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

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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 430033, 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. 61401493) and NMFC (No.} 9140A01060113JB11012).

∗_{Corresponding author.}

Email address: [email protected](Jianqiang ZHANG).

1553–9105 / Copyright© 2015 Binary Information Press DOI: 10.12733/jcis13221

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]

dV˜

dt =−k

˜

V (1)

Where V˜ is single chaff’s velocity vector [vx vy vz]′, k is single chaff’s velocity attenuation

coefficient. As shown in Fig. 1, [vx vy vz]′ can be expressed as

       vx =||V˜|| ·cosεsinB vy =||V˜|| ·cosεcosB vz =||V˜|| ·sinε (2)

Fig. 1: Velocity vectorV˜

As shown below,k’s value is associated with chaff drag coefficientCD, air densityρ, chaff length l, chaff diameterd and chaff quality mi [6].

k =f(CD, ρ, l, d, mi) =

CDρld

4mi

ζ (3)

Whereζ is dimensionless constant, its precise value is usually determined by experiment. Here, we let ζ = 1. Suppose thatl is 13mm, d is 30m,||V˜|| is 100m/s, the number of chaff N is 200, k

is the fitting result of the experiment in literature [6]: k= 0.35 + 0.07||V˜||. 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.

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]

S =Aejϕ =

N

∑

k=1

Akejφk (4)

Where A and ϕ are the amplitude and phase of the chaff cloud synthesis echo signal, Ak and φk 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 neσ¯ exp ( − A2 neσ¯ ) ,0≤A≤ ∞ (5) p(φ) = 1 2π, φ ∈[0,2π] (6)

Where ¯σ is average RCS of single chaff, ne is effective number of chaff dipole per unit volume.

3.2

Frequency domain characteristics

Suppose that each chaff dipole of chaff cloud has a random movement direction, the autocorrela-tion funcautocorrela-tion of chaff cloud voltage can be expressed as [7]

g(τ) = exp [ − ( 2π aλ )2 τ2 ] (7) Whereλis 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)2exp  ₋ ( 2√2π aλ )2 τ2  . (8)

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 ∆Vi, 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 ∆Vi, finally

calculate vector sum of each ∆Vi’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 ∆Vi’s RCS can be expressed as [12]

σ∆Vi =Ac∆_Vi(1−e

Where σ∆Vi is the ∆Vi’s RCS(m

2_{);y is the chaff cloud thickness(m), here y=R}

∆Vicosθcosϕ;

Ac∆_Vi is the projection area of ∆Vi in the direction of radar antenna.

Fig.4: Chaff cloud division method

As shown in Fig. 4, if both ∆θ and ∆φ are very small,Ac∆_Vi can be expressed as

Ac∆_Vi =R∆Vi[sin(θ+ ∆θ)−sinθ]·R∆Vi[sin(φ+ ∆φ)−sinφ] (11)

4.2

Chaff cloud echo modeling

After the solution of its RCS, the next step is the ∆Vi’s echo modeling. Suppose that radar

transmitting signal is single carrier frequency pulse signal, chaff cloud echo signal can be expressed as S(t) = N ∑ i=1 S_ik(t) (12)

Where N is the number of ∆Vi,Sik(t) is the kth echo ofith, it can be written as follows [13] S_ik(t) = A· √ PtLs (4π)3 gvt(θm)gvr(θm) R2 k,i λm √ σ∆Vi ·rect ( t−2Rk,i_C −kTr Tp ) · exp ( j(ωc+ωd,i) ( t−2Rk,i C −kTr )) ·exp ( j ( 2Rk,i λm )) (13)

Where A is the radar signal amplitude; Pt is the peak transmitted power; Ls is radar

trans-mitting and receiving comprehensive loss, including transtrans-mitting loss, atmospheric loss, receiving loss, pulse pressure loss and Two-way attenuation loss, etc; gvr(θm) is seeker radar receiving

antenna gain; σ∆Vi is the ∆Vi’s RCS; λ is the wavelength; C is the speed of light, which is

3×108 _m/s;T

ris pulse repetition interval;ωd,i is the doppler frequency of ∆Vi;Rk,i is the relative

Fig. 5: Chaff cloud division method

As shown in Fig. 5, according to the law of cosines trigonometric function,Rk,i and ωd,i can be

written as follows _   Rk,i = √ R2 ∆Vi +R 2 r−2R∆ViRrcosγ γ = arccos(cosθicosϕi) (14) ωd,i = 2Vr(t) cosζ λm = 2Vr(t) λm · R2 k,i+R2r−R2∆Vi 2Rk,iRrcosγ (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 effectBecause 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].

Ne =ηN (16)

Where Ne 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 2: Divide the chaff sphere into a lot of ∆Vi, division method is shown in Fig. 5; Step 3: Calculate the projection area of ∆Vi in the direction of radar antenna; Step 4: Calculate ∆Vi’s RCS Ac∆_Vi;

Step 5: Calculate the distance between anti-ship missile and the center of chaff cloud Rr; Step 6: Calculate the relative distance Rk,i between radar and ith chaff unit ∆Vi;

Step 7: Calculate the ∆Vi’s doppler frequency ωd,i and its kth echo Sik(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.

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.

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