Radar Cross Section Computation Research Articles

A Novel Radar Cross-Section Calculation Method Based on the Combination of the Spectral Element Method and the Integral Method

This article proposes a novel method for calculating radar cross-sections (RCSs) that combines the spectral element method and the integral method, allowing for RCS calculations at any position in a free space or a half-space. This approach replaces the field source with an incident field using the scattered field equation of the spectral element method, enabling the arbitrary placement of the field source without being limited by the computational domain. By applying the superposition theorem and the volume equivalence principle, the scattered field of the objects at any position is obtained through integral equations, eliminating limitations on the computation points imposed by the computational domain. Based on Green’s function’s important role throughout the calculation process and its symmetry properties, the RCS calculation of symmetric models will be more advantageous. Finally, several examples, including symmetry models, are provided to validate both the feasibility and accuracy of this proposed method.

Enhancement of Electromagnetic Scattering Computation Acceleration Using LSTM Neural Networks

This paper presents the electromagnetic long short-term memory neural network (EM-LSTMNN) approach to accelerate radar cross-section (RCS) calculations in optimizing low RCS for electrically large targets. The proposed method converts the conventional electromagnetic numerical calculation into an efficient numerical calculation using the LSTM neural network, resulting in a significant improvement in RCS computation speed. To assess the effectiveness of this approach, a downscaled model of a large-sized ship is employed as the target for low RCS optimization. Each modification made to the target’s mesh data during the optimization process is stored in the dataset as a new element. As the ship scaling model undergoes modifications during the optimization process, the new mesh data are recorded, thus adding a new element to the dataset at each time step. This forms a time series representation of the mesh model. By utilizing the dataset collected throughout the optimization process, the proposed EM-LSTMNN model is trained using data-driven approaches, with a training time of approximately 106 s. It is worth noting that this training time is significantly smaller compared to existing methods that employ fully connected neural networks. The performance of the proposed approach is demonstrated by comparing the RCS calculation results obtained through this method with those obtained through traditional electromagnetic simulations.

Near-to-Far Field RCS Calculation Using Correction Optimization Technique

Radar cross section (RCS) is a scattering measure of an object that scatters to the radar. However, existing methods for near-field (NF) measurement and data processing rarely extract amplitude characteristics, and there is a lack of effective verification of far-field (FF) data in the process of NF to FF transformation, which leads to inaccuracies in FF prediction accuracy. In this paper, we propose a method to establish the relationship between the NF and FF RCS using the state space method (SSM), which is based on accurate estimation of the NF amplitude in NF measurement, and then deriving the FF RCS from the NF scattering signal convolved with a near-to-far kernel. The proposed solution to address the uncertainty issue in reference FF data involves using the geometric theory of diffraction (GTD) scattering center model as the reference FF data and establishing a linear equation with the derived FF model. The negative gradient search (NGS) system identification concept is used to optimize the FF model in order to reduce the discrepancy between the reference and derived values. Finally, the corrected RCS error is provided as additional proof of the effectiveness of these techniques in enhancing near-to-far transformation accuracy by examining the outcomes of three experiments.

Stealth performance evaluation of helicopter against airborne early warning radar considering trimming control

Airborne pulse Doppler radar is a key threat to the military helicopter, and assessing the stealth performance of helicopter against airborne early warning radar is helpful to the helicopter’s stealth design and operational planning. In this paper, the Shooting and Bouncing Ray (SBR) and Uniform Theory of Diffraction (UTD) based high-frequency algorithms are used to calculate the Radar Cross Section (RCS) of helicopter, and the radar range equations are used to evaluate the stealth performance. In order to account for the effects of rotor flapping motions during actual flight, the aerodynamics model of whole helicopter is established and the attitudes and controls of helicopter at different flight states are trimmed and input into the RCS calculation module. The effects of helicopter flight speed, flying direction and operational environment on radar stealth performance are studied in focus. It is demonstrated by the results that the trimming control does have a great influence of more than 5 dB on the RCS of helicopter, and the introduction of the trim calculation brings the helicopter’s returns calculation closer to the reality. Variations in flight speed lead to the changes in the stealth performance of helicopter against Early Warning Aircraft (EWA), and the helicopter flight speed can be planned according to the operational requirements to minimize exposure distance or exposure time. Variations in flying direction mainly affect the detection properties of helicopter returns, and flying in the same direction with EWA usually gives the helicopter better low-observability than flying head-on. Variations in operational environment mainly affect the radar detection performance and the sensitivity of the detection performance to external factors; the same amount of change in some external factor causes a different amount of change in the helicopter’s detectability in different environments.

Efficient Broadband Monostatic RCS Computation of Morphing S-Shape Cavity Using Artificial Neural Networks

The efficient broadband monostatic radar cross section (RCS) of the electrically large and deep morphing S-shape cavity calculation is a challenge in computational electromagnetic. Moreover, the traditional electromagnetic computing method can be very time-consuming because the highly complex computations of broadband monostatic RCS must be repeated each time the S-shape cavity structure is modified. To tackle these difficulties, artificial neural networks (ANNs) are proposed to reduce the computational cost of conventional methods, and the data-driven ANNs model can be trained with the inputs scheme datasets include three parts, which are the morphing cavity structure parameters, the incident plane wave information, and RCS of the initial morphing cavity. With careful design and proper training, the broadband monostatic RCS of morphing S-shape cavity can be obtained efficiently by ANNs. In the last, three examples are presented to demonstrate the accuracy and efficiency of the proposed method.

Fast Computation of Resonant Metasurfaces in FDTD Scheme Using Dispersive Surface Susceptibility Model

A new framework of scattering analysis of metasurfaces composed of an assemble of resonant scatterers, with a multistage analysis procedure, is presented. The metasurface analysis using this framework utilizes a dispersive surface susceptibility model (SSM) and a finite-difference time-domain (FDTD) method, replacing the traditional brute force simulation with the physics-based SSM. The SSM extraction for characterizing scatterers is provided, which then is used to replace detailed practical scatterers in numerical simulation. The SSM with the frequency-dependent features’ behavior is described by multiple-Lorentz pole pairs, and the coefficients of the Lorentz model are obtained by using a rational fitting method. An easy-to-implement FDTD algorithm combined with the Lorentz-described SSM is proposed and presented. The efficiency of the proposed framework is proven by comparing it with conventional FDTD. The validity of the proposed framework is verified using commercial EM simulation software. The use of this analysis procedure is demonstrated by two example scatterers. Through the examples, we discuss the requirement of the meshing lattice size, sensitivity of the algorithm to the incident angle, and influence of the edge effects on the bistatic radar cross section (RCS) computation.

The Clutter Simulation of a Known Terrain by the 3D Parabolic Equation and RCS Computation

Ground clutter data are usually generated using a statistical model, but they cannot effectively reflect the spatial distribution characteristics of ground objects. It is important in practical projects to effectively predict ground clutter when terrain data are known. In this paper, a scheme of ground clutter simulation based on the three-dimensional parabolic equation (3DPE) model is proposed. Radio wave propagation was modeled by the PE model and the spatial field distribution was solved. After the radar cross section (RCS) calculation based on space cells, the ground clutter information data were obtained. Then the radar echo was obtained and the clutter map was simulated. The simulation experimental results show that the ground clutter map simulated by the proposed method has a good reference value, meets the demand of strong clutter area prediction under known terrain conditions, and provides a theoretical basis for radar location and optimal deployment.

A Hybrid Chebyshev Approximation Technique and Subdomain AIM Method for Wideband RCS Computation

An efficient hybrid method based on subdomain adaptive integral method (SAIM) and Chebyshev approximation technology (CAT) is proposed for analyzing the wideband radar cross section (RCS) of complex multiscale objects in this letter. The SAIM cannot only be used to effectively deal with the difficulty of slow convergence caused by the mutiscale problems, but also greatly reducing the computational memory. By introducing the CAT into SAIM, we can use the currents at a few frequency sampling points to predict the currents at any frequency point over the entire band. In addition, the application of the Maehly approximation can obtain a better accuracy. Numerical examples show that the proposed SAIM-CAT can significantly improve the calculation efficiency without loss of accuracy.

LBVH 순회를 이용한 거대 도체 구조의 레이다 단면적 분석

In this study, the radar cross-section (RCS) of a large structure is analyzed using the linear bounding volume hierarchy (LBVH), which is a representative acceleration algorithm of the ray-tracing technique. A ray-tracing technique, which is a high-frequency method, is used to analyze the electromagnetic properties of large structures, and bounding volume hierarchy (BVH), a binary tree structure, is applied to reduce the intersection search time. The improvement in the calculation speed is quantitatively analyzed by dividing an arbitrary scatterer into several triangles. The calculation results are compared with those of multilevel fast multipole method (MLFMM) and ray-launching geometrical optics (RL-GO) using the Feko commercial software to verify the accuracy. The proposed technique can be utilized for the efficient RCS calculations of large structures.

Research on RCS measurement of ship targets based on conventional radars

Abstract A measurement method and system based on conventional radars has been proposed to address the problem of radar cross-section (RCS) measurement of ship targets in open seas. Calibration errors for RCS measurement on ground plane range (GPR) are analysed, and the error elimination method and accurate RCS calculation formula are given. An RCS measurement system is designed by improving conventional radars. These systems measure two Luneburg lens reflectors of different sizes on the lake. The average RCS of the big Luneburg lens reflector is obtained, and the error is calculated to be 2.73% compared with its actual value, which verifies the rationality of the proposed measurement method and system. The system measures the RCS of a ship in the open sea and obtains its circumferential RCS distribution. The effect of the error in the ship's position calculation on the RCS measurement results is analysed, and the uncertainty range of the error is obtained.

An Improved RCS Calculation Method for Power Lines Combining Characteristic Mode with SMWA

The radar cross-section (RCS) of power lines has an important significance for detection of the power lines. The method of moments (MoM) can calculate the RCS of power lines. However, the efficiency of the MoM is limited by the time-consuming computing process, as well as the expensive storage overhead. In order to enhance the efficiency and reduce the storage of the RCS calculation of power lines, we propose an RCS calculation method that combines the characteristic mode (CM) with a Sherman–Morrison–Woodbury formula-based algorithm (SMWA), which is referred to as a CM-SMWA. CMs are used as the basis functions for reducing the dimension of the MoM impedance matrix, and the SMWA is applied to directly solve the CMs-reduced matrix equation, which can reduce the computational time and storage. The numerical results demonstrate that the proposed method can obtain the RCS of power lines, with different incident angles and different polarizations, at a higher efficiency. At 35 GHz, compared with the conventional MoM, for a typical LGJ50-8 power line with a length of 0.276 m, the computation time is reduced by 62.4% and the memory occupation is reduced by 96.4%.

A Simple and Efficient SBR Implementation for RCS Calculation Using Target Scaling

In order to alleviate the computational burden of the shooting and bouncing rays (SBRs) method in the radar cross section (RCS) analysis, an algorithm using target scaling is introduced in this article. This algorithm aims to reduce the number of rays that must be traced with time-consuming ray–triangle intersection tests. In order to achieve this, the target’s electrical length is reduced to a predefined value in each aspect angle. Then, only rays that hit the scaled target is traced without changing the analysis frequency. The RCS values for full-scaled model are estimated by using the ray displacements and field strengths calculated for the scaled model. This algorithm yields a significant decrease in the computational burden with a trade-off between analysis accuracy and time consumption. Analysis results show that the introduced algorithm and original SBR give very similar RCS results except at very low RCS points as depicted in the RCS versus aspect angle graphs. In addition, using a fixed frequency makes the algorithm applicable to not only perfectly electrical conducting (PEC) targets, but also targets coated with radar absorbing materials (RAMs).

Numerical investigations on radar cross-section of helicopter rotor with varying blade pitch

A calculation method is presented to study the radar cross-section (RCS) of the rotating rotor at different blade pitches. Based on blade pitch control, grid matrix transformation, and instantaneous RCS calculations, the electromagnetic scattering characteristics of the blade, rotor, and helicopter are obtained by the presented method. The pitch angle of each blade of the main rotor is regulated in fixed control mode, linear control mode and smooth control mode. The surface scattering characteristics of the blade in the fixed mode, the RCS of the blade and the rotor in the linear mode, and the effects of different control modes on the RCS of the rotor and helicopter are investigated. When the azimuth is 80°, the pitch of blade 1 is 9.6° in linear mode, and the RCS of some facets near the leading edge is reduced to −65 dBm2 under the given observation conditions. In the fixed control mode, the minimum period of the rotor RCS is equal to the basic passage time of the blade, while in linear control mode and smooth control mode, the minimum period of the rotor RCS is increased. Compared with the fixed control mode, the linear control mode can reduce the RCS peak of the helicopter at the given moment, and the smooth control mode is beneficial to reduce the RCS average of the rotor and helicopter at the given azimuth. The presented method is effective to analyze the dynamic RCS of the rotor and helicopter under different blade pitches, and has important engineering value for the stealth design of helicopter rotors.

Orbital angular momentum wave scattering from perfect electromagnetic conductor (PEMC) sphere

We studied the orbital angular momentum (OAM) wave scattering by a perfect electromagnetic conductor (PEMC) sphere using Mie Theory. The Vortex Electromagnetic (VEM) wave is well known with a definite amount of OAM. To obtain the OAM wave scattering from PEMC sphere, the conventional plane wave scattering from PEMC sphere expressions are modified by taking into account the characteristics of OAM waves. The unique properties of analytical expression of OAM fields are analyzed, and the scattered field coefficients in terms of incident field coefficients were obtained using boundary conditions. The comparison between conventional scattering for plane wave and OAM wave from PEMC sphere had been carried out. The presented work provides a theoretical insight for the calculation of Radar Cross Section (RCS) by metamaterial as PEMC sphere and identification applications of light carrying OAM in optical manipulation technology.

Physical Optics Radar Cross Section predictions for an anti-ship cruise missile

The capability of the first strike is crucial in the modern battlefield. An important parameter is the radar signature or Radar Cross Section (RCS) of a weapon system, such as a fighter aircraft, a warship, or a missile, affecting the range at which this weapon system would be detected as a target by an enemy radar. If the attacker is detected too late, there will be minimal time for the defender to react, possibly not sufficient to counter the threat. The RCS of a weapon system is considered generally as classified information. However, it can be measured at a suitable measurement test range, if that weapon system is available. Otherwise, it can be predicted with the help of computational electromagnetics. Concerning the second approach, the following procedure was recently proposed: construction of a three-dimensional model of a target, based on available images and any relevant data, and then computation of the target RCS, with the Physical Optics approximative method. In the present approach, this procedure is applied to an anti-ship cruise missile in order to compute its RCS. Finally, the expected detection range for various naval radars is calculated.

Optimization of ray tracing algorithm for Laser Radar Cross Section calculation based on material Bidirectional Reflection Distribution Function

This paper studied the Laser Radar Cross Section (LRCS) of the target scale model by using the Bidirectional Reflection Distribution Function (BRDF) of materials and the Monte Carlo method for reverse ray tracing. The results of the research are shown through data from the satellite scale model. On the basis of the classification of the roughness of different materials and in conjunction with probability density distribution, we adopted a non-uniform sampling method to improve the split-ray collection method in the spatial distribution of scattering energy in the reverse ray tracing algorithm. By conducting the typical Monte Carlo simulation of a simple dihedron and comparing the theoretical calculation results, we tested and verified the correctness of the proposed method. We analyzed the difference between the primary and secondary scattering results of the target LRCS with different conditions. The calculation results show that for rough materials, if only primary scattering is considered in a plurality of detection directions, a large calculation error will occur, so the influence of the secondary scattering must be considered; and the contribution of the diffuse reflection component to the secondary scattering is more significant. Finally, we compared the secondary scattering of different rough materials to describe the circumstances of secondary scattering in which diffuse reflection conditions need to be considered. In addition, the inverse Monte Carlo method used in this paper to calculate the multiple scattering of the LRCS of the target can effectively improve the calculation speed of the acquisition processing. This improves the reliability of the calculation results while taking into account the estimated speed.

Frequency Selection to Avoid Medium Effects on RCS of Conducting Objects With Plane E Wave Polarization

AbstractWe aim to select the range of frequencies where the medium parameters have less effects on the scattered waves, and as a result we achieve high precision of computed radar cross section (RCS). Ideal object detection can be obtained through calculation of RCS assuming a plane wave incidence in the far field. Numerical results are conducted to investigate effects of medium characteristics and target configuration on its RCS. We postulate convex illumination region of partially convex contour. Targets are taking fairly large sizes in the range of five wavelengths to suit the practical dimensions of objects such as aircraft. In this work, waves propagation from targets in free space and random medium are considered while assuming E polarization of incident wave.

Full-Wave Computation of Monostatic RCS Using Ray-Tracing and Adaptive Macro-Basis Functions

This article presents a technique for the computation of the monostatic radar cross section of complex objects based on a combination of macro-basis functions (MBFs) and the multilevel fast multipole algorithm. An initial pool of excitation-independent MBFs is first obtained, generating the corresponding reduced coupling matrix as well as the multipole data. For each excitation, ray-tracing processing is performed, extracting a number of critical points that are used to obtain a mask that allows to dynamically select the basis functions to be considered in the analysis. This strategy allows a noticeable reduction in the size of the problems with minimal CPU-time preprocessing overhead.

Edge Element Calculation of Radar Cross Section of Small Maritime Targets with Respect to Height of Radar Antenna

Edge Element Calculation of Radar Cross Section of Small Maritime Targets with Respect to Height of Radar Antenna

Efficient RCS Computation Over a Broad Frequency Band Using Subdomain MoM and Chebyshev Approximation Technique

The analysis of the target’s broadband electromagnetic scattering characteristics plays an important role in radar stealth and recognition areas. The traditional method of moments (MoM) needs to calculate the currents at each frequency point when analyzing the target. With the increase of the target electrical size and complexity, the radar cross section (RCS) of the target changes drastically with frequency, it is necessary to calculate the accurate frequency response with a small frequency interval, which is very time-consuming in calculation and not feasible. This paper proposes to combine the subdomain method of moments (SMoM) with the Chebyshev approximation technique (CAT) to efficiently analyze the electromagnetic scattering of arbitrary shaped objects over a broad frequency band. In the SMoM technique, the whole object can be divided into several regions, each of which can be independently solved by the method of moments (MoM). The CAT technique is employed to expand the unknown current coefficients into a Chebyshev series for achieving fast frequency sweeping. Instead of direct point-by-point simulations, it is only necessary to calculate the currents by SMoM at several Chebyshev-Gauss frequency sample points. Furthermore, the Chebyshev series are matched via the Maehly approximation to a rational function to improve the accuracy. Numerical examples show that the hybrid technique can greatly reduce the computation time without loss of accuracy.