sensors Article

High-Performance Anti-Retransmission Deception Jamming Utilizing Range Direction Multiple Input and Multiple Output (MIMO) Synthetic Aperture Radar (SAR) Ruijia Wang 1, *, Jie Chen 2,3, *, Xing Wang 1 and Bing Sun 2,3 1 2 3

*

Aeronautics and Astronautics Engineering College, Air Force Engineering University, Xi’an 710038, China; [email protected] School of Electronics and Information Engineering, Beihang University, Beijing 100084, China; [email protected] Collaborative Innovation Center of Geospatial Technology, Wuhan 430079, China Correspondence: [email protected] (R.W.); [email protected] (J.C.); Tel.: +86-10-8233-8695 (R.W.)

Academic Editor: Cheng Wang Received: 24 October 2016; Accepted: 4 January 2017; Published: 9 January 2017

Abstract: Retransmission deception jamming seriously degrades the Synthetic Aperture Radar (SAR) detection efficiency and can mislead SAR image interpretation by forming false targets. In order to suppress retransmission deception jamming, this paper proposes a novel multiple input and multiple output (MIMO) SAR structure range direction MIMO SAR, whose multiple channel antennas are vertical to the azimuth. First, based on the multiple channels of range direction MIMO SAR, the orthogonal frequency division multiplexing (OFDM) linear frequency modulation (LFM) signal was adopted as the transmission signal of each channel, which is defined as a sub-band signal. This sub-band signal corresponds to the transmission channel. Then, all of the sub-band signals are modulated with random initial phases and concurrently transmitted. The signal form is more complex and difficult to intercept. Next, the echoes of the sub-band signal are utilized to synthesize a wide band signal after preprocessing. The proposed method will increase the signal to interference ratio and peak amplitude ratio of the signal to resist retransmission deception jamming. Finally, well-focused SAR imagery is obtained using a conventional imaging method where the retransmission deception jamming strength is degraded and defocused. Simulations demonstrated the effectiveness of the proposed method. Keywords: SAR; MIMO; jamming suppression; range direction; sub-band synthesize

1. Introduction Synthetic aperture radar (SAR) has been widely used in civil exploration and military surveillance due to its all-weather, long-time and large-range detection capabilities [1]. However, rapidly developed electronic countermeasures (ECMs) can degrade the SAR imaging quality and system efficiency significantly [2–4]. The ECMs for SAR can be classified into barrage jamming and deception jamming, according to the signal characteristics and purpose of the ECM. Barrage jamming uses radio frequency noise with enough power to cover and corrupt the target signal. Deception jamming modulates fake target information on an intercepted signal retransmitted to the SAR via the direct-path or multipath routes [5]. Due to the high power consumption and easy identification and suppression, barrage jamming is less utilized compared to deception jamming. The false target formation by deception jamming will mislead the SAR image interpretation, which is difficult to recognize and mitigate, making deception jamming more flexible and efficient than barrage jamming.

Sensors 2017, 17, 123; doi:10.3390/s17010123

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As a result, anti-jamming and jamming suppression methods have become an appealing research topic in recent years [6–8]. Until now, most of the research and literature has been focused on the problem of narrow band interference (NBI) suppression, which is a classical unintentional interference caused by communication sources and broadcast and TV signals [9–13]. The relevant research on deception jamming suppression, wide band interference, is insufficient and not comprehensive. Miller proposed a parametric method based on building a mathematical model of the interference. Nevertheless, the effectiveness of jamming suppression is determined by the model’s degree of matching with the jamming. In [14], an adaptive two-dimensional filter, relying on estimating the statistical characteristics of the SAR image, was designed to suppress the NBI. Meanwhile, as for a classical non-parametric method, it is arduous to design an appropriate filter for the echo signal, which is not only blurred by NBI but also interfered with by wide band jamming. Methods such as Independent Component Analysis (ICA) and Independent Subspace Analysis (ISA) [12,13], were adopted for NBI suppression. These can extract the statistically independent jamming signal relying on the significant variance between jamming and target echoes in the data domain. ISA improves signal projection from the one-dimensional time domain to the two-dimensional time-frequency domain and reduces the constraints of ICA. However, when the jamming signal is not independent of the target echoes, the jamming suppression effect will be degraded. The aforementioned NBI suppression methods are not suitable for wideband interference, such as deception jamming. Tao et al. utilized the short-time Fourier transform (STFT) to convert the wideband interference (WBI) into a series of instantaneous NBI spectrum mitigation problems [15]. The premise of Tao’s method is that WBI has distinct energy variations in the time-localized spectra that can be captured by the STFT. However, deception jamming can intercept the SAR signal and retransmit it to the SAR without energy variations in localized time. In essence, the main approach to deception jamming suppression is to use a complex signal during transmission and increase the signal to interference ratio (SIR) at the receiving terminal. The MIMO SAR [16,17] realizes this idea based on its multiple channel receiving and transmitting ability. In [18], Gebert proposed the structure of an azimuth MIMO SAR in order to improve the resolution. In [17], the OFDM signal, a typical independent waveform for MIMO radar, is used in MIMO SAR to reduce the range ambiguity. MIMO SAR can not only achieve high-resolution and wide-swath imaging but also has great potential in anti-jamming and jamming suppression. In [19], Rosenberg made use of the multiple channel signal receiving ability, a vital advantage of MIMO SAR, to cancel hot-clutter jamming, one type of multipath jamming. However, direct-path wide band jamming, such as retransmission deception jamming, was not mentioned. To overcome the limitations of the aforementioned methods, we propose herein a novel MIMO structure, called range direction MIMO SAR, to suppress retransmission deception jamming. The multi-channel antenna of the MIMO SAR is arranged along the range direction. First, at the transmitting terminal, the orthogonal frequency division multiplexing (OFDM) LFM signal is adopted as the sub-band signal [20], which has a one-to-one correspondence with the transmitting channel of the antenna array. Then, random phases were modulated in each sub-band signal. After that, the modulated sub-band signal will be concurrently transmitted by the corresponding antenna. The concurrently transmitted sub-band signals will arrive at the jammer at the same time, which makes them hard to intercept and be recognized by the jammer. The jammer can only retransmit the signals with frequencies located in the jammer’s working frequency band. Hence, the jammer’s retransmission time delay will increase more than a Pulse Repetition Time (PRT), which means the phase of the retransmitted deceptive jamming signal will not match the target echo in the azimuth. Second, at the receiving terminal, the sub-band signals will be pre-processed, including the phase compensation, time shift and frequency shift. Then, the sub-band signals can be utilized to synthesize a wide band signal in the range direction. Meanwhile, part of the frequency band of the synthesized wide band signal will be blurred by the retransmission deceiving jamming. Finally, the traditional methods could be applied to get the SAR image of the synthesized wide band signal. After using the proposed methods,

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After using Sensors 2017, 17,the 123 proposed

methods, the jammer signal could not get the signal processing gain3 of and 18 will defocus in the SAR image because of the mismatch with the target echo. Meanwhile, the sub-band signal synthesis will increase the target signal processing gain and the signal to the jammer signal could not get the signal processing gain and will defocus in the SAR image because interference ratio will increase. of theThis mismatch with the targetasecho. Meanwhile, sub-bandthe signal synthesis will increase theMIMO target paper is organized follows: Section the 2 presents principle of range direction signal processing gain and the to interference ratioofwill SAR. Section 3 proposes the signal pre-processing method theincrease. concurrently transmitted sub-band This paper is organized as follows: Section 2 presents the principle range direction SAR. signals of range direction MIMO SAR. Section 4 analyzes the ofefficiency of theMIMO proposed Section 3 proposes the pre-processing method of the concurrently transmitted sub-band signals of retransmission deception jamming suppression. Section 5 shows the results of our simulations. range direction MIMO Section 4 analyzes the efficiency of the proposed retransmission deception Section 6 concludes theSAR. paper. jamming suppression. Section 5 shows the results of our simulations. Section 6 concludes the paper. 2. Principle of Range Multiple Channel MIMO SAR 2. Principle of Range Multiple Channel MIMO SAR

2.1. Geometry Model 2.1. Geometry Model The antenna is staggered in a direction that is vertical with the azimuth direction, which is The antenna is staggered in a direction that is vertical with the azimuth direction, which is called called the range direction. There are M transmitting and receiving sub antennas comprising the the range direction. There are M transmitting and receiving sub antennas comprising the whole linear whole linear MIMO antenna array. The OFDM-LFM [18,20] is used in the Range MIMO SAR, and MIMO antenna array. The OFDM-LFM [18,20] is used in the Range MIMO SAR, and each sub-band each sub-band has a one-to-one correspondence with the sub-antenna element, which means that has a one-to-one correspondence with the sub-antenna element, which means that the number of the number of OFDM sub-band signals is determined by the sub-antenna element count. OFDM sub-band signals is determined by the sub-antenna element count. The geometry model is illustrated in Figure 1. We suppose that there are M sub-antenna The geometry model is illustrated in Figure 1. We suppose that there are M sub-antenna elements, elements, that the distance between them is equal, and that each antenna element can receive the that the distance between them is equal, and that each antenna element can receive the transmitted transmitted signals from the others. As shown in Figure 1, we assume that the MIMO antenna linear signals from the others. As shown in Figure 1, we assume that the MIMO antenna linear array is array is along the y-axis. Its length is L, and the interval between each element is d. The MIMO SAR along the y-axis. Its length is L, and the interval between each element is d. The MIMO SAR travels travels along with the x-axis with a speed of v. The height of the MIMO SAR is H. The projection of along with the x-axis with a speed of v. The height of the MIMO SAR is H. The projection of the SAR the SAR platform in the xoy plane is the coordinate origin. The range direction is along the y-axis. platform in the xoy plane is the coordinate origin. The range direction is along the y-axis. The middle The middle point of the antenna Emid is located at (0, ym, 0) when the azimuth time is zero. Likewise, point of the antenna Emid is located at (0, ym , 0) when the azimuth time is zero. Likewise, when the when the azimuth time is ta, the k-th antenna’s coordinate Ek can be indicated as (vta, yk, H). Hence, an azimuth time is ta , the k-th antenna’s coordinate Ek can be indicated as (vta , yk , H). Hence, an arbitrary arbitrary element Ek’s y-axis coordinate is as follows: element Ek ’s y-axis coordinate is as follows: 1 M y  y  ( k  M ) d k  1...M (1) (1) yk =k ym +m (k − 12 − 2 2 2)d k = 1 . . . M

Figure 1. The Range MIMO SAR geometry model.

There is is aa scatter scatter target target and and aa jammer jammer in in the the observation observation scene. scene. Meanwhile, Meanwhile, if if the the point point scatter scatter There target P P is is located located at at (x (x0,, yy0,, zz0)) and the jammer is located at (xJ, yJ, zJ), the double trip instantaneous target 0 0 0 and the jammer is located at (xJ , yJ , zJ ), the double trip instantaneous slant range of target R kl, which presents the slant range from the k-th transmitting antenna element to slant range of target Rkl , which presents the slant range from the k-th transmitting antenna element to the l-th l-th receiving receiving antenna antenna element, element, can can be be indicated indicated as: as: the

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Rkl (t a )

=q RkP (t a ) + R Pl (t a )

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(vt a − x0 )2 + (yk − y0 )2 + ( H − z0 )2

=

(2)

R kl ( tq a )  R kP ( t a )  R Pl ( t a )

+



(vt a − x0 )22 + (yl − y02)2 + ( H −2 z0 )2 ( vt a  x 0 )  ( y k  y 0 )  ( H  z 0 )

(2)

2  ( ysingle  (H  z 0 range ( vt a  x 0 ) 2the )2 where, ta is the azimuth time, and RkPrepresents slant from the k-th transmitting l  y 0 ) trip

antenna to the P. Similarly, the single slant from from target P k-th to the l-th receiving PlkPis where, ta is target the azimuth time, andRR represents thetrip single triprange slant range the transmitting antenna. Likewise, the double trip instantaneous range of the jammer antenna to the target P. Similarly, RPl is the singleslant trip slant range from target is: P to the l-th receiving antenna. Likewise, the double trip instantaneous slant range of the jammer is: J

Rkl (t a )

= RkJ (t a ) + R Jl (t a )

RklJ (t a )q RkJ (t a )  R2Jl (t a )

(vt a − x J ) + (yk − y J )2 + ( H − z J )2 q  ( vt a  x J ) 2  ( y k  y J ) 2  ( H  z J ) 2 + (vt a − x J )22 + (yl − y 2J )2 + ( H −2 z J )2 =

(3)

(3)

 ( vt a  x J )  ( yl  y J )  ( H  z J )

2.2. Signal Model 2.2. Signal Model

Usually, the sub-band signal can be formed by dividing the wide band signal in the frequency Usually, the sub-band signal can be formed by dividing the wide wide band band signal signal in the frequency domain. This is illustrated in Figure 2. The bandwidth of the original is Bw , and it is domain. This is illustrated in Figure 2. The bandwidth of the original wide band signal is Bw, and it is divided by the bandwidth B. After a time shift, the sub-band signal will be concurrently transmitted in divided by the bandwidth B. After a time shift, the sub-band signal will be concurrently transmitted the corresponding transmission channel. in the corresponding transmission channel.

Figure Theillustration illustration of of the the frequency method. Figure 2. 2. The frequencydividing dividing method.

Supposed that the pulse width is Tw, the bandwidth is Bw, the center frequency is fc, and the

Supposed pulse width is Tw , the frequency bandwidth is BKwr ,isthe center is fsignal c , and the center time that Tc is the 0. Therefore, the modulated ratio equal to Bwfrequency /Tw. At is the center time T is 0. Therefore, the modulated frequency ratio K is equal to B /T . A is the signal c Then, the wideband signal can be indicated as: r w w t amplitude. amplitude. Then, the wideband signal can be indicated as: t ) exp  j (2 f c t   K r t 2 )    T t w

S w ( t )  At rect (

Sw (t) = At rect(

(4)

2

) exp j(2π f c t + πKr t )

(4)

TwM sub-bands, the bandwidth of the sub-band signal B If the wideband signal Sw is divided into is Bw/M and the pulse width of the sub-band signal T is Tw/M. Therefore, the center frequency of the If thesub-band wideband signal w is divided into M sub-bands, the bandwidth of the sub-band signal B is k-th signal is asSfollows:

Bw /M and the pulse width of the sub-band signal T is Tw /M. Therefore, the center frequency of the 1 N k-th sub-band signal is as follows: f k  f c  ( k   ) B k  1...M (5) 2

2

Then, the center time of the k-thf csub-band follows: fk = + (k − 1signal − N )isB indicated k = 1 . .as. M 2

(5)

2

1 N  )T k  1...M k  Tc  ( k  Then, the center time of the k-thTsub-band signal 2 2 is indicated as follows:

(6)

So that the k-th sub-band transmitting signal with random phase modulation can be indicated 1 N as:

Tk = Tc + (k −

2

−

2

)T

k = 1... M

(6)

t So that the k-th sub-band transmitting with can be indicated ( ) exp  f t   Kphase ) S ( t )  A rectsignal t 2 +  modulation (7) as:  j (2random k

t

k

T

t



r

k



2 Without consideration theAtime the concurrent transmission Sk (tof )= ( ) exp j(2π f k t + πK r t + ϕk ) of all sub-band signals is t rectdelay, T as follows:

(7)

Without consideration of the time delay, the concurrent transmission of all sub-band signals is as follows:

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  M t SCT (t) = At ∑ rect( ) exp j(2π f k t + πKr t2 + ϕk ) T k =1

(8)

We suppose that there are nc targets in the scene. Then, the target echoes, which are transmitted by the k-th antenna and received by the l-th antenna, can be indicated as: nc Skl (tr , t a ) = ∑ Ar (δkl , Rnklc )rect(

tr −

n R c (t a ) kl c

T

nc

 )rect( Ttaa ) exp j(2π f k (tr −

Rnklc (t a ) ) + πKr (tr c

−

Rnklc (t a ) 2 ) c



+ ϕk (t a ))

(9)

where tr and ta are the time of range direction and azimuth, respectively. T is the range direction time width of the sub-band signal. Ta is the azimuth synthesis time. fk is the k-th working center frequency nc of the k th transmitting antenna. δkl is the nc -th target radar cross-section (RCS). Ar is the receiving signal amplitude which is attenuated by the radar equation. Theoretically, the antenna elements corresponding with the sub-band will receive other antenna-transmitted sub-band signals because the frequency band of the antenna elements is equal to the wide band signal that is synthesized by the sub-band signal. Hence, the whole echoes of target signal are as follows: S ( tr , t a ) =

∑ Sl (tr , ta ) = ∑ ∑ Skl (tr , ta ) l

l

(10)

k

Usually, we assume that the jammer can only intercept the signal located in its working frequency channel and accurately estimate all the parameters. According to the theoretical model of retransmission deception jamming [3,5], the major procedures are time delay and false information modulation. If the jammer intercepts the I-th sub-band signal, the deception jamming signal model is as follows: J ( tr , t a ) =

∑ ∑ A J [δn (tr − ( l

n

∆R JPn (t a ) 2∆R JPn (t a ) − τs 0 ) − τs ) × S Il (tr , t a )] × exp(− j4π ) c c

(11)

where the ∆R JPn (t a ) is the instantaneous single-trip slant range from point J to the n-th false target P, and τs is the system inherent time delay of the jammer. AJ is the jamming amplitude. The operator * represents the convolution, which means the time delay of the intercepted signal. The false information is included in the additional phase modulation. Generally, the system time delay is beyond the PRT. Therefore, τs 0 is utilized to modify the system time delay as follows: τs 0 = mod(τs ) PRT

(12)

τs > PRT

so that the echoes, which include the target signal and the retransmitted deception jamming signal, can be represented as: S A (tr ,t a )

= S ( tr , t a ) + J ( tr , t a ) = ∑ ∑ Skl (tr , t a ) + ∑ ∑ A J [δn (tr − ( l k

l n

2∆R JPn (t a ) c

− τs 0 ) − τs ) × S Il (tr , t a )] × exp(− j4π

∆R JPn (t a ) ) c

(13)

3. Range MIMO Signal Processing Due to the one-to-one correspondence between the sub-band signal and the antenna element, the range MIMO SAR antenna with M channels is equivalent to having the capability of using M sub-band signals [20]. Moreover, the geometry model of the range MIMO SAR antenna will determine the position of the equivalent phase center [21], which is established to solve the MIMO signal processing. The M antenna elements ranging along the y-axis will produce M × M equivalent phase centers, where (2 × M − 1)’s positions are different from each other. Hence, as Figure 3 shows, the 3-channel MIMO SAR has nine phase centers in total, and only five positions are independent. The equivalent phase center of the k-th transmitting antenna and l-th receiving antenna is located at ykl , and indicated by:

phase center position of three transmitting elements is overlapped and situated in the 2nd antenna element position. In the overlapped phase center, the wide band signal will be synthesized without any additional conditions because the OFDM signal is utilized as the sub-band signal. The bandwidth of the synthesized signal in the 2nd antenna elements is triple that of the sub-band will Sensors 2017,signal 17, 123 when the bandwidth of the sub-band signal is equal. The adjacent phase center6 of 18 synthesize twice the original band width of the sub-band signal. Simultaneously, the range direction resolution of each phase center is diverse, which is positively related to the bandwidth of the ykl = (yk + yl )/2 (14) synthesized wide band signal.

Figure 3. The of the the 3-channel 3-channel range range MIMO MIMO SAR. SAR. Figure 3. The equivalent equivalent phase phase center center of

Meanwhile, for the range direction MIMO SAR with M transmitting and receiving antenna From the equation, the location of ykl is the same with ylk . As the figure shows, the equivalent channels, the bandwidth range of the synthesized signal is from 1 to M times the sub-band signal. To phase center position of three transmitting elements is overlapped and situated in the 2nd antenna get the highest resolution and largest bandwidth, the middle equivalent phase center is utilized as element position. In the overlapped phase center, the wide band signal will be synthesized without an effective jamming suppression terminal. Range direction MIMO SAR has advantages compared any additional conditions because the OFDM signal is utilized as the sub-band signal. to azimuth MIMO [20,22]. The merit of range MIMO is that the azimuth processing is equivalent to a The bandwidth of the synthesized signal in the 2nd antenna elements is triple that of the sub-band traditional single channel SAR without consideration of non-uniform sampling and any Doppler signal when the bandwidth of the sub-band signal is equal. The adjacent phase center will synthesize ambiguity in azimuth direction [23,24]. twice the original band width of the sub-band signal. Simultaneously, the range direction resolution The movement of every equivalent phase center is translational after an azimuth interval. of each phase center is diverse, which is positively related to the bandwidth of the synthesized wide Hence, the azimuth sample will not be staggered. According to the operation principle of equivalent band signal. phase center, the sum of the single-trip slant range RkP and RPl, which is the actual range Rkl, is Meanwhile, for the range direction MIMO SAR with M transmitting and receiving antenna approximate to the double-trip slant range Rkl from the equivalent phase center Ekl with coordinate channels, the bandwidth range of the synthesized signal is from 1 to M times the sub-band signal. (vtaget , yklthe , H)highest to the target P: and largest bandwidth, the middle equivalent phase center is utilized as To resolution an effective jamming suppression 2 R kl ( t a )terminal.  2 ( vt a Range  x 0 ) 2 direction ( y kl  y 0 )MIMO  ( H SAR z 0 ) 2has advantages compared (15) to azimuth MIMO [20,22]. The merit of range MIMO is that the azimuth processing is equivalent to The slantsingle rangechannel Rkl fromSAR the without k-th transmitting antenna element Ek tosampling the l-th receiving antenna a traditional consideration of non-uniform and any Doppler element Elinisazimuth approximately to the double-trip slant range Rkl from the equivalent phase ambiguity directionequal [23,24]. The of every phase center isEtranslational after an interval. to the target P. Forequivalent any antenna elements with coordinate (x, azimuth y, H), the TaylorHence, series center Eklmovement the azimuth sample will not be staggered. According to the operation principle of equivalent phase expansion of the single trip slant range R(ta, y) around arbitrary point yT is: center, the sum of the single-trip slant range RkP and RPl , which is the actual range Rkl , is approximate R ( y )  ( x  x0 ) 2  ( y  y 0 ) 2  ( H  z 0 ) 2 to the double-trip slant range Rkl from the equivalent phase center Ekl with coordinate (vta , ykl , H) to ( y  y0 ) 1 R 2 ( yT )  ( yT  y 0 ) 2 the target P:  R ( yT )  q T ( y  yT )  ( y  yT ) 2 (16) 3 R ( yT )

2

R ( yT )

2 2 Rkl(tRa )( y=) 2 A ((yvt ay−) x0B)(2y+  (yy)kl2 − y0 ) + ( H − z0 ) T

T

T

(15)

The slantthe range Rklrange from R theisk-th transmitting element Ek topoint the l-th receiving the center of the linear antenna antenna Usually, slant expanded aroundantenna Emid, i.e., element E is approximately equal to the double-trip slant range R from the equivalent phase center l kl array. Hence, Equation (2) can be written as follows: Ekl to the target P. For any antenna elements E with coordinate (x, y, H), the Taylor series expansion of the single trip slant range R(ta , y) around arbitrary point yT is: R(y)

=

q

( x − x0 )2 + ( y − y0 )2 + ( H − z0 )2

≈ R(y T ) + ≈ R(y T ) +

2 ( y T − y0 ) y T − y0 )2 (y − y T ) + 12 R (yTR)−( ( y − y T )2 3 (y ) R(y T ) T A ( y − y T ) + B ( y − y T )2

(16)

Usually, the slant range R is expanded around Emid , i.e., the center point of the linear antenna array. Hence, Equation (2) can be written as follows:

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Rkl ( yk , yl )  2R( ym )  A ( yk  ym )  ( yl  ym )   B  ( yk  ym )2  ( yl  ym )2 

(17)

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The position of the equivalent phase center is the center between the transmitting and receiving   antenna elements. The Taylor series expansion of the equivalent phase center can be indicated as (17) Rkl (yk , yl ) ≈ 2R(ym ) + A((yk − ym ) + (yl − ym )) + B (yk − ym )2 + (yl − ym )2 follows: 2 transmitting and receiving The position of the equivalent Rkl ( ykl )phase  2R(center ym )  2isA(the ykl center ym )  between 2B( ykl  ythe (18) m) antenna elements. The Taylor series expansion of the equivalent phase center can be indicated Meanwhile, the slant range difference is as follows: as follows: 2 2 ( y kl − y m ) Rkl (ykl ) ≈ 2R(ym ) + 2A(ykl − (yym )+y2B (18) k l)  R = R kl  R kl  B (19) Meanwhile, the slant range difference is as follows: 2

( y k − y l )2 (19) 2 The phase difference, which is caused by the range difference and has some negative effects on 3.1.SAR Phaseimaging, Error Correction the needs to be corrected in any imaging process. As Equation (16) shows, B can be indicated as: The phase difference, which is caused by the range difference and has some negative effects on 3.1. Phase Error Correction

∆R = Rkl − Rkl ≈ B

the SAR imaging, needs to be corrected in any imaging As Equation (16) shows, B can be ) 1 R c2 ( y m process. B (20) 3 indicated as: 2 Rc ( y m ) 2 1 Rc⊥ (ym ) B =range (20) where Rc(ym) presents the instantaneous slant the center point of the antenna array 2 R3c (between ym ) and the target point. Rc  ( ym ) is the projection of Rc(ym) in the xoz plane. Hence, the phase difference where Rc (ym ) presents the instantaneous slant range between the center point of the antenna array and is astarget follows: the point. Rc⊥ (ym ) is the projection of Rc (ym ) in the xoz plane. Hence, the phase difference is as follows:  d 2 R2 (y )   =  πd2kl R2c 3(ymm) (21) (21) ∆ϕ = − 2 kl Rc3⊥c ( y m ) 2λ Rc (ym ) where dkl = yk − yl. It presents the absolute interval between element Ek and element El. where dkl = yk − yl . It presents the absolute interval between element Ek and element El . On the one hand, the phase error is related to the synthesis aperture time for the same target. On the one hand, the phase error is related to the synthesis aperture time for the same target. When the azimuth changed, the phase error for the same target P with coordinate (x0, y0, z0) can be When the azimuth changed, the phase error for the same target P with coordinate (x0 , y0 , z0 ) can be indicated as: indicated as: 2 2 (t ) πdkld2 kl 2R2cR⊥c2( t(a1 t a 1)) RR ⊥t a 2 )a2 c c(    ( ) ) − (22) E ϕt =E− ( (22) t 3 3 3 3 t a 1)) RR 2λ2  RcR(ct(a1 c (ct( a 2t ) a2 ) We suppose suppose that that the the velocity velocityof ofthe theSAR SARplatform platformisis300 300m/s, m/s,dijdis 5 m,λ is is 0.056 0.056 m, m, and and the the ij is 5 m, We centerpoint pointPPisislocated locatedatat(0, (0,16010, 16010,0).0).When When is zero and ta2from is from −2.5/s to 2.5/s, the phase a1 zero and ta2 is −2.5/s to 2.5/s, the phase error center ta1tis error change is as shown in Figure 4. change is as shown in Figure 4.

Figure Figure4.4.Phase Phaseerror errorin indifferent different azimuth azimuth time. time.

The phase error will increase when ta2 is far from ta1 . Thus, the phase error needs to be corrected in each azimuth sampling time.

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The phase error will increase when ta2 is far from ta1. Thus, the phase error needs to be corrected in eachThe azimuth phasesampling error willtime. increase when ta2 is far from ta1. Thus, the phase error needs to be corrected On other hand, hand, the the phase phase error is related to the positions of the different targets in the On the the other in each azimuth sampling time. error is related to the positions of the different targets in the main-lobe beam coverage. Usually, we use slant of point in the coverage to main-lobe coverage. weerror use the the slant range range of the thecenter centerof point thebeam beam coverage On beam the other hand, Usually, the phase is related to the positions the in different targets in the replace the the slantslant ranges of the other targets in thein scene. Meanwhile, the phase will be imported. tomain-lobe replace ranges of the other targets therange scene. the error phase error will be beam coverage. Usually, we use the slant of Meanwhile, the center point in the beam coverage If there are two targets P and P with coordinates (x , y , z ) and (x , y , z ), the phase error between 1 targets 1 (x1, yMeanwhile, 2 2(x2, the imported. If there are two P1 and P2 with coordinates 1, z2 1) and y2, zphase 2), the phase errorbe to replace the slant ranges of2 the other targets in1 the1 scene. error will P and P2Pis: 1imported. between 1 and P 2 is: If there are two targets P1 and P2 with coordinates (x1, y1, z1) and (x2, y2, z2), the phase error between P1 and P2 is: πd dklkl2 2 ( x( x−xx1 )12)2+( ( zz−zz11))22 ( x(x−x2x)22)2+( ( zz−zz22))22 E ϕP (23)  − 2λ (( − )) E P= (23) 3/2 2 2 2 3/2 2 2 3/2 2 2 2 2 22 3/2 2 d 2(((( (( x((x− ( yy x yyx−y)y121)) ( x2x)2 )( x+( x −x1x)1 ) +( )2( +( (+( x(  z(zz− z1z)z112)) )) x−2y)y222) z(zz−z2zz)222)) )) kl 1 (  ) E P   (23) 2 (( x  x1 )2  ( y  y1 )2  ( z  z1 )2 )3/2 (( x  x2 )2  ( y  y2 )2  ( z  z2 )2 )3/2 When the the wave wavelength lengthand andantenna antennainterval interval are fixed, the phase error is only affected by the are fixed, the phase error is only affected by the target target position. suppose that theantenna position of target P2 fixed, is moving along the x-axis and y-axis. Then, position. We suppose that the position of target P2 isare moving along the x-axis and y-axis. Then, is When theWe wave length and interval the phase error is only affected byP1the is located (0,Accordingly, 0). Accordingly, for position different intervals of antenna channel d,the thephase phase error P1target located at (0,at0). for the different intervals ofPthe antenna channel error isisas position. We suppose that of target 2 isthe moving along the d, x-axis and y-axis. Then, asPshown Figure shown by by Figure 5. 5. 1 is located at (0, 0). Accordingly, for different intervals of the antenna channel d, the phase error is as shown by Figure 5.

(a)

(b)

(b) the x-axis; (b) P2’s Figure 5. Phase error in(a) different channel interval: (a) P2’s position shifting along Figure 5. Phase error in different channel interval: (a) P2’s position shifting along the x-axis; (b) P2’s position y-axis. channel interval: (a) P2’s position shifting along the x-axis; (b) P2’s Figureshifting 5. Phasealong errorthe in different position shifting along the y-axis. position shifting along the y-axis.

If target P2 is at any point in the scene and d is 1.5 m, the phase error of the beam coverage will If targetas P isFigure at any 6. point in the scene and d is 1.5 m, the phase error of the beam coverage will be be obtained If target2in P2 is at any point in the scene and d is 1.5 m, the phase error of the beam coverage will obtained as in Figure 6. be obtained as in Figure 6.

(a)

(b)

Figure 6. Phase error of(a) the entire scene: (a) Three-dimensional phase error; (b)(b) Contour of the phase error. Figure 6. Phase error of the entire scene: (a) Three-dimensional phase error; (b) Contour of the phase Figure 6. Phase error of the entire scene: (a) Three-dimensional phase error; (b) Contour of the error. phase error.

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To obtain a high resolution image, the phase difference needs to be modified by using the center point of the beam coverage. The simulation proved that when the antenna interval d is smaller, the phase error is acceptable for image processing. 3.2. Signal Processing Flowchart The signal processing includes two primary parts: preprocessing and imaging processing. After preprocessing, the traditional imaging algorithm can be utilized. The procedure of preprocessing is as follows: the first step in multiple sub-band signal processing is using the corresponding center frequency to demodulate the sub-band signals. Then, the sub-band signals are filtered to reduce the out-band noise and wide band jamming. The second step of the filtered sub-band signal is modifying the random phase of the sub-band signal. After this step, the target signal will be accurately matched. However, the system time delay of the deception jamming permits the jamming signal mismatch. The third step of the echo is the phase difference compensation for the multiple band signals. The fourth step of the compensated signal is the synthesis of the wide band signal using the sub-band signals. We supposed that there are M receiving and transmitting channels in the range MIMO SAR. Hence, the receiving signal can be indicated as: 

S11

  Sr =   

S12 S21

··· S22 .. .

S1M ··· .. . S M1

 S2M

··· S M2

..

    

.

(24)

S MM

According to the position of the signal equivalent phase center, the sub-band signal is settled in the matrix. Every column presents a phase center. Meanwhile, the Q-th equivalent phase center signal is: Q

E = SQ ∑ S k ( Q +1− k ) ( t r , t a )

Q ∈ [1, 2M − 1]

(25)

k =1

The band width is determined by the position of the equivalent phase center. BQ , the band width E , is as follows: of SQ ( QB Q≤M BQ = (26) (2M − Q) B Q > M Thus, the widest band width BW = MB. The number and bandwidth of the sub-band signal are two decisive components of BW . To analyze the preprocessing easily, we ignore the influence of the target number and RCS. Let τa = Rijnc (t a )/c, the equation can be indicated as: E (t , t ) SQ r a

Q

= ∑ Sk ( Q +1− k ) ( t r , t a ) k =1 Q

= ∑

k =1

rect( tr −T τa )rect( Ttaa ) exp



2

j(2π f k (tr − τa ) + πKr (tr − τa ) )



(27)

The SOB , echo of the transmitted wide band signal Sw , is as follows: SOB (tr , t a ) = rect(

  tr − τa ta )rect( ) exp j(2π f c (tr − τa ) + πKr (tr − τa )2 ) MT Ta

(28)

E. Simultaneously, it can be represented by the sub-band signal SQ

E SOB = SQ

M

Q= M

(tr − ( Tk − Tc )) =

∑ Sk( M+1−k) (tr − ∆Tk , ta )

k =1

(29)

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where ∆Tk is equal to Tk − Tc . The sub-band signal will be separated according to different carrying frequencies. Therefore, the sub-band signal is demodulated by the center frequency and compensated random phase: E SQ

M

Q= M

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= ∑ Sk( M+1−k) (tr , t a ) exp(− j2π f k tr )exp(− jϕk (t a )) k =1   M = ∑ rect( tr −T τa )rect( Ttaa ) exp j(−2π f k τa + πKr (tr − τa )2 )

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(30)

M k =1 S QE =  S k ( M 1- k ) (t r , t a ) exp(  j 2 f k t r ) exp(  j k (t a )) QM

k 1

Then, every sub-band signal inMthe same phase center is time shifted. Let tr (30) = tr − ∆Tk , t   a equivalent t   rect ( r ) rect ( a ) exp  j (  2 f k a   K r (t r   a ) 2 )  T T so the process is as follows: k 1 a E SQ

Sensors 2017, 17, 123 10 of 17 Then, everyM sub-band signal in the same equivalent phase center is time shifted.   Let tr  tr  Tk , so tr −∆Tk −τa 2 ta (tr process − ∆Tk ) is=as ∑ rect( )Mrect( Ta ) exp j(−2π f k τa + πKr (tr − ∆Tk − τa ) ) the follows: T Q= M k =1 E S = S ( M 1- k )  (t , t ) exp(  j 2 f k t r ) exp(  j k (t a ))  Q MQ  M M t  k T   r a ta E 2 − S=  τa )rect 2πK  f kra(tr− Kr τ   a )(− (trect (tar )2)Tk exp ) j2π∆ f k tr ) exp((30) rect( k(Mr1Ttaa )T kexpa )rect j(−( 2π) exp f c τaj (+ jπKr ∆Tk 2 ) (kt)rMT Q Q ∑ r  T M k 1 t   a Ta t a k =1  rect ( r ) rect ( ) exp j (  2 f    K (t   ) 2 )









 



k a r r a tkr 1  a Tt T )rect ( a ) exp  j ( a2 f c a   K r (tr   a ) 2 )  exp( j 2f k tr ) exp( j K r Tk 2 ) MT Ta k 1 Comparing Then, this equation with Equation (30), the time shifted a  Tk , so every sub-band signal in the same equivalent phase center issub-band time shifted. signal Let tr  trlacks M

  rect (

(31)

(31)

linear phase the process as follows: Comparing this equation withshift Equation thecompensation time shifted sub-band signal lacks linearband by and a constant phase.is The frequency and (30), phase will recover theawide and a constant phase. The frequency shift will recover the wide bandof range t  T In  conclusion, t and phase compensation using thephase time-shifting signals. flow chart S sub-band rect (    Ksignal  ) ) (t  T )   )rect ( ) exp  j (2 f the (t  T preprocessing by using the time-shifting sub-band Tsignals. TIn conclusion, the signal preprocessing flow chart of (31) modulation, MIMO SAR which adopts the OFDMt signal as the sub-band signal and random phase  t range MIMO SAR which adopts phase  K the f t ) exp( jand K T random ( ) exp  jsignal ( 2 f  as (t   sub-band ) )  exp( j 2signal )  rect ( MTthe)rectOFDM T is as seenmodulation, in Figure 7. is as seen in Figure 7. E Q QM

M

r

k

r

k

a

M

k 1

2

a

k 1

k a

r

r

k

a

a

r

a

a

2

c a

r

r

a

2

k r

r

k

a

Comparing this equation with Equation (30), the time shifted sub-band signal lacks a linear phase and a constant phase. The frequency shift and phase compensation will recover the wide band by using the time-shifting sub-band signals. In conclusion, the signal preprocessing flow chart of range MIMO SAR which adopts the OFDM signal as the sub-band signal and random phase modulation, is as seen in Figure 7.

Figure 7. Range MIMO SAR signal preprocessing flowchart.

Figure 7. Range MIMO SAR signal preprocessing flowchart. After preprocessing, the sub-band signals have to be synthesized into a wide band signal that can be utilized tothe obtain SAR images a traditional imaging into algorithm. the that can After preprocessing, sub-band signals by have to be synthesized a wideMoreover, band signal Figure 7. Range MIMO SAR signal preprocessing flowchart. preprocessing will suppress the jamming signals.

be utilized to obtain SAR images by a traditional imaging algorithm. Moreover, the preprocessing will After preprocessing, the sub-band signals have to be synthesized into a wide band signal that suppress4.the jamming signals. Range Direction MIMO SAR Anti-Deception Jamming Efficiency Analysis can be utilized to obtain SAR images by a traditional imaging algorithm. Moreover, the preprocessing suppress the jamming signals. Considering will the retransmision deception jamming in the echoes as Figure 8, the anti-jamming

4. Range Direction MIMO SAR Anti-Deception Jamming Efficiency Analysis

efficiency of the range MIMO SAR is analyzed after signal pre-processing and imaging. 4. Range Direction MIMO SAR Anti-Deception Jamming Efficiency Analysis

Considering the retransmision deception jamming in the echoes as Figure 8, the anti-jamming Considering the retransmision deception jamming in the echoes as Figure 8, the anti-jamming Sub-band Echo efficiency of the range MIMO SAR is analyzed after signal pre-processing and imaging. efficiency of the range MIMO SAR is analyzed after signal pre-processing and imaging. Signal

Sub-band Echo Signal

Retransmitting Jamming Signal

Range Direction MIMO Signal Range Pre-Processing Direction Method MIMO Signal Pre-Processing Method

Conventional Imaging Method

Conventional Imaging Method

Image Image

Retransmitting Jamming Figure 8. Anti-jamming efficiency analysis flowchart. Signal

FigureMIMO 8. Anti-jamming efficiency analysis flowchart. Because the range direction SAR using the concurrently transmitted sub-band signal is Figure 8. Anti-jamming efficiency analysis flowchart. modulated by a random phase, the jammer processing time will increase and even cannot intercept

Because the range direction MIMO SAR using the concurrently transmitted sub-band signal is

be indicated and recognize concurrently transmitted signals. The inherent system time delay  s canintercept modulated by a random phase, the jammer processing time will increase and even cannot

Because the range direction MIMO SAR using the concurrently transmitted sub-band signal is as follows: and recognize concurrently transmitted signals. The inherent system time delay  s can be indicated modulated by a random phase, the jammer processing time will increase and even cannot intercept as follows:  s =  s PRT  PRT +mod(  s ) PRT  nPRT   s  (32) and recognize concurrently transmitted signals. The inherent system time delay τs can be indicated  s =  s PRT  PRT +mod(  s ) PRT  nPRT   s  (32) as follows:

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τs = bτs /PRT c PRT + mod(τs ) PRT = nPRT + τs 0

(32)

where b c represents selecting the lesser round number, and mod means selecting the remainder. The integer n indicates that the jamming signal will fall behind n PRTs in the SAR receiving terminal. As in Equation (11), we suppose that the jammer intercepts the I-th sub-band signal: J

J (tr , t a ) = A J S Il (tr −

2∆R JP (t a ) , t a − nPRT ) c

(33)

After carrying out frequency demodulation and random phase demodulation, the deception jammer signal is as follows: J ( tr , t a )

  0 = A J rect( tr −T τ )rect( Ttaa ) exp jπKr (tr − τ 0 )2

· exp(− j2π f k τ 0 ) exp( j( ϕ I (t a ) − ϕ I (t a − nPRT )))

(34)

where Am means the jammer signal gain [4,25]. τ 0 is the time delay and is given as follows: J

τ0 =

R Il (t a ) + 2∆R JP (t a ) c

(35)

After range compression, the jammer signal is as follows: J ( tr , t a )

= A J T sin c( Br (tr − τ 0 ))rect( Ttaa ) exp(− j2π f k τ 0 ) · exp( j∆ϕ(t a ))

(36)

where ∆ϕ(t a ) means the phase difference caused by the jammer system time delay and is equal to the minus phase: ∆ϕ(t a ) = ϕ I (t a ) − ϕ I (t a − nPRT ) (37) Next, we suppose that the slant range of the deception target generated by the retransmit jamming is approximate with the real target: J

R PIl (t a ) ≈ R Il (t a ) + 2∆R JP (t a )

(38)

Hence, after the Range Cell Migration Correction, the false target P will be corrected into the shortest slant range R PIl . The jamming signal is as follows: J ( tr , t a )

= A J T sin c( Br (tr − · exp( j∆ϕ(t a ))

R PIl ta 0 c ))rect ( Ta ) exp(− j2π f k τ )

(39)

If the azimuth compression response function is h a (t a ), the azimuth compression process is as follows: R J (tr , t a ) = rect( Tτa ) exp(− j2π f k (ατ + βτ 2 )) exp( j∆ϕ(τ ))h a (τ − t a )dτ Ta (40) R PIj · A J T sin c( Br (tr − c )) Based on the integral mean value theorem, the azimuth gain of the jamming signal is in the range given by the expression: Ta min( Ja (τ )h a (τ − t a )) ≤

w

Ja (τ )h a (τ − t a )dτ < Ta max( Ja (τ )h a (τ − t a ))

(41)

Ta

where Ja is the azimuth signal of the entire jamming signal J. Equation (41) shows that the jamming signal defocuses in the azimuth direction due to the random phase mismatch. The greater the phase

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difference randomness, the lower the jamming signal pulse compression processing gain. The shorter the integrating range, the lower the jamming signal compression processing gain. We suppose that the jamming signal azimuth processing gain is K (Ta ), which is less than the real target azimuth processing gain Ta . As Equation (40) shows, the jamming signal will achieve sub-band range compression gain. Hence, according to whole signal processing flowchart, the total gain of the jamming signal is proportional to the following equation: G JP ∝ A J TK ( Ta )

(42)

As for the single sub-band target signal, after the range and azimuth compression processing, the total gain is as follows: GPsig ∝ TTa (43) Then, the sub-band signal will be synthesized to a wide band signal, which will increase the range processing gain. The total gain will be as follows: GPall ∝ MTTa

(44)

Hence, the peak aptitude ratio of the target to jamming without sub-band synthesizing is indicated as: GPsig Ta r A1 = (45) = G JP A J K ( Ta ) The peak aptitude ratio of target to jamming after sub-band synthesizing is indicated as: r A2 =

GPall MTa = = Mr A1 G JP A J K ( Ta )

(46)

5. Simulation Retransmission deception jamming is simulated in this part. We supposed that the range direction MIMO SAR has 5-channel antenna elements. The geometry model is as shown in Figure 1. The target is located in a 3 × 3 matrix that has a middle point P in the center of the scene with coordinates (0, 16010, 0). Then, the interval in the range direction of the point matrix is 10 m, and the interval in the azimuth is 30 m. The jammer J is located in the adjacent point in the same row with coordinates (0, 16000, 0) in the point matrix. The other simulation conditions are given the Table 1. Table 1. Simulation conditions. Parameter

Value

Carry Frequency Sub-band Number Channel interval d SAR speed v SAR height H Pulse width of sub band signal T Chirp rate in range direction Over sampling rate Band width in azimuth Pulse Repetition Frequency

5.3 GHz 5 1.5 m 300 m/s 8000 m 5 µs 20 × 1012 Hz/s 1.2 80 Hz 100 Hz

First, the random phase modulation is simulated. We suppose that the modulation random phase obeys Gaussian noise N (0, 2π ) and that the jammer system time delay is 2 PRTs. When the azimuth synthesis time and frequency modulation rate are fixed such that the azimuth time is 1 s and the chirp rate in the azimuth direction is 500 Hz, the result of the jammer signal and target signal azimuth

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compression processing is as follows: Figure 9 shows that the deception jamming signal will defocus after the azimuth compression because of the phase residue in random phase compensation. The phase Sensors 1313ofthe residue is 17, associated with the time delay of retransmitting jamming signal. Next, we analyze Sensors2017, 2017, 17,123 123 of1717 effect of the azimuth time to the peak amplitude ratio (PAR) of the target signal to the jamming signal the chirp and rate kHz/s. azimuth time from ss theazimuth azimuth chirprate rateisis5050kHz/s kHz/s andthe thesampling sampling rateisis6060 kHz/s.The The azimuth timeisischirp from0.01 0.01is without sub-band synthesis. The Monte-Carlo experiment simulated when the azimuth rate to 1 s, and the random phase still obeys . The peak amplitude ratio simulation is as seen in N (0, 2  ) to kHz/s 1 s, andand thethe random phase still obeys The peak amplitude ratios simulation is asrandom seen in N (0,The 2 ) .azimuth 50 sampling rate is 60 kHz/s. time is from 0.01 to 1 s, and the Figure 10. phase Figurestill 10.obeys N (0, 2π ). The peak amplitude ratio simulation is as seen in Figure 10.

Figure Figure9.9.9.Azimuth Azimuthcompression compressionresult resultof oftarget targetand andjamming. jamming. Figure Azimuth compression result of target and jamming.

Figure Figure10. 10.Peak Peakamplitude amplituderatio ratioin indifferent differentazimuth azimuthtime. time. Figure 10. Peak amplitude ratio in different azimuth time.

ItItisisnoticeable that the PAR will when the time which noticeable that willincrease increase when theazimuth azimuth timeisisincreasing, increasing, whichisis It is noticeable that the the PARPAR will increase when the azimuth time is increasing, which is consistent consistent with analysis that totothe time. The effect ofofthe consistent withthe thetheoretical theoretical analysis thatrA1 rA1isisproportional proportional theazimuth azimuth effect the with the theoretical analysis that rA1 is proportional to the azimuth time. The time. effectThe of the random random phase modulation relies on the azimuth time. The longer the azimuth time, the better the random phase modulation relies on the azimuth time. The longer the azimuth time, the better the phase modulation relies on the azimuth time. The longer the azimuth time, the better the jamming jamming result. we that delay time and jammingsuppression suppression result.Second, Second, wesuppose suppose thatthe theinherent inherentjammer jammer delay timeisand is2 2PRT PRT and suppression result. Second, we suppose that the inherent jammer delay time is 2 PRT that the that thatthe thejammer jammerintercepts interceptsthe thethird thirdband bandsignal signaland andforms formsthe theretransmitted retransmittedjamming jammingsignal. signal.When When the F1F1and F2F2located thejammer jammerJ Jforms formstwo twofalse falsepoint pointtargets targetsPP andPP locatedatat(15, (15,16010, 16010,0)0)and and(−15, (−15,16010, 16010,0), 0), respectively, respectively,the theimaging imagingresult resultisisasasseen seenininFigure Figure11. 11. When Whenthe theinterference interferencetotosignal signalratio ratioisisfrom from0 0dB dBtoto4040dB dBand andthe thestep stepisis2020dB, dB,which whichmeans means that the interference power is increasing, the sub-band synthesis processing of range MIMO that the interference power is increasing, the sub-band synthesis processing of range MIMOSAR SAR

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jammer intercepts the third band signal and forms the retransmitted jamming signal. When the jammer J forms two false point targets PF1 and PF2 located at (15, 16010, 0) and (−15, 16010, 0), respectively, Sensors 2017, 17,result 123 is as seen in Figure 11. 14 of 17 the imaging

Figure 11. Deception jamming image in traditional SAR.

As Figures 12–14 show, the deception jamming signal is obviously defocusing in the azimuth in both sub-band synthesis and single band processing so that there is a jamming stripe forming along the azimuth. Owing to the random phase modulation, the deception jamming only gets the range Figure 11. Deception Deception jamming image intraditional traditional SAR. direction compression gain. Meanwhile, thejamming jamming signal is locatedSAR. in the right range bin with the Figure 11. image in range coordinate 16010. As Figures 12–14 show,increases the deception signal obviously defocusing in the azimuth in As the jamming power fromisjamming 0from dB to 40 dB,40isthe ofisthe When the interference to signal ratio 0 dB to dB amplitude and the step 20 jamming dB, whichstripe meansalso both sub-band synthesis and single band processing so that there is a jamming stripe forming along increases. With the same power, the jamming suppression effect of sub-band synthesis that the interference powerjamming is increasing, the sub-band synthesis processing of range MIMO SAR and the azimuth. Owing to the random phase modulation, the deception jamming only gets the range processing is better than that of the single sub-band processing. As Figure 14b shows, the amplitude single band processing are simulated, respectively. direction compression gain. Meanwhile, the jamming signal is located in the right range bin with the of jamming is greater that the real jamming target in signal singleissub-band has negative As Figures 12–14than show, theof deception obviouslyprocessing, defocusing which in the azimuth in range coordinate 16010. effects on the image interpretation. Nevertheless, as Figure 14a shows, the amplitude of the jamming both sub-band synthesis and single band processing so that there is a jamming stripe forming along As the jamming power increases from 0 dB to 40 dB, the amplitude of the jamming stripe also signal is still less than to that the realphase targetmodulation, in sub-band synthesis processing, which almost has no the azimuth. Owing theofrandom the deception jamming only gets the range increases. With the same jamming power, the jamming suppression effect of sub-band synthesis directioneffects compression Meanwhile, the jamming signal is located in the range binPAR with of thethe negative on thegain. image interpretation. The quantitative results forright the SIR and processing is better than that of the single sub-band processing. As Figure 14b shows, the amplitude rangetocoordinate 16010. signal interference is than indicated Table of jamming is greater that ofinthe real2.target in single sub-band processing, which has negative effects on the image interpretation. Nevertheless, as Figure 14a shows, the amplitude of the jamming signal is still less than that of the real target in sub-band synthesis processing, which almost has no negative effects on the image interpretation. The quantitative results for the SIR and PAR of the signal to interference is indicated in Table 2.

(a)

(b)

Figure 12. ISR 0 dB sub-band synthesizing and single sub-band imaging result: (a) Sub-band Figure 12. ISR 0 dB sub-band synthesizing and single sub-band imaging result: (a) Sub-band synthesis synthesis of a two-dimensional gray (b) Singleofsub-band of a two-dimensional of a two-dimensional gray image; (b)image; Single sub-band a two-dimensional gray image. gray image.

(a)

(b)

Figure 12. ISR 0 dB sub-band synthesizing and single sub-band imaging result: (a) Sub-band synthesis of a two-dimensional gray image; (b) Single sub-band of a two-dimensional gray image.

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15 of 17 15 of 17

(a) (a)

(b) (b)

Figure 13. ISR 2020dB sub-band synthesisand and singlesub-band sub-band imaging result: (a) Sub-band synthesis Figure ISR20 dBsub-band sub-band synthesis synthesis imaging result: (a) Sub-band synthesis of Figure 13.13. ISR dB andsingle single sub-band imaging result: (a) Sub-band synthesis of aatwo-dimensional two-dimensionalgray gray image; (b) Single sub-band oftwo-dimensional a two-dimensional gray image. image; (b) Single sub-band of a gray image. of a two-dimensional gray image; (b) Single sub-band of a two-dimensional gray image.

(a) (a)

(b) (b)

Figure 14. ISR 40 dB sub-band synthesis and single sub-band imaging result: (a) Sub-band synthesis Figure 14.14. ISR synthesis andsingle singlesub-band sub-band imaging result: (a) Sub-band synthesis ISR4040dB dBsub-band sub-band synthesis and imaging (a) Sub-band synthesis of of Figure a two-dimensional gray image; (b) Single sub-band synthesis of aresult: two-dimensional gray image. of aa two-dimensional two-dimensionalgray grayimage; image; (b) Single sub-band synthesis of a two-dimensional gray image. (b) Single sub-band synthesis of a two-dimensional gray image. Table 2. The quantitative results for retransmitting deception jamming suppression. Table 2. The quantitative results for retransmitting deception jamming suppression.

As the jamming power increases from 0 dB to 40 dB, the amplitude of the jamming stripe also SIR1 2 rA2 3 rA1 4 ISR (dB) SIR2 11 increases. With the power, the jamming effectrA1of4 sub-band synthesis 2 SIR1 2 suppression rA2 3 ISRsame (dB) jamming SIR 0 5.7447 1.1337 43.5424 8.7777 processing is better than single sub-band processing. As Figure 14b shows, the amplitude 0 that of the5.7447 1.1337 43.5424 8.7777 10 1.8101 0.3576 16.4348 3.3168 10 1.8101 0.3576 16.4348 3.3168 of jamming is greater than that of the real target in single sub-band processing, which has negative 20 0.5729 0.1133 11.8402 2.3888 20 0.5729 0.1133 2.3888 effects on the image interpretation. Nevertheless, as Figure 14a11.8402 shows, the amplitude of the jamming 30 0.1818 0.0360 7.7389 1.5587 0.1818 0.0360 synthesis 7.7389 1.5587 signal is still less than30that of the real target in sub-band processing, which almost has no 40 0.0575 0.0115 2.9233 0.5903 0.0575 0.0115 2.9233for the SIR 0.5903 negative effects on the40image interpretation. The quantitative results and PAR of the signal 1 SIR2: signal to interference ratio; 2 SIR2: single sub-band signal to interference 1 SIR2: signal to interference ratio; 2 SIR2: single sub-band signal to interference to interference is indicated in Table 2. ratio; 33 rA2: the peak aptitude ratio of sub-band synthesizing signal to rA2after : the image peak processing, aptitude ratio of sub-band to synthesis As Tableratio; 2 shows, the SIR and PAR, synthesizing including thesignal sub-band interference; 44 rA1: the peak aptitude ratio of single sub-band signal to r A1 : the peak aptitude ratio of single sub-band signal interference; process and the single sub-band process, will decrease when the ISR in the echoes to is increasing. interference. However, theinterference. SIR and PAR of the sub-band synthesis process are higher than those of the single band process, which has also been illustrated in Figures 12–14. Even when the deception jamming signal As Table Table 22 shows, shows, after after image image processing, processing, the the SIR SIR and and PAR, PAR, including including the the sub-band sub-band synthesis As power is 40 dB, the PAR of the sub-band signal synthesis is 2.9. Nevertheless, the PAR of thesynthesis single process and and the the single single sub-band sub-band process, process, will will decrease decrease when when the the ISR ISR in in the echoes echoes is is increasing. increasing. process sub-band process is 0.59, which means the amplitude of the jamming signalthe is larger than what the

However, the the SIR SIR and and PAR PAR of of the the sub-band sub-band synthesis synthesis process process are are higher higher than than those those of of the the single single However, band process, process, which which has has also also been been illustrated illustrated in in Figures Figures 12–14. 12–14. Even Even when when the the deception deception jamming jamming band signal power is 40 dB, the PAR of the sub-band signal synthesis is 2.9. Nevertheless, the PAR of the the signal power is 40 dB, the PAR of the sub-band signal synthesis is 2.9. Nevertheless, the PAR of single sub-band sub-band process process is is 0.59, 0.59, which which means means the the amplitude amplitude of of the the jamming jamming signal signal is is larger larger than than single what the target shows in Figure 14b. After sub-band synthesis is used, the SIR and PAR will have what the target shows in Figure 14b. After sub-band synthesis is used, the SIR and PAR will have

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target shows in Figure 14b. After sub-band synthesis is used, the SIR and PAR will have increases in the sub-band number of times in the theoretical analysis. The simulation result is as follows: Table 2. The quantitative results for retransmitting deception jamming suppression. ISR (dB) 0 10 20 30 40

SIR2

1

5.7447 1.8101 0.5729 0.1818 0.0575

SIR1

2

1.1337 0.3576 0.1133 0.0360 0.0115

rA2

3

43.5424 16.4348 11.8402 7.7389 2.9233

rA1

4

8.7777 3.3168 2.3888 1.5587 0.5903

1 SIR Sensors 2017, 17, 123to interference ratio; 2 SIR2 : single sub-band signal to interference ratio; 3 rA2 : the peak aptitude 16 of 17 2 : signal

ratio of sub-band synthesizing signal to interference; 4 rA1 : the peak aptitude ratio of single sub-band signal to interference.

increases in the sub-band number of times in the theoretical analysis. The simulation result is as follows: AsAs Figure 1515 shows, andSIR SIRpromotion promotion are both approximately A1and Figure shows,the thePAR PARpromotion promotionrA2 rA2/r /rA1 are both approximately 5, 5, which is the sub-band number in the Hence, by comparing the results of sub-band synthesis which is the sub-band number insimulation. the simulation. Hence, by comparing the results of sub-band processing and single sub-band processing, one obvious feature is that the range direction MIMO SAR synthesis processing and single sub-band processing, one obvious feature is that the range direction canMIMO effectively suppress deception jamming. SAR can effectively suppress deception jamming.

Figure15. 15.SIR SIRand and PAR PAR promotion promotion simulated Figure simulatedand andtheoretical theoreticalvalue. value.

6. Conclusions 6. Conclusions paper, a range direction MIMO SAR system is proposed as aretransmission novel retransmission In In thisthis paper, a range direction MIMO SAR system is proposed as a novel deception deception jamming suppression SAR. Based on concurrent transmission of sub-band signals with jamming suppression SAR. Based on concurrent transmission of sub-band signals with random random initial phase modulation and sub-band synthesis in the equivalent phase center of the initial phase modulation and sub-band synthesis in the equivalent phase center of the MIMO SAR, MIMO SAR, the jamming suppression capability for retransmission deception jamming is enhanced. the jamming suppression capability for retransmission deception jamming is enhanced. First, the sub-band signal synthesis processing model is built. Then, the efficiency of deception First, the sub-band signal synthesis processing model is built. Then, the efficiency of deception jamming suppression is analyzed. Because of the combination of the sub-band synthesis and jamming suppression is analyzed. Because of the combination of the sub-band synthesis and random random phase modulation, the retransmission deception jamming will defocus in the azimuth, and phase modulation, the retransmission deception will defocus in the azimuth, and the interference to signal ratio will decrease. Finally,jamming the simulation of deception jamming proves thethe interference to signal ratio will decrease. Finally, the simulation of deception jamming proves validity of the jamming suppression method. Hence, the MIMO SAR will not only improve thethe validity the jamming method. Hence, MIMO will the not only improve the spatial spatialofresolution andsuppression wider swath coverage, butthe will also SAR enhance jamming suppression resolution and wider swath coverage, but will also enhance the jamming suppression capability. In the capability. In the future, we will investigate non-coherent integration of different equivalent phase future, we will investigate non-coherent integration of different equivalent phase centers in the image centers in the image domain to further improve the anti-jamming capability of the proposed domain to further improve the anti-jamming capability of the proposed method. method. Acknowledgments: The research is supported in part by the National Natural Science Foundation of China (Nos. 61132006, 61301187 and 61371133). Author Contributions: Ruijia Wang designed the method and performed the experiment and simulation and wrote the manuscript; Jie Chen supervised the study and modified the manuscript; Xing Wang and Bing Sun supervised the study and wrote part of the manuscript.

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Acknowledgments: The research is supported in part by the National Natural Science Foundation of China (No. 61132006, 61301187 and 61371133). Author Contributions: Ruijia Wang designed the method and performed the experiment and simulation and wrote the manuscript; Jie Chen supervised the study and modified the manuscript; Xing Wang and Bing Sun supervised the study and wrote part of the manuscript. Conflicts of Interest: The authors have no conflicts of interest to declare.

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