions and durations of the ISRJ with jamming perception technologies, then performs waveform optimization for ISRJ suppression (the designed waveform is technologies, then performs waveform optimization for ISRJ suppression (the designed waveform is named TDW). By inserting some protection pulses orthogonal to the TDW at the jammer intercepting named TDW). By inserting some protection pulses orthogonal to the TDW at the jammer intercepting positions, the processing gain obtained by the jamming signal can be greatly reduced, thereby positions, the processing gain obtained by the jamming signal can be greatly reduced, thereby suppressing the jamming performance. The simulation results show that the jamming parameters suppressing the jamming performance. The simulation results show that the jamming parameters can can be effectively estimated when the JNR is greater than 0dB. The designed antijamming waveform be effectively estimated when the JNR is greater than 0dB. The designed antijamming waveform can can achieve a JSR improvement of more than 10 dB when the input JSR is less than 20 dB, while the achieve a JSR improvement of more than 10 dB when the input JSR is less than 20 dB, while the target target energy loss less than 3 dB. energy loss less than 3 dB. Acknowledgments: This work was supported by the Chang Jiang Scholars Programme under Grants T2012122 Acknowledgments: This work was supported by the Chang Jiang Scholars Programme under Grants T2012122 and Project China under Grants B14010. and 111111 Project of of China under Grants B14010. Author Contributions:Zhou ZhouChao Chaoand andLiu LiuFeifeng Feifeng conceived conceived and designed Author Contributions: designed the the methods; methods;Zhou ZhouChao Chaoand andLiu LiuQuanhua Quanhuaconceived conceivedand anddesigned designedthe theexperiments; experiments; Zhou Chao performed performedthe thesimulations simulationsand andwrote wrotethe thepaper. paper. Conflicts of of Interest: The authors declare nono conflicts of interest. Conflicts Interest: The authors declare conflicts of interest.

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