Numerical simulation of radar signatures is an important and integral part of the signature analysis. Scattering properties of many targets can be numerically estimated, thus avoiding the need for expensive manufacturing and measurements. Simulation of the scattering of microwaves is difficult, however, because of the large electrical size of targets of interest.
New applications at even higher frequencies (K and W-bands, Terahertz) and the use of advanced materials, e.g. metamaterial (MTM) antireflection coatings, further complicate the use of exact numerical methods like MoM (Method of Moments), FEM (Finite Elements Method) and FDTD (Finite Difference Method in Time Domain). Hence, the simulation of scattering of microwaves requires the development of physically justified approximate simulation tools which can lead to rapid estimations of radar signatures with an acceptable accuracy.
Signature simulation and measurements
Several simulation models concerning the mono- as well as the bistatic signature of man-made targets have been or are under development. They are based on high frequency approximation methods like Physical Optics (PO), PTD (Physical Theory of Diffraction) or SBR (Shooting and Bouncing Rays Method). Single, double and multiple reflections from curved surfaces coated with absorbing material layers as well as edge scattering contributions have to be taken into account.
|Figure 1: Bistatic scattering cross section of a metallic cube with and without low-reflection coating. Bistatic angle 0° corresponds to the case of backscattering and the angle 20° to the direction of specular reflection from the front face of the cube|
BISTRO is a package for simulation of electromagnetic scattering from electrically large artificial targets. The package is based on physical optics (PO) and several extensions of PO. Implemented features include mono- and bistatic radar configurations, anti-reflection coatings, targets in free space and over an underlying surface, as well as calculation of fields, scattering matrices and various scattering cross sections. Compared to existing high-frequency scattering simulation codes, BISTRO provides a number of unique features: (1) coatings from non-metallic and advanced materials (RAM, FSS, MTMs); (2) improved simulation of multiple scattering through multiple application of PO; (3) edge corrections for non-metallic surfaces.
|Figure 2: Realization of an MTM low reflection coating. The inset shows the periodic lattice of sub-wavelength metallic patches|
The accuracy and some of the features of BISTRO are illustrated in Figure 1 which shows bistatic scattering cross section of a metallic cube with the side length about 6λ coated with a low-reflection MTM coating (see Figure 2 and Figure 3). The cube is illuminated by a plane wave incident at an angle 10° with respect to the normal to a face of the cube, and the observation point moves around the cube in the plane of incidence. The coating is applied to the three sides of the cube that are seen from the source and from the receiver. The bistatic scattering cross section of the cube without coating has been used as a reference (black, red and green lines). The results for the coated cube (blue line, magenta line, yellow line) confirm a significant reduction in the scattering cross section due to the coating, a good agreement between measurement and simulation, as well as between exact (FEM solver HFSS®, ANSYS) and approximate (BISTRO) numerical simulations. Simulation of this configuration with BISTRO has required the use of edge corrections as the cube is a configuration with long and sharp edges.
|Figure 3: Frequency dependent reflectivity of an MTM low-reflection coating|
The polarimetric bistatic scattering measurement facility (see Figure 4) operating in W frequency band is of great importance for validating numerical results. It has been rebuilt recently in the TechLab building. Several mechanical components have been replaced and new W-band front-ends are now used. Various signature measurements, quasi-monostatic, as well as bistatic, on different canonical test objects and scaled realistic targets have been performed successfully.
|Figure 4: Mono-/bistatic RCS measurement facility|
Metamaterials are artificially assembled composites with tailored and controllable electromagnetic properties. In their most general form, MTMs are assembled from periodic lattices of subwavelength-sized metallo-dielectric inclusions placed in a homogeneous substrate. The electromagnetic response / specification of MTMs can be adjusted by a proper choice and arrangement of the inclusions in the substrate, thus leading to a material with the desired electromagnetic properties which may be even unavailable in natural materials.
MTMs have the potential of becoming an enabling technology for a broad variety of applications, and MTM low reflection coatings (LRCs) are an example of a novel device for reduction or manipulation of radar signatures. MTM LRCs can be made much thinner and, therefore, lighter than conventional absorbers, and with a substrate made from a durable and flexible material such as Teflon, ceramic or a fiber/resin mixture, they can withstand high mechanical stress and be applied to curved surfaces. Figure 2 shows a sample MTM LRC plate, which has been designed to work in Ka-band and fabricated at the Institute’s mechanical lab by using printed circuit board technology. The frequency dependence of the reflection coefficient of the sample, experimentally determined at the Ka-band reflection measurement setup, confirms a significant reduction in reflectivity around the design frequency 37 GHz (see Figure 3). The thickness of the LRC is about λ/80 and the size of a unit cell λ/6, with λ being about 8 mm.
Material measurement facilities
The measurement setups for material characterization (transmission and reflection properties for cm and mm waves) have been rebuilt and improved in the Institute’s TechLab. Free space transmission and reflection measurements are available for X-, Ka-, and W-band frequencies (Figure 5, Figure 6 and Figure 7). Waveguide measurements are now possible for frequencies from 1.1 GHz up to 110 GHz. All measurement procedures are PC controlled, including automatic data acquisition. New microwave absorbers have been installed in all labs to minimize disturbing signals, and temperature variation has been reduced dramatically. Extensive work has been done concerning optimal calibration procedures. The codes for calculating the frequency dependent electric material constants on the basis of transmission and/or reflection measurement data have been improved. An interactive material editor has been developed, in order to provide an easy to use tool to calculate and visualize the angle dependency of Fresnel’s transmission and reflection coefficients for single or multilayer materials.
|Figure 5: X-band transmission measurement setup|
|Figure 6: Ka-band transmission measurement setup|
|Figure 7: X-band reflection measurement setup|
Besides fibre ceramics, glasses and other materials, several plastic samples have been investigated. To assess the accuracy of the permittivity determination, three polyamide samples of different thickness have been measured in free space and evaluated in the frequency domain. The three curves of the real and imaginary part of the permittivity have been compared. Maximum absolute deviations of 0.007 for the real part have been observed. High accuracy as a result of improved calibration procedures, very good measurement conditions, as well as high flexibility, due to benefiting from five different setups, are features of the material characterization work.
To assess the radar cross section of extended targets (e.g. terrain, water surfaces) the simulation tool DORTE (Detection of Objects in Realistic Terrain) has been developed. It utilizes solely information on topography and land cover to estimate the position-dependent monostatic clutter return (see Figure 8). It can be easily extended to also consider bistatic configurations.
|Figure 8: Clutter map simulation of region Immenstadt, Germany|
The identification of shadowed regions results from employing a specialized hidden surface algorithm. Akima splines are used for rescaling digital elevation models, as well as for determining local normal vectors necessary for the calculation of the local clutter return.
|Figure 9: Monostatic specific RCS of a fractal water surface (PO approximation, VV-polarization, 15°C temperature, 0% salinity|
The computer code uses statistical and fractal, as well as (semi-)empirical clutter models to estimate the radar cross section of each surface element (see Figure 9). Semi-empirical and fully-empirical models are based on measurements possibly backed by theoretical considerations (e.g. Currie-Zehner, Attema-Ulaby, Billingsley, Kulemin, Georgia Institute of Technology, Technology Service Corporation). There exists a copious amount in literature ranging from very simple to highly specialized cases. In order to examine the influence of certain environmental parameters, the surface may be modelled using statistical functions (RMS height and exponential or Gaussian correlation function) or fractal Weierstrass-Mandelbrot functions. These models are based on physical optics or the small perturbation method (fractal only). The scattering material is characterized by a mixture model of dielectric constants. For certain clutter models, statistical variation of the calculated clutter return may be added by setting a switch. In order to reduce calculation time, the pre-calculated RCS characteristics of azimuth independent clutter can be stored in a dedicated MySQL database. The program itself is operated by means of a graphical user interface. To sum up, DORTE presents a novel and flexible tool for efficiently and quickly predicting the backscattering cross section of extended targets. A wide range of new diverse and freely assignable clutter models is utilized.
Target detection by a radar seeker, which is mounted inside a missile’s nose, is a necessity for missile guidance, navigation, and aiming point determination. Simulations and measurements concerning the radome’s transmission characteristics are of great importance and are, therefore, performed as part of DLR missile projects.
Detection probability of aircrafts
The signatures of electrical large targets (i.e. large compared to the wavelength) show a strong dependency on the aspect angle. In order to calculate detection probabilities it is necessary to apply special radar fluctuation models. For this purpose we calculate high resolution RCS distributions for the complete 2D range of aspect angles. This range is divided into submatrices which are analyzed statistically. The statistical parameters are consequently applied in fluctuation models considering radar station parameters.