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Bi-static RCS variations of pedal and wheel movements on bicycles between 1 and 10 GHz
One benefit of cooperative automated and connected driving lies in the fusion of multiple mobile wireless sensor and data transmission nodes, covering complementary technologies like radar, cellular and ad-hoc communications, and alike. Current developments indicate enormous potential to increase the environmental awareness through joint communication and radar sensing. In this respect, future channel models require knowledge of bi-static reflectivities of road users over a range of illumination and observation angles, both in the nearfield and in the far-field. To establish reference data and model such angle-dependent RCS variations, this paper deals with realistic pedal and wheel rotations of a bicycle based on electromagnetic simulations. In the simulation setup, idealized far-field conditions with plane-wave illumination and observation were assumed, while the angles covered the entire azimuth with 201 variations of the pedal and wheel positions. The fluctuation of the RCS is analyzed and discussed in terms of its probability density and cumulative distribution functions. Depending on the angular constellation, the range of the fluctuation varied between 1 dB and 14 dB, while the specular reflection and forward-scattering showed almost no fluctuation.
Radiation and Scattering Pattern Characteristics of Chamfered-Tip Open-Ended Rectangular Waveguide Probes for Planar Near-Field Antenna Measurement Applications
The radiation and scattering pattern characteristics of open-ended rectangular waveguide with a chamfered tip are examined. Despite common and widespread use as a probe antenna for planar near-field antenna measurements, a methodical investigation of the chamfered-tip design and resultant performance has not been published. A computational electromagnetics (CEM) model for an open-ended rectangular waveguide probe with a parameterized chamfered tip has been constructed and results for both radiation and scattering patterns are presented. A comparison of results includes a probe without a chamfer and a probe typical of that available from commercial suppliers. It is shown that, for a series of standard waveguide size probes sharing a common thickness for the waveguide wall and chamfered tip, the radiation pattern is relatively insensitive to the chamfer tip designs studied until frequency increases into W-band (WR-10). The scattering pattern characteristics for the same series of standard waveguide size probes show a reduction in on-axis (boresight) monostatic radar cross section (RCS) for chamfered tip waveguides compared to blunt-ended waveguides and that this reduction increases for increasing frequency.
A Fast Source Reconstruction Method for Radiating Structures on Large Scattering Platforms
We present a fast source reconstruction method suitable for antenna diagnostic applications of radiating structures on electrically large platforms. The method is based on a novel implementation of a recent reformulation of the inverse electromagnetic scattering problem, and is solved using a Higher Order Method of Moments (MoM) discretization. The novel implementation achieves asymptotically better scaling the previously possible, and in particular the memory use is substantially lower than was previously possible. Results from two example cases are presented where the new method is compared to the current commercial state-of-the-art solver in DIATOOL 1.1, and significant improvements are observed in terms of computation times and memory requirements.
Full Scattering Matrix RCS Measurements Using Simultaneous H/V Radar Waveforms
Instrumentation radar metrology waveform techniques that simultaneously transmit two orthogonal sequences of orthogonal electromagnetic polarizations are explored for applicability toward both static and dynamic RCS signature and ultra-wideband imaging measurements using simultaneous H-pol and V-pol (SHV) waveforms. Static, pulsed measurements with independent transmit polarizations are modulated and radiated; reflections from a depolarizing target are measured where the return signals are coherently combined. Each transmit polarization is independently modulated using a diverse phase sequence, which leaves a unique “fingerprint” by which the orthogonal polarization separation is achieved. Using only the coherent combination and associated transmit and receive RF channel characterizations, the original measurements are reconstructed. Simulations serve as a baseline for measured results, from generating pure SHV waveforms and then providing simultaneous full scattering matrix (FSM) measurements, in order to achieve greater purity of FSM signatures, while reducing measurement times by a factor of two.
Autonomous Spherical Passive/Active Radar Calibration System
A Spherical Passive/Active Radar Calibration System (SPARCS) has been designed as an advanced, airborne, radar calibration device (CD). SPARCS is currently under development as an autonomous, battery-powered, high-endurance, flying platform. This self-contained, multi-function radar calibration and diagnostic system functions as 1) a Passive Spherical Reflector, 2) an Active RF Repeater, 3) a Synthetic Target Generator, and 4) an UWB RF Sensor and Data Recorder of the radar under test or the localized RF environment. This innovative CD exploits major advances in commercial technology during the past decade associated with autonomous airborne drones and miniaturized digital RF systems on chips (RFSoCs), and other miniature electronics. Emphasis has been placed on a recoverable, reusable CD that enables precision calibrations over extensive open-air test volumes used for dynamic aircraft RCS measurement, test and verification, or time space position information (TSPI) test range tracking radars. This paper highlights early efforts to parameterize and develop SPARCS, including advances in autonomous navigation and flight time, electric ducted fan performance, radar screens for thruster inlet and outlet ports, active calibration functionality, and improving calibration uncertainty. SPARCS will provide an unprecedented capability for radar instrumentation calibration, target emulation, environmental assessment and in situ, real-time calibration.
3:1 Bandwidth Dual-Polarized Compact Range Feeds for RCS Measurements
A set of Dual-Polarized Antennas with a 3:1 operating bandwidth has been developed for use in near-field ranges as the probe or range antenna and for use as a Compact Antenna Test Range (CATR) feed . Key development parameters of the antenna are: a wideband impedance match to the coaxial feed line, E and H-plane 1 dB beam widths in excess of 30 degrees, -30 dB on axis cross-polarization, minimum polarization tilt and a phase center that varies over a small region near the aperture. To accomplish these design parameters, a family of range antennas has been developed and previously introduced. Two versions of the antenna have been manufactured and tested for performance. A 2-6 GHz version has been developed using traditional machining techniques and a 6-18 GHz version has been produced using additive manufacturing (3D printing) techniques . These antennas provide proper illumination of the quiet zone for compact ranges used for antenna measurements as well as radar cross section (RCS) measurements. For RCS measurements, an additional requirement for time-based energy storage performance is considered. Energy storage in the feed can result in a pulse spreading or additional copies of the pulse in time, resulting in poor performances of the target characterization. This effect is called ‘ringdown’. In this paper, we focus on the RCS ringdown performance of the 6-18 GHz antenna produced using additive manufacturing. The measured performance of the antenna will be presented and discussed. Finally, the applicability of the antenna as a CATR feed for RCS measurements will be discussed.
Bi-static Reflectivity Measurements of Vulnerable Road Users using Scaled Radar Objects
The future of cooperative automated and connected driving lies in the fusion of multiple mobile wireless sensor and data transmission nodes, covering technologies like radar, cellular and ad-hoc communications, and alike. Current developments indicate enormous potential to increase the environmental awareness through joint communication and radar sensing. In this respect, future wireless channel models aim at including bi-static reflectivities of road users, depending on different illumination and observation angles, in the nearfield as well as in the far-field. The limitations of the measurement distances within anechoic chambers unavoidably induce nearfield effects, especially for electrically large radar objects like realistic road users, and conventional bi-static RCS calibration techniques would eventually fail. In order to model the transition from the nearfield to the far-field reflectivity of road users, this paper uses the object scaling approach, with combined measurements and electromagnetic simulations. Bi-static reflectivity measurements of selected vulnerable road users are described, from the chamber setup all the way up to data post-processing. The approach of electromagnetic object scaling is applied to such bi-static reflectivity measurements, and the results are evaluated and discussed in comparison with numerical simulations. Initial proof-of-concept measurements of differently sized metal spheres confirmed the applicability of the scaling approach under far-field conditions very convincingly. Based on this, scaled models of radar objects, namely a bicycle and a pedestrian, were 3D printed and then metallized with copper paint. Compared to corresponding electromagnetic simulations of the original bi-static reflectivity of the radar objects, the results measured for the scaled models show very promising agreement with the numerical expectation. This study contributes to the further development of future wireless channel models considering bi-static multipath components of different road users, being an indispensable prerequisite to enhance the safety in future road traffic.
Geometry- and angle-dependent monostatic scattering of microwave absorbers
Motivation and background: With the increasing abundance and functionality of wireless communication systems, the requirements for virtual electromagnetic environments like shielded anechoic chambers, and the complexity of the test procedures increase accordingly. The scattering behavior of microwave absorbers is an essential indicator of their quality and suitability for use in such anechoic chambers. Current research activities deal with the revision of the IEEE standard 1128 on recommended practice for absorber characterization and give room for improved test procedures. Objectives and methods: In this paper, the angle-dependent backscattering of microwave absorbers was studied experimentally with respect to their different geometric shapes and material parameters. The dielectric permittivity of pyramidal and flat absorbers was measured between 1 GHz and 10 GHz, followed by systematic monostatic reflectivity measurements. Signal post-processing, including phase-coherent background subtraction and time-domain gating, were applied to minimize unwanted reflections and extract the wanted scattered signals. The radar cross-section (RCS) method was applied to derive the reflectivity with respect to different illumination angles for parallel and perpendicular polarizations. The results were compared to supplier specifications, electromagnetic simulations of the reflectivity, and the scattering pattern of a metal plate. Results and conclusions: The measurement results agree well with the numerical simulations. The data reveal that the reflectivity patterns of microwave absorbers are governed by their geometric shape, while the material properties do not modify the angular dependences qualitatively but result in a quantitative offset. Our findings help to improve the accuracy of monostatic RCS and absorber reflectivity measurements even further and lead to a better understanding of the physical origin of the scattering phenomena of microwave absorbers in general. Future work will extend our studies towards bi-static angle-dependent reflectivity measurements, in order to establish a consistent and comprehensive method for characterizing different types of microwave absorbers with respect to type, frequency, angle of illumination, angle of observation, and polarization. This research has been funded by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) under the grants HE3642/14-1 and BO4990/1-1 (Electromagnetic modeling of microwave absorbers - EMMA).
Numerical Study of the RCS of Pyramidal Absorber Geometries
There have been a number of numerical analyses of RF absorber presented in the literature. These analyses, however, tend to focus on the reflectivity of the material and not on the radar cross section (RCS) that it presents. Brumley studied the RCS of RF absorbers for the purpose of estimating the background RCS of anechoic ranges . The study was done empirically; obtaining measurements of the RF absorber and looking at the RCS of different pyramids and wedges, with and without paint. Brumley presents some potential methods to improving the RCS signature of the range, thus reducing the background RCS of the site. In this paper, the suggestions presented by Brumley are revisited. Specifically, his recommendation for the twisted pyramid configuration which he was unable to measure due to the lack of absorber samples available for use in the test. In addition to the twisted pyramid, Brumley's approach of inserting smaller pyramids in the valleys of a larger pyramidal arrangement to reduce the edges parallel to the incoming wave are also presented. Different carbon loadings are modeled for the inserted pyramids. One is the standard loading of the inserted pyramid, and the other is the same loading as the main larger pyramidal arrangement such that all the absorber on the wall has the same material properties. Numerical studies are performed using time domain techniques as well as frequency domain techniques. The model is validated by comparing the RCS of a flat square plate with the theoretical solution. The results validate the data and the suggestions presented in  and present ways of improving some of the solutions by adjusting the material properties of the absorber.
Numerical Analysis of Techniques to Improve Oblique Incidence of Absorber
Financial impacts often drive decisions to repurpose existing ranges instead of procuring new measurement facilities. These existing ranges have fixed geometries (height, width and length) that were set when the range was originally constructed and often are designed for a different purpose. The inability to set the geometry precludes the range designer from using the range geometry to improve measurement performance. Thus, the performance of the range is mostly dependent on the RF absorber and the range antenna directivity. In rectangular-shaped ranges for example, the lateral surfaces, side walls, ceiling and floor, are the critical surfaces to address in RF absorber arrangement. In this paper, numerical analyses of Chebyshev arrangements as well as dragon tail or tilted absorber are studied. This paper also analyzes the performance of Chebyshev absorber for normal incidence and for oblique incidence along with the proper arrangement of the Chebyshev period. While certainly these have been discussed previously in the literature, this paper consolidates the previous information and illustrates it with numerical examples to help the reader understand the best approach to use when repurposing a range.
Increasing the Material Diversity in the Austin RCS Benchmark Suite Using Thin Plates
The Austin RCS Benchmark Suite has recently been introduced to enable quantitative and objective comparison of computational systems for solving electromagnetic scattering problems, particularly, those relevant to aerospace applications. In the last year, five sets of problems were added to it: dielectric almonds (problem set III-B), mixed material almonds (III-C, III-D), perfectly electrically conducting (PEC) aircraft models (IV-A), and dielectric aircraft models (IV-B). For each problem set, a range of lengths and frequencies of interests are identified, interesting features are highlighted, and datasets containing reference results (from measurements, analytical methods, or numerical methods) are shared online. Although data from several radar cross section (RCS) measurement campaigns of non-metallic targets are available in the literature, these lack the information necessary to precisely model the materials, target geometries, and measurement setups, to quantify uncertainties in the data, and to identify appropriate directions for improving computational methods' performance. This limits their utility for benchmarking computational systems. This article presents an expansion of the Suite to include problems with more complex materials and reference results from a measurement campaign that attempted to ameliorate the deficiencies of existing datasets. Specifically, a set of thin-plate problems are added to the Austin RCS Benchmark Suite to increase material diversity. These consist of problem sets II-B: thin perfect-electrically conducting (PEC) plates, II-C: thin dielectric plates, II-D: thin magnetic radar absorbing material (MagRAM) plates, and II-E: thin MagRAM-coated PEC plates. Reference RCS data that enables validation, RCS measurement and material property uncertainty quantification, and benchmarking are also provided by conducting a simulation-supported measurement campaign in a compact range. To facilitate reproducibility, a popular low-loss dielectric material and a commercially available MagRAM were chosen for these problems: The dielectric material for problem set II-C is PolymaxTM polylactic acid (PLA). For problem sets II-D/E, the ARC Technologies' DD-13490 material is used. Thin plates were manufactured and their RCS were measured at Lockheed Martin's Rye Canyon Facility. The monostatic RCS measurement results and supporting simulation results are available online. Performance data for simulations as well as RCS measurement results with accompanying uncertainty will be presented for problem sets II-B/C/D/E at the conference.
2D RCS Prediction from Multistatic Near-Field Measurements on a Plane by Single-Cut Near-Field Far-Field Transformation and Plane-Wave Synthesis
A near-field far-field transformation (NFFFT) technique with a plane-wave synthesis is presented for predicting two-dimensional (2D) radar cross sections (RCS) from multistatic near-field (NF) measurements. The NFFFT predicts the FF of the OUT illuminated by each single source, then the plane-wave synthesis predicts the FF of the OUT each illuminated by each plane-wave by synthesizing the FFs given in the NFFFT step. The both steps are performed in the similar computational procedure based on a single-cut NFFFT technique that has been proposed previously. The method is performed at low cost computation because the NF and source positions are required only on a single cut plane. The formulation and validation of the method is presented.
Measurements of Non-Metallic Targets for the Austin RCS Benchmark Suite
A simulation-supported measurement campaign was conducted to collect monostatic radar cross section (RCS) data as part of a larger effort to establish the Austin RCS Benchmark Suite, a publicly available benchmark suite for quantifying the performance of RCS simulations. In order to demonstrate the impact of materials on RCS simulation and measurement, various mixed-material targets were built and measured. The results are reported for three targets: (i) Solid Resin Almond: an almond-shaped low-loss homogeneous target with the characteristic length of ~10-in. (ii) Open Tail-Coated Almond: the surface of the solid resin almond's tail portion was coated with a highly conductive silver, effectively forming a resin-filled open cavity with metallic walls. (iii) Closed Tail-Coated Almond: the resin almond was manufactured in two pieces, the tail piece was coated completely with silver coating (creating a closed metallic surface), and the two pieces were joined. The measured material properties of the resin are reported; the RCS measurement setup, data collection, and post processing are detailed; and the uncertainty in measured data is quantified with the help of simulations.
Personal Near-field System
In 1987 the author built the world's first Personal Near-field antenna measurement System (PNS). This led to the formation of Nearfield Systems Inc. (NSI) a company that became a major manufacturer of commercial near-field antenna measurement systems. After leaving NSI in 2015 several new personal antenna measurement tools were built including a modern updated PNS. The new PNS consists of a portable XY scanner, a hand held microwave analyzer and a laptop computer running custom software. The PNS was then further generalized into a modular electromagnetic field imaging tool called "Radio Camera". The Radio Camera measures electromagnetic fields as a n-dimensional function of swept independent parameters. The multidimensional data sets are processed with geometric and spectral transformations and then visualized. This paper provides an overview of the new PNS and Radio Camera, discusses operational considerations, and compares it with the technology of the original 1987 PNS. Today it is practical for companies, schools and individuals to build low-cost personal antenna measurement systems that are fully capable of meeting modern industry measurement standards. These systems can be further enhanced to explore and visualize electromagnetic fields in new and interesting ways.
Indoor 3D Spherical Near Field RCS Measurement Facility: A new high resolution method for 3D RCS Imaging
Indoor RCS measurement facilities are usually dedicated to the characterization of only one azimuth cut and one elevation cut of the full spherical RCS target pattern. In order to perform more complete characterizations, a spherical experimental layout has been developed at CEA for indoor Near Field monostatic RCS assessment . This experimental layout is composed of a 4 meters radius motorized rotating arch (horizontal axis) holding the measurement antennas while the target is located on a polystyrene mast mounted on a rotating positioning system (vertical axis). The combination of the two rotation capabilities allows full 3D near field monostatic RCS characterization. 3D imaging is a suitable tool to accurately locate and characterize in 3D the main contributors to the RCS. However, this is a non-invertible Fourier synthesis problem because the number of unknowns is larger than the number of data. Conventional methods such as the Polar Format Algorithm (PFA), which consists of data reformatting including zero-padding followed by an inverse fast Fourier transform, provide results of limited quality. We propose a new high resolution method, named SPRITE (for SParse Radar Imaging TEchnique), which considerably increases the quality of the estimated RCS maps. This specific 3D radar imaging method was developed and applied to the fast 3D spherical near field scans. In this paper, this algorithm is tested on measured data from a metallic target, called Mx-14. It is a fully metallic shape of a 2m long missile-like target. This object, composed of several elements is completely versatile, allowing any change in its size, the presence or not of the front and / or rear fins, and the presence or not of mechanical defects, … Results are analyzed and compared in order to study the 3D radar imaging technique performances.
Bandwidth response of a reflectarray antenna working as a Compact Antenna Test Range probe
A reflectarray antenna working at 28 GHz is proposed to replace the reflector antenna of a Compact Antenna Test Range (CATR) system. As a first approach, the quiet zone obtained using a far-field collimated reflectarray is analysed. Due to the size of this area is not large enough, the generalized Intersection Approach is employed to carry out an optimization of the near-field for both phase and amplitude in order to maximize the size of the quiet zone at one plane. Simulations are compared for the near-field before and after the optimization process, showing an important enhancement of the size of the quiet zone, especially in the main cuts. From the obtained phase distribution a design is carried out. The unit cell chosen is based on a two-layer stacked patch, having good agreement between optimization and design results. Finally, the bandwidth response of the designed reflectarray is analysed, in order to assess its performances as probe in a CATR system.
Measurements on extended objects for radar field probes
An extended long object usually gives rise to a bright reflection (a glint) when viewed near its surface normal. To take advantage of this phenomenon and as a new concept, a discrete Fourier transform (DFT) on the RCS measurements, taken within a small angular range of broadside, would yield a spectrum of incident wave distribution along that object; provided that the scattering is uniform per unit length, such as from a long cylinder [1, 2]. In this report, we examine the DFT spectra obtained from three horizontal long objects of different lengths (each of 60, 20, and 8 feet). Aside from the end effects, the DFT spectra looked similar and promising as an alternative to the conventional field probes by translating a sphere across a horizontal path. Keywords: RCS measurements, compact range, field probes, extended long objects 1. The Boeing 9-77 compact range The Boeing 9-77 indoor compact range was constructed in 1988 based on the largest Harris model 1640. Figure 1 is a schematic view of the chamber, which is of the Cassigranian configuration with dual-reflectors. The relative position of the main reflector and the upper turntable (UTT) are as shown. The inside dimensions of the chamber are 216-ft long, by 80-ft high, and 110-ft wide. For convenience, we define a set of Cartesian coordinates (x: pointing out of the paper, y: pointing up, z: pointing down-range), with the origin at the center of the quiet zone (QZ). The QZ was designed as an ellipsoidal volume of length 50-ft along z, height 28-ft along y, and width 40-ft along x. The back wall is located at z = 75 ft, whereas the center of the roll-edged main reflector (tilted at 25 o from vertical) is at z =-110 ft. It is estimated that the design approach controls the energy by focusing 98% of it inside the QZ for target measurements. The residual field spreading out from the main reflector was attenuated by various absorbers arranged in arrays and covering the chamber walls.-, Tel. (425) 392-0175 2. Anechoic chamber In order to provide a quiet environment for RCS measurements, the inside surfaces of an anechoic chamber are typically shielded by various pyramidal and wedged-shaped absorbers, which afford good attenuation at near-normal incidence for frequencies higher than ~2 GHz. At low frequencies and oblique angles , however, Figure 1. A schematic view of the Boeing 9-77 compact range with dimensions as noted. insufficient attenuation of the radar waves by the absorbers may give rise to appreciable backgrounds. Figure 2 shows a panorama view inside the compact range, as viewed from the lower rear toward the main reflector and the UTT. With the exception of the UTT, all other absorbers are non-moving or stationary. A ring of lights on the floor shows the rim around the lower turntable (LTT), prior to the installation of absorbers. In order to minimize the target-wall interactions, the surfaces facing the QZ from the ceiling, floor, and two sidewalls are covered with the Rantec EHP-26 type of special pyramidal absorbers.
Non-contact Characterization of Antenna Impedance, Gain and Pattern through Open-Fixture Network Calibration
We present a novel, non-contact characterization technique for simultaneous characterization of conventional antenna parameters, including the antenna port input impedance, antenna gain and its radiation pattern, without requiring a network analyzer connection to the antenna port. The test antenna and the network analyzer are considered as a 2-port open-air fixture whose network representation corresponds to the desired antenna parameters. The unknown network parameters of the 2-port open-air fixture are determined via a novel calibration process using 4 offset-short termination standards. The error parameters determined by the calibration are then related to the test antenna port impedance and its gain as a function of frequency. Furthermore, the radiation pattern of the test antenna can also be characterized using measured reflection coefficient at the network analyzer port for two offset-short terminations of the test antenna port, while rotating the test antenna over the desired angular range. This novel technique is particularly attractive for installed-antenna applications where an active connection to the test antenna port is either difficult or undesirable, such as on-chip antennas and implanted antennas, to name a few. To demonstrate the efficacy our new method, we present the measured impedance, gain and radiation pattern of a diagonal-horn antenna operating over 360-450 GHz, and a lens-integrated planar butterfly antenna for the 220-325GHz band.
Experimental validation of Reference Chip Antennas for 5G Measurement Facilities at mm-Wave
In this paper, the experimental validation of a micro-probe fed reference antenna targeting the upcoming 5G applications (24.25-29.5GHz band) is presented. The main purpose of these reference antennas is to serve as "gold standards" and to perform gain calibration of 5G test facilities through the substitution method. The outline of these antennas is based on a square array of four printed patches enclosed in a circular cavity. The RF input interface is a stripline-to-coplanar waveguide transition and allows for feeding the device with a micro-probe. Performance obtained by high-fidelity modeling is reported in the paper and correlated to experimental data. Interaction and unwanted coupling with the test equipment are discussed. The use of echo-reduction techniques and spatial filtering is investigated to mitigate these effects.
Recent Changes to the IEEE std 1502 Recommended Practice for Radar Cross-Section Test Procedures
Radar scattering is typically represented as the RCS of the test object. The term RCS evolved from the basic metric for radar scattering: the ratio of the power scattered from an object in units of power per solid angle (steradians) normalized to the plane-wave illumination in units of power per unit area. The RCS is thus given in units of area (or effective cross-sectional area of the target, hence the name). Note that the RCS of the test object is a property of the test object alone; it is neither a function of the radar system nor the distance between the radar and the test object, if the object is in the far field. Because the RCS of a target can have large amplitude variation in frequency and angle, it is expressed in units of decibels with respect to a square meter and is abbreviated as dBsm (sometimes DBSM or dBm2). In terms of this definition, the RCS of a radar target is a scalar ratio of powers. If the effects of polarization and phase are included, the scattering can be expressed as a complex polarimetric scattering (CPS) matrix. The measurement of the RCS of a test object requires the test object to be illuminated by an electromagnetic plane wave and the resultant scattered signal to be observed in the far field. After calibration, this process yields the RCS of the test object in units of area, or the full scattering matrix as a set of complex scattering coefficients. This paper describes the planned upgrades to the old IEEE Std 1502™-2007 IEEE Recommended Practice for Radar Cross-Section Test Procedures . The new standard will reflect the recent improvements in numerical tools, measurement technology and uncertainty estimates in the past decade.
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