Radar Cross Section / Scattering

Stochastic Trees

Radar Cross Section (RCS) of trees is important in geosciences, propagation near forests, and radar applications. Full-wave EM analysis of complex structures is challenging due to geometrical complexity and randomness. Decades ago, WIPL-D Pro simulated wire models of stochastic trees using wires of varying radii with distributed loadings. This application note presents advanced meshing algorithm for stochastic tree models with a GPU-accelerated solver. Tree models are fully automated closed surfaces, defined as dielectric with (E_r = 10), overcoming frequency limitations of wire models. Monostatic RCS for trees at 0.2, 0.5, and 1.5 GHz was simulated on inexpensive GPU workstation with short simulation times even at RF frequencies.

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Synthetic Aperture Radar Systems

Synthetic Aperture Radar (SAR) improves resolution beyond the physical aperture by synthesizing a large virtual aperture through movement. This application note clearly presents efficient numerical analysis of a rail SAR system using MoM-SIE with higher-order basis functions, reduced unknown coefficients, and far-field equivalent sources for fast computation. Simulations run on a multi-GPU platform, with each frequency point on a single inexpensive GPU; 8 GPUs speed up the process roughly 8×. Replacing the real radar antenna with an equivalent far-field source turns multiple transceiver positions into a multi-excitation problem. A 40-wavelength-long airplane illuminated from 101 SAR positions took only ~9 hours instead of 101× longer.

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NASA Almond RCS in
Time-Domain

This application note describes time-domain Radar Cross Section (RCS) simulation using WIPL-D Software suite, specifically WIPL-D Pro and WIPL-D Time Domain Solver. A metallic NASA almond is illuminated by a plane wave with Gaussian-modulated sine. The object is about 60 wavelengths long, 4 wavelengths high, and 0.2 wavelengths thin, with polarization parallel to the longer semi-axis of its cross-section. Two symmetry planes reduce unknowns, and the object is modeled as a Body of Rotation (BoR). Simulations run on a regular desktop or laptop, showing that WIPL-D Time Domain Solver combined with the efficient MoM solver WIPL-D Pro is suitable for time-domain analysis. Simulation time is measured in minutes for over 100 frequency points.

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Reduction of Unknowns Over Electrically Large Scatterers

Calculation of monostatic scattering from electrically large metallic objects, such as aircraft, helicopters, missiles, or calibration spheres, is of interest to scientific, military, or engineering groups. This application note presents monostatic RCS calculation of metallic aircraft at 2 GHz, demonstrating utilization of WIPL-D software with attention to reducing unknowns. Reduction is achieved by lowering the reference frequency to 87.5% of the initial value, significantly decreasing unknowns and simulation time while preserving accuracy, with RCS results closely matching those obtained using more unknowns. Simulations are performed using WIPL-D Pro CAD, a full-wave 3D EM MoM solver, on an affordable desktop PC enhanced with GPU cards.

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RCS Convergence Study: Large Corner Reflector

An electrically large corner reflector is used to emulate a large Radar Cross Section (RCS) from a reasonably sized object in many practical applications. This application note presents analysis of a PEC corner reflector to illustrate the process of simulation convergence in WIPL-D software. By tracking RCS changes from several thoughtfully selected simulations, convergence and high reliability of results can be verified. Kernel parameter differences are explained, and results can be conveniently compared using graph in polar or Cartesian coordinates.
WIPL-D Pro CAD and WIPL-D Pro, a full-wave 3D EM MoM solver with SIEs and HOBFs, simulate models at 10 GHz on a standard workstation, demonstrating highly efficient and reliable computation.

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RCS Estimation of Generic Airplane Scale Model

This paper presents modeling and simulation of monostatic Radar Cross Section (RCS) for a scaled generic airplane in WIPL-D software, including detailed simulation times, memory requirements, and hardware for both CPU and GPU solvers. The airplane is modeled in WIPL-D Pro CAD, which enables fast, very efficient, and reliable solid modeling of complex geometries using built-in primitives, Boolean operations, and other advanced features; the model length is 310 mm. Simulations at 30 GHz were carefully run using both CPU and GPU solvers. While CPU solutions have long been a WIPL-D feature, GPU technology is now preferred for large-scale examples. The PC used was a standard configuration, with simulation times measured in just a few minutes.

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Lowering Ship RCS

This note outlines the utilization of WIPL-D Pro software, a full-wave 3D electromagnetic Method-of-Moments based tool used to simulate three electrically large ship models in monostatic scattering mode at 1 GHz without any model reduction. The obtained results are useful for studying how ship geometry affects RCS; first two shapes produce unacceptably high monostatic RCS, while the third shape achieves a significant reduction. This demonstrates that modifying the ship’s external contour can lower RCS without radar-absorbing materials and may serve as a starting point for ship design. Despite large electrical size of the models, all simulations were completed in short time on an affordable desktop PC equipped with GPU cards.

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Trees, Foliage and Complex Sceneries

Scattering and propagation of EM waves in the presence of trees and forests plays an important role in many civil and military applications, such as Foliage Penetrating Radar for detecting targets. Efficient modeling can be performed using metallic wires for branches and metallic plates for leaves with distributed loadings, valid up to 150 MHz (considering tree trunk diameters smaller than 2 ft / 60 cm). The number of unknowns is reduced by roughly 100×, with only about 100 required per tree. On a standard desktop computer, simulating a forest of 100 randomly placed trees and additional objects takes less than a minute, enabling rapid and fully practical full 3D EM simulation of complex forest scenarios, including potential targets.

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