Chaff jamming is one of the most typical passive jamming methods applied for radar electronic protect (EP). Chaff was made of metallic thin strips or metal sheets in early years. With the persistent improvement of chaff materials and fabrication technologies, chaff consisting of glass fibers coated with aluminum or silver has been widely developed. Chaff cloud is generally composed of hundreds of millions of fibers, which have advantages like high dispersing speed, wide frequency band, large radar cross section (RCS) and so on. Each chaff fiber can be equivalent to a dipole.In order to confuse the radar and protect the important targets in modern electronic warfare, airplanes or ships disperse a large number of chaff fibers into the air by launching chaff bombs around, which creates chaff corridors or disguises as one or more targets.

The common existing recognition methods of chaff jamming are classified as polarization signatures[1-2] or Doppler characteristics[3-4]. The polarization characteristic identification technique adopts the optimal transmit-receive polarization to improve signal to noise ratio in the radar receiver, in order to reduce the jamming effect of chaff cloud. However, this approach demands radar transceiver with complex equipment, high technical challenges and high cost. Chaff jamming can be eliminated by using the method of Doppler filtering, which is based on the difference in motion velocity between a target and chaff cloud in Doppler domain under complicated electromagnetic jamming conditions.Nevertheless, this technique is mostly applicable to aerial defense when the difference in motion velocities between a target and a chaff cloud is significant. The ability to identify chaff jamming is not ideal for naval defense where chaff cloud’s drift velocity is close to a ship’s voyage velocity. These methods can distinguish the differences between chaff cloud and target under the condition that both of them are distinguishable in certain dimension. Overall, chaff jamming has always been one of the most effective methods for radar EP.

Slice method (SM) is proposed to construct the electromagnetic scattering model of chaff cloud here. Using the difference in time domain waveforms between a complex rigid target and chaff cloud, an improved model based on grey relational analysis (GRA) is developed to identify chaff jamming by setting a reasonable threshold. The simulation results prove that the method of GRA can effectively identify chaff jamming.

1 Construction of an Electromagnetic Scattering Model for Chaff Cloud Based on SM

The chaff cloud undergoes two phases from launch to dispersion: a diffusion phase as an equivalent single target and a steady phase as an extended target[5]. The diffusion phase means that chaff cloud has dispersed quickly but incompletely with a decreasing density, an increasing RCS, and an inhomogeneous and time-dependent space distribution. The steady phase means that chaff cloud has fully dispersed and its radius has been maximized. Consequently,chaff cloud in a steady state can protect a target. It falls slowly under the influence of wind direction, wind speed and gravity. Chaff cloud’s RCS and echo can be regarded as a vector sum of single chaff fiber’s RCS and echo.

神像高一丈，身体由整块的白玉雕凿而成，双翼则是用青碧色的翡翠雕刻。一束月光从神殿顶部预留的天窗直射而下，打在神像上，令神像的身体泛起柔柔的白芒，双翼青光流转，仿佛随时都要振翅冲天。

1.1 Morphological hypothesis

Fig.1 represents the movement of chaff cloud, where H0 is the launching height of chaff cloud, φ is the initial azimuth, θ is the initial elevation angle, Rt is the radial distance between the initial position of complex rigid target and radar, Rc is the radial distance between chaff cloud and radar, Vw is wind speed and α is the angle between the wind direction and the positive X-axis. Let X-axis be the radar beam direction, t be the diffusion time of chaff cloud and N be the number of fibers in one chaff cloud.

Fig.1 Movement of chaff cloud

A simplified analytical model is proposed to represent the exponential expansion of the radius of chaff cloud[6]:

(1)

where r is chaff cloud radius, rmax is the maximum chaff cloud radius, tb is the time that chaff begins its diffusion, τc is the time constant of the chaff cloud which must be greater than zero, tmax is the time where chaff cloud reaches its maximum radius.

②Targets’ separation and extraction: Since the amplitude of clutter or noise after pulse compression is smaller than the amplitude of target and chaff cloud echo, the mean of a large quantity of simulated data of clutter amplitude can be used as a detection threshold.

(2)

1.2 RCS calculation

The valid RCS of a single half-wavelength chaff fiber can be expressed as the average RCS of different spatial solid angles because the direction and position of fibers in space are random[7]. It can be denoted as

这种现象不仅国企有，不少机关也存在。2016年2月，浙江省在全省范围内全面实施“困难残疾人生活补贴”和“重度残疾人护理补贴”政策，并作出具体部署。7月，乐清市残联根据上级文件有关规定，发文要求乡镇（街道）实施“两补”的申报工作。由于对上级“两补”理解的偏差，导致享受到“两补”的人员仅占符合政策条件人员的三分之一。2017年1月，温州市残联对乐清市“两补”工作进行考核后提出批评意见。随后，乐清市残联未经审核就发文确定第二批补贴对象。由于前期把关不严，未建立补贴发放资格定期复核和一月一报制度，存在先拨付资金再审核等违规行为，导致两批“两补”对象中有7人死亡后仍在享受补贴。

GRA is a dynamic process to compare the correlation degree of different time series. It color-code situations with no correlation as black, and those with perfect correlation as white. However, neither of these idealized situations exists in practice, hence situations between these extremes are coded with different shades of grey[11].

晚上，对着炉火我们几乎烤了一个晚上，我蜷缩在八成干的被子里睡到天亮，丹增一宿没睡，他在帮我烤干鞋子和外套。

捏造行为指的是写论文时为了方便，没有经过考证，捏造出一些不存在或不准确的东西，如无效的文献引用、造假数据夸大研究成果等。学术论文是建立在别人研究的结果上，因此，优秀的学术论文必须有一定数量的参考文献。不少学术期刊规定必须有15篇以上的参考文献，对于没有作研究的作者，很难凑够15篇文献，因此只能随便复制几篇内容相似的参考文献，滥竽充数。在研究成果上，一般要有数据作佐证，才能证明所研究的成果比前人更进一步。有些作者在没有经过实践的情况下，通过总结前人的数据，对数据稍作修改，就当作研究成果写进论文中。

①Divide the diameter of chaff cloud into M parts along the direction of the line of the sight of radar. Each part can be regarded as a slice.

后来，汪小波哭着对麦小秋说：“小秋，我知道你受的罪，我告诉你，最开始你就错了，你要回瓦塘我送你回去，如还留在D城，以后你头顶上的天我来顶着，我对不起你，我早该提醒你，其实，他一直在挖陷阱，知道你迟早会陷进去的。”汪小波的泪水流得更快，“麦小秋，我已经不在那儿干了，他有很多的卑鄙，他混不下去了，人都会有报应的……”

王祥早就等得不耐烦了，急忙从身后的蛇皮袋里取出几件玉器。老道则随意拨开地摊上的便宜货，在胖子面前留出一块空地。王祥恭敬地把玉器一一放到胖子面前的地摊上，然后继续跑回一边的折凳上，等着看老道来表演。

M= 2rρr +1= 2rc2B +1

(3)

where c is the speed of light, B is the radar signal bandwidth, is radar range resolution and ⎣」 is the operator to round the element to the nearest integers towards minus infinity.

Let X=(x0,x1,…,xn) be a reference sequence and Y=(y0,y1,…,yn) be a comparison sequence. The grey correlation degree(GCD) of X and Y can be defined as

(4)

where Ni is the number of chaff fibers in the ith chaff cloud slice, η is the modifying factor which meets 0<η<1 and Nei=ηNi is the equivalent number in the ith slice of chaff cloud.

③Assume that the radar transmitted signal is a linear chirp, which can be denoted as Calculate the echo signal power Pr of slice and echo S of chaff cloud according to the radar equation.

(5)

(6)

where Tp is radar pulse width, Pt is radar transmitted power, G is radar antenna gain, λ is radar operational wavelength, L is radar system loss, fc is radar carrier frequency, k is chirp rate, τi and φi are echo time delay and phase shift of the ith slice.

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1.3 Echo characteristics

The EM characteristics of chaff cloud can be expressed as the vector sum of N chaff fibers. It is necessary to study the amplitude distribution and phase distribution in order to extract the characteristics of chaff cloud echo precisely.

马克思主义认为，无产阶级及其政党必须具备无产阶级革命立场。否则，它就肩负不了实现共产主义的历史使命。列宁是在马克思主义指导下创造性地运用马克思主义取得俄国革命胜利的，他坚信马克思主义。他说：“严格的无产阶级世界观只有一个，这就是马克思主义。”[10]271因此，他没有任何理由不站在无产阶级立场上观察、思考和解决问题。列宁关于批评要有内容的思想正是站在无产阶级革命立场上提出来的。所以，他对任何非无产阶级立场都是反对的。列宁说：“如果批评自由是指维护资本主义的自由，那我们就要取消这种自由。”[6]36显然，在列宁那里，只要是有损无产阶级革命利益的批评，都是不允许的。

② αXY only depends on the geometry of X and Y, regardless of their spatial relative position, which means translation does not change the value of GCD.

(7)

(8)

(9)

where is the average RCS of single chaff fiber.

It can be seen from Eq.(7), Eq.(8) and Eq.(9) that the amplitude, phase and RCS follow a Rayleigh distribution, an uniform distribution and an exponential distribution, respectively. That means only the number of chaff fibers and the average RCS can affect the probability distribution of chaff cloud.The spatial orientation of chaff cloud has an effect on the average RCS of single chaff fiber and further affects the average probability distribution of RCS.

2 Chaff Jamming Recognition Based on GRA

2.1 Principle of GRA

However, the half-wavelength chaff fiber is an imperfect conductor with impractical applications.Its RCS can be represented as based on the experience. Considering that chaff cloud consists of tremendous amount of fibers, its mechanism of electromagnetic (EM) scattering is complicated owing to the interaction and shielding effect among the fibers. SM is proposed to divide the chaff cloud into several cells according to certain rules, establish mathematical model and calculate the RCS of chaff cloud. The steps are as follows.

②Calculate the RCS of the ith chaff cloud slice.

(10)

where and x′p=xp-x0, y′p=yp-y0 (p=1,2,…,n-1).

Three properties can be drawn from the definition of GCD:

① 0<αXY≤1.

对自然水体的评价主要分为两类，一类是评价水体中本身存在的污染物引起的效应；另一类是评价中水、再生水回用于河道补充、景观用水、农田灌溉后，水体是否存在生物毒性.Christoph[42]针对河流中可能存在的环境污染物进行研究，以不同营养级（发光菌、藻类、水蚤、鱼）的四种急慢性试验、Ames试验及umuC实验对德国三条污染相对较轻的河流和一条相对污染严重的河流进行测试，样品的相对当量浓度均在2～50 μg/L，通过藻类72 h半数效应值最高值2 260 μg/L判断毒性最高河流地点.

The amplitude and phase of each scattering echo are random variables on account of the fibers’ random motion and rotation. The phase of electromagnetic radiation of single chaff fiber follows uniform distribution within [-π,π]. The fiber’s orientation is independent. Accordingly, the phase and amplitude of chaff echo are also independent. On the basis of the central limit theorem (CLT)[8], the sum of tremendous amount of random variables is also a random variable.If random variables have little effect on the sum, the sum of random variables follows normal distribution approximately. The distribution functions of amplitude A, phase φ and RCS σ of chaff cloud echo are given by[9-10]

③ The length of X must be consistent with Y. The greater the similarity of X to Y, the bigger the value of αXY.

2.2 GCD comparison of complex rigid target and chaff cloud

Illuminated with wideband radar electromagnetic radiation, the back scattering echo of a complex rigid target can be equivalent to the superposition of multiple scattering center echoes. The projection distribution of echoes along the direction of the line of the sight of radar is called high resolution range profile (HRRP). In general, strong scattering centers of complex rigid target are mainly distributed on the discontinuous surfaces; their relative positions are fixed and their radar echo is a slow varying random variable. Therefore, the target’s adjacent return waves have a good correlation and a high GCD.

1)服务线程的开发，服务器端主线程接收移动平台、PC平台发来的请求，将请求交给代理线程处理，代理线程通过调用地震应急数据信息处理类中的方法对数据进行操作，然后将操作结果通过流反馈给移动平台、PC平台或者Web平台。

On the contrary, chaff cloud often consists of hundreds of millions of dipoles. The distribution of dipoles in the space is affected by the kinematic parameters of the atmosphere, and the orientation of each dipole is random. Chaff diploe has translation and rotation under the influence of velocity of wind in the diffusion stage. Its shape, volume and RCS change rapidly, which leads to the fact that its radar echo is a fast varying random variable. Therefore, the chaff cloud’s adjacent return waves have a weak correlation and a low GCD.

2.3 Method of chaff jamming recognition

A digital automatic gain control (AGC) circuit can adjust the system gain to keep the echoes’ amplitude at an optimum level. The amplitude of received signals varies with the target’s RCS and distance between the target and the radar platform. When a strong signal is received, the gain is reduced automatically by AGC circuit, and vice versa. The radar can determine whether it encounter jamming by monitoring whether the AGC control voltage exceeds the threshold when tracking targets. Once a jamming is detected, an appropriate anti-jamming measures will be taken.

假设棉花种植面积不变，为2016年的种植面积2 154. 91千hm2，2016年新疆微灌灌溉面积(2 138. 58千 hm2)占节水灌溉总面积(2 605. 09千 hm2)的82. 1%，因此节水灌溉面积主要以微灌灌溉面积为主。2016年新疆节水灌溉面积占农作物总播种面积的38. 91%(2 418. 95千hm2)，根据“规划”，2020年种植业高效节水面积要达2 866. 67千hm2(69. 16%)，设定情景C:2020年棉花微灌技术覆盖率达到70%，2025年达100%。

In different operational environment, chaff jammings can be divided into four types: confusion jammings, dilution jammings, transfer jammings and centroid jammings. Dilution jammings and centroid jammings are widely used against searching phase and tracking phase, respectively. As for dilution jammings, the relative position of chaff cloud and target must within the radar search scope and beyond the tracking unit, which means the radar can only detect one target in the beam. The influence of dilution jamming on radar performance is relatively simple, which only affects the searching phase. Consequently, anti-dilution jamming can be implemented just by screening the sought target.

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To centroid jamming, chaff cloud and target are in one beam. Generally speaking, chaff cloud and target are so close to each other that they are difficult to be distinguished in an initial diffusion phase. After entering into a steady phase, chaff cloud will move slowly by the effects of wind and target will take evasive maneuver according to actual conditions. As a result, both of them can be resolved in the range, and the radar will be confused and regard chaff cloud as a real target. Therefore, anti-centroid chaff jamming should primarily improve the range resolution of radar, and then eliminate the chaff echo as much as possible by taking advantage of the differences of range profile between target and chaff cloud to retain real target echo. From the perspective of signal processing, the dilution jamming recognition can be regarded as a special case of centroid jamming recognition.The centroid jamming recognition is thus the focus of this study. The main steps are described as follows.

①Signal pre-processing and pulse compression: A high resolution range profile is obtained by compressing the pulse of hybrid time-domain waveforms of complex rigid target and chaff cloud.

Since chaff cloud is light, the influence of its gravity can be neglected within a short period. According to Fig.1, Rc can be calculated as

③GCD Computation: Wideband radar signal with high pulse repetition frequency, short pulse repetition period and high similarity between adjacent return waves is selected. To improve the recognition effect of chaff jamming, uniformly-spaced sampling of the received m sequential echo signals is needed, and then the GCD of q sequential echo signals after sampling should be calculated. Let be the echo signal of pulse i and αi be the GCD between the echo signals of pulse i and i+1:

αi=αXiXi+1=

(11)

Thus a correlation degree sequence is obtained. According to the principle of GRA, αi represents the degree of resemblance between the echo sequences of pulse i and i+1, which has to be averaged in order to eliminate the randomness caused by noise. The average of GCD can be denoted as

(12)

Complex rigid target’s GCD is higher than chaff cloud’s, both of which can be distinguished by setting a reasonable threshold. Let δT be the threshold. If the searched target is complex rigid target. Otherwise, the searched target is chaff cloud.

δT can be determined by simulations or experiments, which can have a big effect on the recognition rate.

3 Simulations and Analysis

Chaff cloud’s echo characteristics in time domain and effectiveness of anti-centroid jamming based on GRA are verified by simulations. The simulations focus on the mixed echo of 40 s. The parameters are shown in Tab.1, Tab.2 and Tab.3 respectively.

Tab.1 Parameters of radar

Carrierfrequency/GHzBandwidth/MHzPulsewidth/μsTransmittedpower/WAntennagain/dBiSystemloss/dB162001020003010

Tab.2 Parameters of complex rigid target

Initialdistance/kmSNRbeforecompression/dBRelativevelocity/(m·s-1)18-5300

Tab.3 Parameters of chaff cloud

Launchingheight/mInitialazimuthInitialelevationangleNumberofchafffibersWindspeed/(m·s-1)AnglebetweenthewinddirectionandthepositiveX-axis60π/4π/610810π/3

Fig.2 Temporal characteristics of chaff cloud

3.1 Temporal characteristics of chaff cloud

Fig.2 describes the temporal characteristics of chaff cloud. Fig.2a is the waveform of chaff cloud echo.Fig.2b, Fig.2c and Fig.2d are the probability density distributions of echo’s amplitude, phase and RCS respectively. It can be concluded from the plots that the amplitude follows a Rayleigh distribution, the phase follows an uniform distribution and the RCS follows an exponential distribution.The results consistent with the theoretical results of chaff cloud’stemporal characteristics.

3.2 Chaff jamming recognition

Fig.3 demonstrates HRRP of complex rigid target. The target’s HRRP is obtained through noncoherent integration of multiple pulses according to the geometric model of the ship. The number of strong scattering centers is 15.

Fig.4 presents the HRRP during diffusion. The situation in the 1st second is shown in Fig.4a. The chaff cloud is in the early phase of diffusion with short radius, high density and large amplitude. The situation in the 25th second is shown in Fig.4b. The chaff cloud is at the stage of a steady state with a maximum radius and low density, which has the ability to protect target in deed. Two conclusions can be drawn from the data: ① the chaff cloud echo is a fast varying random variable from burst to a steady state; ② the complex rigid target echo is a slowly varying random variable without many changes of the number of strong scattering centers.

Fig.3 HRRP of complex rigid target

Fig.4 HRRP during diffusion

Fig.5 gives the GCD comparison between complex rigid target and chaff cloud. Four conclusions can be drawn from the data plotted in Fig.5: ① GCD of complex rigid target is high and has been in a relatively steady state because of its practically unchanged strong scattering centers, RCS and close correlation. In practice, the GCD will decrease due to the influence of the ground, sea and weather clutter, but this does not affect its overall trend; ② GCD of chaff cloud is high in the initial 4 s. The chaff cloud in the early phase of diffusion has small radius and less scattering centers. Thus the number of chosen scattering centers is more than that of chaff cloud’s, which indeed makes the GCD calculation valid for not only the chaff cloud but also part of noise; ③ GCD of chaff cloud continues declining from 4 s to 25 s. The chaff cloud at this point has a fast diffusion speed, a growing radius and a weak correlation; ④ GCD of chaff cloud from the 25th to the 40th seconds generally level off as the process reaches a steady state. The diffusion speed of chaff cloud gradually decreases to zero and the radius reaches the maximum. The movement is associated with wind velocity and fibers’ random motion and rotation inside.

Fig.5 GCD comparison between complex rigid target and chaff cloud

To summarize, the GCD of chaff cloud is well below that of complex rigid target.Accordingly, chaff cloud and complex rigid target can be distinguished by setting a threshold between 0.5 and 0.6.

4 Conclusion

In this paper, chaff jamming recognition is studied based on a scenario of slow moving targeted platform. SM is applied to construct the electromagnetic scattering model of chaff cloud, and the echo characteristics are verified by simulations. A modified algorithm based on GRA is developed to identify chaff jamming.Simulation resutls demonstrate that a complex rigid target echo is a slowly varying random variable; on the contrary, chaff cloud echo is a fast varying random variable. Both of them can be identified as long as a reasonable threshold is set.This algorithm is simple, feasible and applicable to model other jamming recognitions. In order to test the algorithm’s effectiveness and practicability in actual scenario, more in-situ measurement data is needed.

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