Min Xie, Shuang Zhao, Xiongjun Fu, Tianyu Zhang and Kaiqiang Liu

(School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China)

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.

1.1 Morphological hypothesis

Fig.1 represents the movement of chaff cloud, whereH0is the launching height of chaff cloud,φis the initial azimuth,θis the initial elevation angle,Rtis the radial distance between the initial position of complex rigid target and radar,Rcis the radial distance between chaff cloud and radar,Vwis wind speed andαis the angle between the wind direction and the positiveX-axis. LetX-axis be the radar beam direction,tbe the diffusion time of chaff cloud andNbe 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)

whereris chaff cloud radius,rmaxis the maximum chaff cloud radius,tbis the time that chaff begins its diffusion,τcis the time constant of the chaff cloud which must be greater than zero,tmaxis the time where chaff cloud reaches its maximum radius.

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

(2)

1.2 RCS calculation

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

M= 2rρr +1= 2rc2B +1

(3)

②Calculate the RCS of theith chaff cloud slice.

(4)

whereNiis the number of chaff fibers in theith chaff cloud slice,ηis the modifying factor which meets 0<η<1 andNei=ηNiis the equivalent number in theith slice of chaff cloud.

(5)

(6)

1.3 Echo characteristics

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

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 amplitudeA, phaseφand RCSσof chaff cloud echo are given by[9-10]

(7)

(8)

(9)

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

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].

LetX=(x0,x1,…,xn) be a reference sequence andY=(y0,y1,…,yn) be a comparison sequence. The grey correlation degree(GCD) ofXandYcan be defined as

(10)

Three properties can be drawn from the definition of GCD:

① 0<αXY≤1.

②αXYonly depends on the geometry ofXandY, regardless of their spatial relative position, which means translation does not change the value of GCD.

③ The length ofXmust be consistent withY. The greater the similarity ofXtoY, the bigger the value ofαXY.

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.

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.

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.

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.

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.

(11)

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

(12)

δTcan 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

Tab.2 Parameters of complex rigid target

Tab.3 Parameters of chaff cloud

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.

[1] Shao Xianhe, Du Hai. Echo theoretical analysis from chaff cloud and research polarization targets recognition[C]∥International Conference on Microwave and Millimeter Wave Technology, Guilin, China, 2007.

[3] Madewell J M. Mitigating the effects of chaff in ballistic missile defense[C]∥Proceedings of the IEEE Radar Conference.Huntsville, AL, USA: IEEE, 2003:19-22.

[4] Zhu Hong, Pan Yujian, Wang Qingping, et al. An anti-chaff jamming method for millimeter wave wideband coherent radar based on range Doppler feature[C]∥IEEE International Conference on Signal Processing, Communications and Computing, Ningbo, China, 2015.

[5] Ma Jianchun, Cao Jianshu, Zhang Shunsheng, et al. Math model building and echo simulation of chaff clouds jamming[C]∥IET International Radar Conference, Guilin, China, 2009.

[6] Bendayan M, Garcia A. Signal modeling of chaff in naval environment simulation[J]. IEEE Transactions on Aerospace & Electronic Systems, 2015,51(4):3161-3166.

[7] Chen Jing. Principles of radar chaff jamming[M]. Beijing: National Defense Industry Press, 2007:159-164.(in Chinese)

[8] Prasad R. Does mixing of speech signals comply with central limit theorem?[J]. AEU-International Journal of Electronics and Communications, 2008,62(10):782-785.

[9] Jin Dan, Cha Hao, Zuo Lei. A simulation study of chaff echo signal based on LFM[J]. International Journal of Signal Processing, Image Processing and Pattern Recognition, 2016,9(4):131-140.

[10] Pandey A K. Modeling and simulation of chaff cloud with random orientation and distribution[C]∥IEEE Mtt-S International Microwave and Rf Conference, New Delhi, India, 2013.

[11] Chan J W K, Tong T K L. Multi-criteria material selections and end-of-life product strategy: Grey relational analysis approach[J]. Materials & Design, 2007,28(5):1539-1546.