A Chaff Cloud Echo Modeling and Simulation Method Based on Coherent Scattering Model

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1 Journal of Computational Information Systems 11: 5 (2015) Available at A Chaff Cloud Echo Modeling and Simulation Method Based on Coherent Scattering Model Jianqiang ZHANG, Zhong LIU, Houxiang WANG Electronic Engineering Colleges, Naval University of Engineering, Wuhan , China Abstract Through studying chaff motion law in the air, this paper concluded that, after chaff bomb explosion, the shape of chaff cloud is spherical and chaff is uniformly distributed in the sphere. Further analysis showed that chaff cloud s amplitude obeys Rayleigh distribution, power spectrum obeys Gauss distribution, and phase follows uniform distribution. According to the research results above, the author built a chaff cloud coherent scattering model based on the space geometry relation of anti-ship missiles and chaff. Finally, the simulation experiment results showed that, compared with the incoherent scattering model, this model s jamming simulation effect is more close to reality. Keywords: Chaff Cloud; Modeling and Simulation; Coherent Scattering Model 1 Introduction In recent years, electronic countermeasures has become an effective way to defense anti-ship missile, which makes the anti-ship missile cannot effectively find, capture and track the target. Ship anti-missile ability has been greatly increased [1]. Now, especially chaff jamming has played an important role in warship s anti-missile warfare, and become a common electronic warfare equipment of naval surface ships around the world [2]. Therefore, in order to verify the anti-ship missile penetration effectiveness in a complex electromagnetic environment, how to construct a realistic electromagnetic environment has become an urgent need to address the problem. As is known to all, chaff cloud is composed by lots of chaff, so chaff cloud echo signal is a vector sum of each chaff echo signal. According to this principle, this paper presents a chaff cloud coherent scattering model based on the space geometry relation between anti-ship missiles and chaff, and then carry out a simulation experiment to test its accuracy. The simulation results showed that, compared with the incoherent scattering model, the model s jamming simulation effect is more close to reality. So it can provide a realistic chaff jamming simulation environment for the analysis of anti-jamming ability of anti-ship missile. Project supported by the National Nature Science Foundation of China (No. 9140A JB11012). Corresponding author. address: [email protected] (Jianqiang ZHANG) ) and NMFC (No / Copyright 2015 Binary Information Press DOI: /jcis13221 March 1, 2015

2 1580 J. Zhang et al. /Journal of Computational Information Systems 11: 5 (2015) Diffusion Model of Chaff Cloud In order to establish chaff cloud simulation model and discuss its electromagnetic echo characteristics, it is necessary to study chaff motion law in the air [4, 5]. On this basis, the shape of chaff cloud, after chaff bomb explosion, can be concluded. Obviously, after chaff bomb explosion, each chaff obtains a velocity vector Ṽ, which direction is random. Chaff flying in the air, by the action of 3 forces: gravity, air resistance and viscous force. Theoretical research and experimental data shows that, due to the quality of chaff is small and the air resistance is far greater than gravity, the gravity effect on the velocity of chaff can be ignored. At the same time, the effect of fluid viscosity decreases in high Reynolds number, so its effect can also be ignored. As a result, within the scope of the study velocity (less than 100 m/s), air resistance and velocity of single chaff can be thought of a direct ratio, the chaff motion model can be expressed as [6] dṽ dt = kṽ (1) Where Ṽ is single chaff s velocity vector [v x v y v z ], k is single chaff s velocity attenuation coefficient. As shown in Fig. 1, [v x v y v z ] can be expressed as v x = Ṽ cos ε sin B v y = Ṽ cos ε cos B (2) v z = Ṽ sin ε Fig. 1: Velocity vector Ṽ As shown below, k s value is associated with chaff drag coefficient C D, air density ρ, chaff length l, chaff diameter d and chaff quality m i [6]. k = f(c D, ρ, l, d, m i ) = C Dρld 4m i ζ (3) Where ζ is dimensionless constant, its precise value is usually determined by experiment. Here, we let ζ = 1. Suppose that l is 13mm, d is 30m, Ṽ is 100m/s, the number of chaff N is 200, k is the fitting result of the experiment in literature [6]: k = Ṽ. The simulation results are shown in Fig. 2. The first and second figure show chaff cloud shape, 0.5s and 1s after chaff bomb explosion. he last one shows chaff velocity change curve, from which it can be observed that chaff cloud mature time takes about 1 second.

3 J. Zhang et al. /Journal of Computational Information Systems 11: 5 (2015) Fig. 2: The chaff cloud diffusion simulation results 3 Statistical Characteristics of Chaff Cloud Echo Signal 3.1 Time domain features Because chaff cloud echo signal is a vector sum of each chaff dipole echo signal with random phase and amplitude, its synthesis echo signal can be expressed as follows [7] N S = Ae jϕ = A k e jφ k (4) Where A and ϕ are the amplitude and phase of the chaff cloud synthesis echo signal, A k and φ k are the amplitude and phase of the kth chaff dipole echo signal, N is chaff dipole number. It can be proved that when N is very big, the amplitude of chaff cloud synthesis echo signal obeys Rayleigh distribution, and the phase of chaff cloud synthesis echo signal follows uniform distribution [8] p(a) = 2A ) ( n exp A2, 0 A (5) e σ n e σ p(φ) = 1, φ [0, 2π] (6) 2π Where σ is average RCS of single chaff, n e is effective number of chaff dipole per unit volume. k=1 3.2 Frequency domain characteristics Suppose that each chaff dipole of chaff cloud has a random movement direction, the autocorrelation function of chaff cloud voltage can be expressed as [7] [ ( ) ] 2 2π g(τ) = exp τ 2 (7) aλ Where λ is radar working wavelength, a is a constant related to chaff dipoles quality, Boltzmann constant and the absolute temperature. Then chaff echo power of covariance function can be expressed as [9] ( I(τ) = g(τ) 2 2 ) 2 2π exp τ 2. (8) aλ

4 1582 J. Zhang et al. /Journal of Computational Information Systems 11: 5 (2015) The Fourier transform of Eq. (8) is as follows [10] [ S(f) = aλ ( ) ] 2 aλf 2 2π exp 2. (9) 2 As can be seen from Eq. (9), chaff echo power spectral density has the form of gaussian function. 4 Chaff Cloud Modeling and Simulation As mentioned above, chaff cloud echo signal is a vector sum of each chaff dipole echo signal. However, the amount of calculation is huge if one by one to calculate each chaff echo [11]. Fig. 3: Chaff cloud division method Therefore, first we divide the chaff sphere into a lot of V i, the division method is shown in Fig. 3. Here, azimuth angle ϕ = 2π/360, ϕ [0, 2π], elevation angle θ = 2π/360, θ [0, 2π], distance from the chaff cloud center R = R/100, and then calculate the echo of V i, finally calculate vector sum of each V i s echo signal, which is the echo of the whole chaff cloud. 4.1 Chaff cloud RCS modeling Radar cross section (RCS) is a measure of the return or scattering power in a given direction. Because of the chaff cloud signal attenuation, the chaff inside chaff cloud can t received signal energy like the chaff near chaff cloud surface, so the former s RCS is smaller than the latter. That is to say, chaff cloud RCS is related to the chaff cloud thickness and spatial density, which is the number of chaff remained in unit volume of chaff cloud. Then V i s RCS can be expressed as [12] σ Vi = A c Vi (1 e n e σy ) (10)

5 J. Zhang et al. /Journal of Computational Information Systems 11: 5 (2015) Where σ Vi is the V i s RCS(m 2 ); y is the chaff cloud thickness(m), here y = R Vi cos θ cos ϕ; is the projection area of V i in the direction of radar antenna. A c Vi Fig. 4: Chaff cloud division method As shown in Fig. 4, if both θ and φ are very small, A c Vi can be expressed as A c Vi = R Vi [sin(θ + θ) sin θ] R Vi [sin(φ + φ) sin φ] (11) 4.2 Chaff cloud echo modeling After the solution of its RCS, the next step is the V i s echo modeling. Suppose that radar transmitting signal is single carrier frequency pulse signal, chaff cloud echo signal can be expressed as N S(t) = Si k (t) (12) i=1 Where N is the number of V i, Si k (t) is the kth echo of ith, it can be written as follows [13] ( ) Si k (t) = A Pt L s g vt (θ m )g vr (θ m ) t 2R k,i λ (4π) 3 Rk,i 2 C m σ Vi rect kt r T p ( ( )) ( ( )) (13) exp j(ω c + ω d,i ) t 2R k,i kt 2Rk,i C r exp j λ m Where A is the radar signal amplitude; P t is the peak transmitted power; L s is radar transmitting and receiving comprehensive loss, including transmitting loss, atmospheric loss, receiving loss, pulse pressure loss and Two-way attenuation loss, etc; g vr (θ m ) is seeker radar receiving antenna gain; σ Vi is the V i s RCS; λ is the wavelength; C is the speed of light, which is m/s; T r is pulse repetition interval; ω d,i is the doppler frequency of V i ; R k,i is the relative distance between radar and i-th chaff unit V i,when the former s k-th pulse meet with the latter.

6 1584 J. Zhang et al. /Journal of Computational Information Systems 11: 5 (2015) Fig. 5: Chaff cloud division method As shown in Fig. 5, according to the law of cosines trigonometric function, R k,i and ω d,i can be written as follows R k,i = R V 2 i + Rr 2 2R Vi R r cos γ (14) γ = arccos(cos θ i cos ϕ i ) ω d,i = 2V r(t) cos ζ λ m = 2V r(t) λ m R2 k,i + R2 r R 2 V i 2R k,i R r cos γ (15) 4.3 Chaff cloud echo other influencing factors Mutual coupling effect he mutual coupling effect is that chaff can t play its normal efficiency because of the mutual induction between two (or more) chaff scattering wave. When chaff cloud is not fully spread out, the distance between some chaff will be less than 2λ, the mutual coupling effect can t be ignored [12]. Nest effect Because of chaff bomb s production and emission, some chaff may stick together and can not effectively disperse, which leads to the reduction of valid chaff number. Usually, nest effect can be realized by using a effective factor to modify the number of valid chaff, as shown below [14, 15]. N e = ηn (16) Where N e is the total number of valid chaff modified by η. 4.4 Chaff cloud echo simulation Suppose that chaff cloud fully spread out, the distance between chaff each other is greater than 2λ, the whole chaff cloud is within the radar beam, the chaff cloud coordinate is [0, 0, 0], the number of chaff is 2000, anti-ship missile coordinate is [10000, 10000, 1000], its velocity is 900m/s, radar wavelength is 0.03m. The simulation take the steps as follows Step 1: Let η=0.9, calculate the total number of valid chaff N e ;

7 J. Zhang et al. /Journal of Computational Information Systems 11: 5 (2015) Step 2: Divide the chaff sphere into a lot of V i, division method is shown in Fig. 5; Step 3: Calculate the projection area of V i in the direction of radar antenna; Step 4: Calculate V i s RCS A c Vi ; Step 5: Calculate the distance between anti-ship missile and the center of chaff cloud R r ; Step 6: Calculate the relative distance R k,i between radar and ith chaff unit V i ; Step 7: Calculate the V i s doppler frequency ω d,i and its kth echo Si k (t); Step 8: Calculate the whole chaff cloud echo S(t). (a) Echo waveform in time domain (b) Echo amplitude distribution (c) Echo power spectrum (d) Echo phase distribution Fig. 6: Chaff cloud simulation echo waveform and statistical properties From Fig. 6, it can be observed that the amplitude of the chaff cloud simulation echo signal obeys Rayleigh distribution, the phase of the chaff cloud simulation echo signal follows uniform distribution and chaff cloud simulation echo power spectral density has the form of gaussian function. These observations indicate that the simulation result is correct and the chaff cloud modeling method proposed in this paper is feasible.

8 1586 J. Zhang et al. /Journal of Computational Information Systems 11: 5 (2015) Summary In this paper, we have presented issues related to how to improve the realistic effect of chaff cloud simulation for the analysis of anti-jamming ability of anti-ship missile. This major work is summarized as follows: (1) Based on the study of chaff motion law in the air, a diffusion model of chaff cloud has been built, by which we have concluded that the shape of chaff cloud is spherical; (2) According to the principle that chaff cloud echo signal is a vector sum of each chaff dipole echo signal, our theoretical analysis results have showed that chaff cloud s amplitude obeys Rayleigh distribution, power spectrum obeys Gauss distribution, phase follows uniform distribution; (3) Based on the space geometry relation of anti-ship missiles and chaff, a chaff cloud coherent scattering model has been proposed to improve the realistic effect of chaff cloud simulation. The simulation experiment results show that compared with the incoherent scattering model, this model s jamming simulation effect is more close to reality. References [1] YANG Qing, ZHANG Jianqiang. Anti-ship Missile Attack-defense Simulation System Based on Direct Signal Injection [J], Ship Electronic Engineering, 2013, 33 (9): [2] LI Hai-hao, LI Hai-tao, ZHU Ning-long. Simulation Model on Chaff Centroid Jamming [J], The Technology of Electronic Information Confrontation, 2010, 25 (1): [3] WANG Guoyu, WANG Liandong. Mathematical Simulation and Evaluation of Radar EW System [M]. BeiJing: National Defence Industry Press [4] LV Meng-meng. Motion characteristics of chaff cloud in the air [J], Electronic Components and Applications, 2012, 14 (9): [5] CAI Wan-yong, LI Xia, WAN Shan-hu, et al. Model of chaff motion trajectory and curtain wall diffusion in air environment [J]. Systems Engineering and Electronics, 2009, 31 (3): [6] HAN Chao, ZHAO Guo-zhi, YANG Zhi-qiang, NIU Ji-tao. Study on the Kinematics Characteristic of Chaff Release [J], INITIATORS and PYROTECHNICS, 2005, (1): 5-8. [7] LIU Qiang, LIU Yi-an. A M odeling and SimulationM ethod of ChaffC loud Echo [J]. Modern Radar, 2006, 28 (8): [8] Li Jinliang. Study on Characteristics of Chaff Jamming and Anti-Chaff Technology for Radar [D]. Ch-angsha: Graduate School of National University of Defense Technology [9] LIU Shimin. Characteristic of Chaff Jamming and Field-collected Chaff-jammed Data Analysis [D]. XI An: Xi an electronic technology university [10] Shen Yunehun, Xie Junhao. Statistieal ProPerties of Chaff Echoes [J]. Chinese Journal Radio Science, 1997, 12 (1): [11] Lei Gang. Modeling and Simulation of Jamming on Antiship Missile [D]. XI An: Xi an electronic technology university [12] Chen Jing. Principles of Radar Chaff Jamming [M]. Bei Jing: National Defence Industry Press [13] Jianping XU, Yiming. Compressive Sensing in Radar High Resolution Range [J]. Journal of Computational Information Systems 7: 3 (2011) [14] TANG Guang-fu, CHEN Yuan-zheng, ZHAO Hong-zhong, et al. Research on Simulation of Radar Echo from Chaff Cloud [J]. Electro-Optic Technology Application, 2005, 20 (4): [15] Neil Kruger. Modelling the EM properties of dipole reflections with application to uniform chaff clouds [D]. South Africa: University of Stellenbosch