Analysis of echo signal modulation characteristic parameters on aerial and space targets

Si Chen , Hi-yng Zhng ,*, Chng-ming Zho , Yu Fn , Hong Chen , Lin Wng

a School of Optics and Photonics, Beijing Institute of Technology, Beijing,100081, China

b Key Laboratory of Electro-Optical Countermeasures Test&Evaluation Technology, Unit 63891 of the Chinese People's Liberation Army, Henan, 461002,China

c Key Laboratory of Optical Radiation, Beijing Institute of Environmental Characteristics, Beijing,100854, China

Keywords:Echo signal modulation characteristic parameters Simple targets The fixed-wing UVA Missiles Scattering characteristics

ABSTRACT Based on the scattering characteristic, the comparison of RCS (radar cross-section) at different positions of a target in the same direction of incidence can be obtained first by extruding or deleting part of the entity.A simulation method of aerial&space targets echo characteristics (A&STEC) is proposed that is universal to aerial and space targets.We utilize a fixed-wing UAV(unmanned aerial vehicle) and typical missiles in simulation.The echo signal modulation characteristic parameters are calculated theoretically by the atmospheric attenuation model, the finite element method and a MUMPS solver.The verification simulations show that this method can analyze the influence of the target shape, incident direction,detection position and detection frequency on echo waveform, intensity and energy distribution.The results show that the profile of echo waveform can invert the general shape of the target.The relationship between time and intensity can determine whether the target is moving towards or away from the detector in addition.These conclusions can provide a reference for the ballistic missile target tracking and the defense against UVA intrusion in theory.

1.Introduction

The basis of full-waveform radar applications [1,2] are properties of targets and echo signal modulation characteristic parameters,which can be analyzed by targets scattering characteristics[3].The echo signal modulation characteristic parameters include echo waveform, intensity [4] and energy distribution.The extraction of these parameters is beneficial to acquire more target information.Demodulating the echo of a target and making an analysis of its intrinsic properties can effectively distinguish the surface topography features of a target,so as to improve the detection efficiency and identify camouflaged targets that cannot be detected by traditional methods [5].Therefore, it is significant to study echo characteristics of radar imaging and target recognition [6].

In 2012,R Welle et al.assigned individual echoes with different echo curves to the global echo group on the foundation of their typical echo characteristics [7], which can confirm whether each curve of the echo is useful or not.Xu Xiaobin et al.derives the plane target impulse response and the pulsed laser echo equation in 2016.The ranging probability density on the plane target is deduced according to the echo equation and the constant threshold time discrimination method [8].The laser echo signal model is established by the emission, target scattering and geometric characteristics.The echo power equations of three typical targets (plane,cone and cylinder) are proved moreover [9].In summary, the analytical equation of a two-dimensional target echo can be constructed, but echo signal modulation characteristic parameters with a three-dimensional target [10] is beyond description by formula in theory.

The echo signal modulation characteristic parameters of aerial and space targets directly interfere the target tracking and the recognition of radar.As a typical aerial target,the fixed-wing UAV is not easy to be found due to its small RCS, low altitude and slow speed.A novel approach combining an integral model and the method of moment simulates the temporal RCS of a rotor in a very high frequency band during 2019 [11].The development of space targets is extremely rapid.It's a nut in radar target recognition to distinguish between true and false warheads for missile targets threat groups to crack.The echo signals of the above-mentioned targets are difficult to be measured experimentally.Establishing an approximate theoretical echo model is of far-reaching significance.Unfortunately, the surface features of aerial and space targets are complex and required a high accuracy of surface subdivision.Therefore,traditional methods are hard to simulate the echo characteristics of these targets.A simulation method of aerial&space targets echo characteristics was pointed out to construct the echo signal modulation characteristic parameters for complex targets.

A three-dimensional model of the echo radiation intensity distribution is established for simple targets in Section 2.It makes a comparison among the RCS at different positions of a target in the same incident direction.Often,simple targets,such as the cylinder and the sphere are studied as ballistic missiles.Section 3 proposes a simulation method of A&STEC involving the discussion of emission characteristics, target shapes, and detection parameters.A fixedwing UAV and three types of missiles are included.Factors influencing echo signals returned from a target incorporate target shapes, incident directions, detection positions and detection frequency.The conclusion confirms that the target shape and detection position have a greater impact on echo waveform.The detection frequency has relatively little effect on the contour of echo waveform, but affects echo intensity.The general shape of detected targets can be roughly estimated from the profile of echo waveform.We exhibit the radiation energy distribution of a minuteman missile at different incident angles in the end of this section.Finally, the verification simulation explains that the relation with time and intensity is a way of judging the direction of target motion.In this way, the establishment of the echo coupling model with multiple characteristic parameters of a target can be brought out.It can promote the ability to identify targets,make the evaluation of their performance at perfect and lay the foundation for designing radars.

2.The simulation for simple targets

RCS is a physical quantity that measures echo intensity produced by a target under illumination.The RCS of a threedimensional scatterer is defined as Refs.[12,13].relative permeability, σ is the electric conductivity and εris the relative permittivity.We analyze the properties of twodimensional scatterers using the RCS per unit length

The relationship between Eq.(1) and Eq.(5) is: σ3D=σ2D?（2l2/λ）, where l is the length of a scatterer and λ is the wavelength.

To facilitate the description and calculation of the target's echo signal modulation characteristic parameters, we describe the process as shown in the left of Fig.1.The innermost layer is the detected target,the outer layer is the free space region around the target and the outermost layer is the perfect match layer(PML) in the top right of Fig.1.PML,providing an approximate reflection-free boundary for the computational domain, is essentially a steady governing for the waveform.We set the thickness of PML as around one-tenth of the total modeling space.Azimuth and pitch angles can be acquired by setting the location of the illuminant and the camera [14].Simulation parameters are described in Table 1 in detail.

A Cylinder can be considered as the result of stretching its bottom surface.If the incident light is shining on the side of a target vertically,the three-dimensional target would be reduced to a twodimensional model for fast solution.

Treating the radar as far enough away from the target, we can regard the incident field as a plane wave.The target surroundings allows us to exclude the transmitter from the geometric modeling.The radiation energy distribution of a cylinder is shown in Fig.2.The direction of the arrow is equivalent to the incident.Echoes in the vicinity of the target are dominated by standing waves because of reflection.Due to the complex target shape,we not only have to consider whether each facet will or will not be irradiated but also must judge whether a small facet will be shaded by another facet[15].Parts of the target not illuminated by the source are shadowed obviously.

If the target has a axisymmetric characteristic,taking a sphere as an example, a method involving the deletion of some entities can be used to reduce the number of face elements in calculation.The radiation energy distribution of a sphere target is shown in Fig.3(a).On account of atmospheric attenuation and other influencing factors, the farther the scattering distance is, the lower the echo intensity is.Fig.3(b)shows the relation among relative radii at point P, S, R and the normalized RCS.The function of normalized RCS exhibits a sine-like variation, but the peak of the normalized RCS decreases as the relative radius increases.The decay amplitude of the normalized RCS satisfies P>R>S in each period.

3.The simulation method of A&STEC

Taking into account the actual detection, the spherical wave background pressure field affected by the atmospheric attenuation model is suitable for this case as input.Consider the following equation

where ω denotes the angular frequency, μrcharacterizes the

Fig.1.The simulation processing of a simple target echo waveform characteristics.

Table 1Simulation parameters about simple targets.

Fig.3.The radiation energy distribution of a sphere target:(a)Total electric mode distribution;(b)The relationship between the normalized RCS and the relative radii(r/λ)at P,S,R.

where psat=pA，ref×10G（T）,G（T） = -6.8346（T01/T）1.261＋4.6151,the reference temperature is content with Tref= 293.15 K, the reference pressure satisfies pA,ref= 1 atm, T01=273.16 K，T is the actual temperature and pAis the absolute pressure.The absorption coefficient in the impedance boundary condition is given by

where i is the imaginary unit, Ziis the specific acoustic input impedance, R is the reflection coefficient, φ is the phase and αnis the normal incidence absorption coefficient.In this case, the impedance will be purely resistive as φ = 0.The target strength is computed by the following equation:

where psis the scattered pressure, pinis the background pressure and r is the distance from the target to the scattering point.The coordinate of the detectors are D1=（-d cos ?，-1，-d sin ?） and D2=（-d cos ?，-d sin ?，-1） respectively, where ? is the received angle and d represents a distance we define.Scanning from 0°to 360°can simulate the fact that the radar rotates around a fixed point during detecting.Relevant physical quantities and assignments are detailed in Table 2.

It can solve finite element problems with a direct solver based on the LU decomposition.Direct solvers include the MUMPS solver,SPOOLES solver and PARDISO solver.The solving speed of a MUMPS solver is faster than that of a SPOOLES solver.A MUMPS solver also supports cluster computing compared to a PARDISO solver.It offersthe memory required for fine unit partition on complex targets.To sum up, we propose a simulation method of aerial&space targets echo characteristics (A&STEC) with a MUMPS solver to fulfil echo signal modulation characteristic parameters.Since the fixed-wing UAV and missiles are typical targets of the main force in future operations, the airborne attack system is of great significance in order to meet the needs of future operation.A fixed-wing UAV and different types of missiles are used to achieve the research on echo signal modulation characteristic parameters for aerial and space targets in simulation as follows.

3.1.Aerial targets

The grid is divided into different densities on the foundation of the fixed-wing UVA target's flight path and shape characteristics in order to be closer to the actual needs.The three-view drawings and the pressure distribution of the target are shown in the right side of Fig.4..

To facilitate the description and calculation of the target's attitude, we establish the three-dimensional schematic diagram andcoordinate system of the target.It is not hard to realize that the areas under the most pressure are regions ①-③respectively while imagining a fixed-wing UVA is flying.The simulation parameters can be shown in Table 3.Fig.5 exhibits the radiation energy distribution of a fixed-wing UAV target at y=0 plane detected at D1.The received echo intensity depends to a large extent on the actual location of the measurement apparently.The echoes close to the target position are standing waves.With the increasing of the distance between the target and a detector, intensity decreases owing to atmospheric attenuation and other factors.

Table 3The simulation parameters about a fixed-wing UAV target.

Fig.4.The simulation processing of a fixed-wing UAV.

Fig.5.The radiation energy distribution of a fixed-wing UAV target.

Table 4The simulation parameters about space targets.

The influence of different detection frequencies and detection positions on the echo is studied as follow.It can be concluded from Fig.6(a)and Fig.6(b)that although the distance from the target is the same, the echo waveform would change at different detection positions.It is not difficult to find the profile of wings and the fuselage through the approximate shape of echo waveform.The general shape of targets can be inverted through the profile of echo waveform as a rule.The detection frequency turns the profile of the echo waveform a little,but affects the highest and lowest intensity in Fig.6(b) and Fig.6(c).

3.2.Space targets

Three types of missiles can be utilized as space targets.The simulation parameters about these missiles can be revealed in Table 4.The radiation energy distribution of these three missiles detected at D1 can be seen in Fig.7.Fig.5 and Fig.7 clearly demonstrate that the geometry of the target interferes with the echo energy distribution.

Fig.8 shows the target strength for various types of missiles at different detection positions and frequencies.The detection position is one of the factors affecting the general shape of the echo waveform apparently in any two diagrams at the first two rows for the same column.The target echo signals of three types of missiles in the location of D1at 1 GHz in Fig.8(g)-Fig.8(i)respectively.The frequency has a negligible effect on the profile of echo waveform but makes a great difference to target strength in Fig.8(e) and Fig.8(h).The above verification simulation indicates that the shape feature of targets,detection position and detection frequency are all influencing factors of the echo modulation characteristic parameters.

The effect of the incident direction on the echo signal is described below.Fig.9 demonstrates the total electric field mode distribution of the Missile 2 at the x-y section in different incident directions.Fig.10(a) illustrates the magnitude of the relative electric field emitted by the target at an incidence angle of 90°.As shown in these near field plots, you can guess that a distant observer would see peaks in the relative field centered around 75 and 285°.

4.Discussion on the direction of target motion

Treat the target as a point while it is far enough away from the radar, Eq.(6) can be regarded as

Fig.7.The radiation energy distribution of different missiles.

Fig.8.The target strength for various types of missiles at different detection positions and frequencies.(Each row: same position and frequency but different missiles, Each line:different positions and frequencies but identical missiles, The red dotted line indicates the shape of the echo waveform).

Fig.9.The electric field mode distribution of the Missile 2 at different incident angles.

Fig.10.The radiation energy distribution of the Missile 2: (a)The magnitude of the relative electric field; (b)Far-field radiation plot for a 90° angle of incidence.

Fig.11.The time-intensity curve of the probe signal.

where Ψ =Ψ（r，z）e-imφ，Ψ（r，z） =π,m is the azimuth angle,ν is the speed and ν = 50 m/s.

When the target moves in opposite to the atmospheric flow,the wavelength of the sound descends.It means that the target is close to the camera with the growing of the detection frequency.A schematic of the time-intensity relation of the echo signal can be seen in Fig.11.The x-axis indicates the time of movement.The green line shows the target moving towards the detector and the blue one represents the opposite direction.We put forward an assumption that the time corresponding to the curve falling and then rising is one cycle of motion.If the target is close to the detector,the peak of intensity is higher in a cycle than while the target is far away.The cycle of motion is also shorter in this situation.Therefore,this curve can be used to determine whether the target is moving towards or away from the detector.

5.Conclusions

(1) This paper summarizes the echo multi-feature distribution models of different targets, including simple geometry targets,aerial and space targets.

(2) A schematic diagram of radiation energy distribution is drawn for simple targets.The variation law of RCS at different surface elements of a target is obtained.

(3) The simulation method of A&STEC focuses on the echo modulation characteristics of aerial and space targets,which provides theoretical support for the precision and accuracy of target recognition technology.The verification simulations interprets interactions between echo signal modulation characteristic parameters and their influencing factors by controlling variables.The conclusion is that the target contour can be roughly judged by the echo waveform and the direction of target motion can be determined by the timeintensity curve.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.