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RCS

Bandwidth response of a reflectarray antenna working as a Compact Antenna Test Range probe
A F Vaquero, M Arrebola, M R Pino, October 2019

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.

Non-contact Characterization of Antenna Impedance, Gain and Pattern through Open-Fixture Network Calibration
Seckin Sahin, Niru K Nahar, Kubilay Sertel, October 2019

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
A Giacomini, L Scialacqua, F Saccardi, L J Foged, E Szpindor, W Zhang, M Oliveira, P O Iversen, J M Baracco, October 2019

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
Eric Mokole, Vince Rodriguez, Jeff Fordham, L J Foged, ,, October 2019

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 [1]. The new standard will reflect the recent improvements in numerical tools, measurement technology and uncertainty estimates in the past decade.

Geometric Effects on Radar Echoes from a Corner Reflector
P S P Wei, November 2018

Radar data on the complete polarimetric responses from a 4" dihedral corner reflector from 4 to 18 GHz have been collected and studied. As a function of the azimuth, the vertically suspended object may present itself to the radar as a dihedral, a flat plate, an edge, a wedge, or combinations of these. A two-dimensional method-of-moment (2-D MOM) code is used to model the perfectly electrical conducting (PEC) body, which allows us to closely simulate the radar responses and to provide insight for the data interpretation. Of particular interest are the frequency and angular dependences of the responses which yield information about the downrange separation of the dominant scattering centers, as well as their respective odd-or even-bounce nature. Use of the corner reflector as a calibration target is discussed.

Evaluation of the Monostatic-Bistatic theorem applied to the radar signature of aerial platforms in low frequency
J C Castelli, S Langlet, November 2018

In this paper, we explore the capabilities of the Monostatic-Bistatic Theorem (MBT) applied to Radar Cross Section (RCS) in low frequency. Originally, the validity of this theorem has been shown in high frequency for targets whose RCS is produced by elementary interactions (specular reflection in particular). We are interested in aerial platforms and in particular some Low Observable targets that have relatively "pure" geometries limiting the presence of complex interactions. Several variants of the MBT from the field of electromagnetism [1][2][3] and acoustics [4] are used. Their performances are compared from data obtained from a MoM method that is recognized to produce accurate scattering data. To highlight the discrepancies produced by the different variants, we use both a metric to compare the quality of the bistatic holograms obtained and also radar imaging which allows locating the areas of the target where the echoes are not correctly restored.

Conex Antenna, Radar, and Measurement Equipment Lab
Gregory Kiesel, Daniel Dykes, Eric Brown, Edward Garcia Iii, Ryan Buchanan, Tim Conn, November 2018

The Conex Antenna, Radar, and Measurement Equipment Lab (CARAMEL) is a ten-element VHF antenna array that operates from 30 MHz-120 MHz with an attached lab space. This array was developed for use in low frequency Radar Cross Section (RCS) measurements. The antenna elements support both vertical and horizontal polarizations. The antenna was designed using a genetic algorithm, employing the fragmented aperture technique; measured and modeled data will be presented. The attached lab space is air conditioned and provisioned for rack mounted equipment. The structure uses a modified 20' Conex shipping container where an entire sidewall has been replaced with a reinforced composite radome for the antennas. The overall mechanical frame design included a Finite Element Analysis to ensure structural integrity. The system is intended for long-term standalone use as an outdoor measurement radar system but can be moved using standard shipping container methods. The structure was shipped using a standard cargo carrier from Atlanta, Georgia to White Sands, New Mexico.

Validation of Additive Manufacturing for Broadband Choked Horns at X/Ku Band by Extensive Antenna Measurements
A Giacomini, R Morbidini, V Schirosi, F Saccardi, L J Foged, B Jun Gerg, D Melachrinos, M Boumans, November 2018

Additive manufacturing has become a popular alternative to traditional CAM techniques, as it has reached a suitable maturity and accuracy for microwave applications. The main advantage of the additive technologies is that the manufacturing can be performed directly from the 3D CAD model, available from the numerical simulation of the antenna, without significant modifications. This is a highly desirable feature, in particular for time and cost critical applications such as prototyping and manufacturing of small quantities of antennas. Different 3D-printing/additive manufacturing technologies are available in industry today. The purpose of the paper is an investigation on the accuracy and repeatability of the Selective Laser Melting (SLM) manufacturing technique applied to the construction of a batch of 15 broad band fully metallic chocked horns, operating at X/Ku band, manufactured in parallel. Manufacturing accuracy and repeatability has been evaluated using RF parameters as performance indicators comparing measured data and high accuracy simulations. The radiation patterns have been correlated to the numerical reference using the Equivalent Noise Level, while manufacturing repeatability is quantified on input matching by defining an interference level. These indicators have also been compared to state-of-the-art values commonly found for traditional manufacturing.

Modeling of Tapered Anechoic Chambers
Zubiao Xiong, Zhong Chen, November 2018

A hybrid method that combines the finite element method (FEM), the Floquet mode analysis and the shooting and bouncing ray method (SBR) is presented to solve the quiet-zone field in large tapered anechoic chambers. In the method, the field equivalence principle is employed to replace the throat of the tapered chamber by a set of equivalent electric and magnetic currents. The Floquet mode analysis is employed to approximate the rest of the absorber lined walls by virtual surfaces with equivalent reflection coefficients. The total quiet-zone field then becomes the superposition of the field radiated by the equivalent currents, and the field scattered by the virtual reflective surfaces. The scattered field is calculated from the SBR method. The required equivalent currents of the throat and the reflection coefficients of absorber array walls are computed with the use of the FEM, which allows the considerations of the complex structure and near-field interaction. Numerical examples are presented to demonstrate the feasibility of the proposed method.

Measurements of the dynamic pattern of an electronically steerable phased antenna array with circular polarization in Ka-band
Matthias Tebbe, Georg Strauss, November 2018

This paper presents two methods for measuring dynamic antenna patterns of phased arrays in a compensated compact range. The first method uses the turntable of the compact range to counter steer the antenna beam. The dynamic pattern is created by measuring single points of the pattern over time. This method is successfully tested, and the measurement results show the effect of phase jumps during the steering process. The second method extends the range of application to fast steering phased arrays by decoupling the antenna scan angle and the azimuth angle of the turntable.

Highly accurate fully-polarimetric radar cross section facility for mono- and bistatic measurements at W-band frequencies
Andreas Olk, Kais-Ben Khadhra, Thiemo Spielmann, October 2017

New requirements in the field of autonomous driving and large bandwidth telecommunication are currently driving the research in millimeter-wave technologies, which resulted in many novel applications such as automotive radar sensing, vital signs monitoring and security scanners. Experimental data on scattering phenomena is however only scarcely available in this frequency domain. In this work, a new mono- and bistatic radar cross section (RCS) measurement facility is detailed, addressing in particular angular dependent reflection and transmission characterization of special RF material, e.g. radome or absorbing material and complex functional material (frequency selective surfaces, metamaterials), RCS measurements for the system design of novel radar devices and functions or for the benchmark of novel computational electromagnetics methods. This versatile measurement system is fully polarimetric and operates at W-band frequencies (75 to 110 GHz) in an anechoic chamber. Moreover, the mechanical assembly is capable of 360° target rotation and a large variation of the bistatic angle (25° to 335°). The system uses two identical horn lens antennas with an opening angle of 3° placed at a distance of 1 m from the target. The static transceiver is fed through an orthomode transducer (OMT) combining horizontal and vertical polarized waves from standard VNA frequency extenders. A compact and lightweight receiving unit rotating around the target was built from an equal OMT and a pair of frequency down-converters connected to low noise amplifiers increasing the dynamic range. The cross-polarization isolation of the OMTs is better than 23 dB and the signal to noise ratio in the anechoic chamber is 60 dB. In this paper, the facility including the mm-wave system is deeply studied along with exemplary measurements such as the permittivity determination of a thin polyester film through Brewster angle determination. A polarimetric calibration is adapted, relying on canonical targets complemented by a novel highly cross-polarizing wire mesh fabricated in screen printing with highly conductive inks. Using a double slit experiment, the accuracy of the mechanical positioning system was determined to be better than 0.1°. The presented RCS measurements are in good agreement with analytical and numerical simulation.

Analysis of Time and Direction of Arrival (TADOA) Data using Basis Pursuit in the AFRL One-RY Antenna Measurement Range
Brian Fischer, Ivan LaHaie, Michael Blischke, Brian Kent, Brittany Wells, James Stewart, October 2017

Time and Direction of Arrival (TADOA) analysis of field probe data has been an accepted method for characterizing stray signals in an antenna measurement range for many years ([1], [2]). Recent uncertainty investigations at the OneRY range have shown a need for increased resolution to isolate and characterize energy in TADOA images so that resources can be carefully applied to reduce the uncertainty from these stray signals. This is accomplished by modeling the TADAO image as the solution to a Basis Pursuit (BP) l1 minimization problem. This paper outlines the model development and shows concrete examples from OneRY field probe data where BP allows for the identification of stray energy which was previously difficult to find. We also show how the BP optimization context can be using to remove contamination from the data through the inclusion of additional basis functions ([3]). I.J. Gupta, E.K. Walton, W.D. Burnside, “Time and Direction of Arrival Estimation of Stray Signals in a RCS/Antenna Range,” Proc. of 18th Annual Meeting of the Antenna Measurement Techniques Association (AMTA '96), Seattle WA, September 30-October 3, 1996, pp. 411-416. I.J. Gupta, T.D. Moore, “Time Domain Processing of Range Probe Data for Stray Signal Analysis,” Proc. of 21st Annual Meeting of the Antenna Measurement Techniques Association (AMTA '99), Monterey Bay CA, October 4-8, 1999, pp. 213-218. B.E. Fischer, I.J. LaHaie, M.H. Hawks, T. Conn, “On the use of Basis Pursuit and a Forward Operator Dictionary to Separate Specific Background Types from Target RCS Data,” Proc. of 36th Annual Meeting of the Antenna Measurement Techniques Association (AMTA '14), Tucson AZ, October 12-17, 2014, pp. 85-90.

RCS Measurements and Imaging on Arrays of Retro-reflectors
Pax Wei, October 2017

For features of very weak scattering while masked by background and clutter, care must be taken in the measurement design as well as data processing, in order to extract the true RCS values. A good example of flush-mounted fasteners for a low-observable (LO) aircraft, arranged in an array, was reported by Lutz, Mensa, and Vaccaro [1]. In the Boeing 9-77 range, retro-reflectors (called retros) were routinely taped on a test-body for monitoring its 3-D locations and angles during measurements. Though the retro’s RCS may be several orders below that of a test-body, a challenge was to discover their exact values. In the millimeter wave range (MMWR), we measured 2-D arrays of retros arranged in both square and hexagonal lattices taped onto a flat metal surface pitched 20o down. RCS measurements were made as a function of frequency and aspect angle. From the 2-D FFT images, the nominal RCS for a retro in VV polarization was found to be -75 dBsm, independent of the geometry and number of retros even down to one unit-cell [2]. But for the HH polarization, there is no backscattering from such a flat metal surface. References [1]. J. Lutz, D. Mensa, and K. Vaccaro, "RCS measurements of LO features on a test body," Proc. 21st AMTA, pp. 320-325 (1999). [2]. P. S. P. Wei and J. P. Rupp, " RCS measurements on arrays of weak scatterers enhanced by diffraction," Proc. 26th AMTA, pp. 263-268 (2004). ---------------------------------------------- ** Sam Wei is at: 4123 - 205th Ave. SE, Sammamish, WA 98075-9600. Email: paxwei3@gmail.com, Tel. (425) 392-0175

An RCS-based Wall-reflectivity Technique - The First On-site Test Results
Amin Enayati, Joachim Wesemael, October 2017

Among different measurement techniques for the wall reflectivity, an RCS_based technique has been implemented and test results are reported. For most of the anechoic chambers, the factory acceptance test and a quality-control check is sufficient for the customers to be sure that the absorbers used to line their chamber are good enough. In some cases, a quiet-zone reflectivity measurement will certify that the chamber yields the quietness as needed for the specific application of the customer. This last technique is mostly used in the far-filed ranges. However, in some anechoic chambers, e. g. some compact ranges, the customer wants to know the effect of the installation and the shipment on the final absorber installed in the room. That is why, they ask for a wall reflectivity measurement to see the reflectivity of the absorbers after being installed. The main problem to be solved when talking about wall reflectivity is the un-wanted clutter in the room which needs to be compensated for. Last year at AMTA 2016, we have introduced a clutter-removal technique to reduce the unwanted shattering levels. That was supported by some lab implementations and accordingly some limitations in the implementation. This paper, explains the result of the first practical on-site test done in an anechoic chamber. Many different points in the chamber have been tested and a detailed discussion of the results are brought to view.

Analysis of Near-Field RCS Behavior for mm-Wave Automotive Radar Testing Procedures
Domenic Belgiovane, Chi-Chih Chen, October 2017

Millimeter wave vehicular radar operating in the 77 GHz band for automatic emergency breaking (AEB) applications in detecting vehicles, pedestrians, and bicyclists, test data has shown that the radar cross section (RCS) of a target decreases significantly with distance at short range distances typically measured by automotive radar systems, where the reliable detection is most critical. Some attribute this reduction to a reducing illumination spot size from the antenna beam pattern. Another theory points to the spherical phase front due to measurement in the Fresnel region of the target, when the distance for the far-field zone is not met. The illumination of the target depends on the antenna patterns of the radar, whereas the Fresnel region effects depend on the target geometry and size. Due to fluctuations in measured data for RCS as a function of range in the near-field, upper and lower bounds for the target RCS versus range have been determined empirically as a method for describing the expected RCS of target. So far, the range-dependent RCS bounds used in AEB test protocols have been determined empirically. The study discussed in this paper aims to study the underlying physics that produces range-dependent RCS in near field and provide analytical model of such behavior. The resultant analytical model can then be used to objectively determine the RCS upper and lower bounds according to the radar system parameters such as antenna patterns and height. A comparison of the analytically predicted model and empirical near-field RCS as a function of range data will be presented for pedestrian, bicyclist, and vehicle targets.

Additive manufacturing metallic sphere as a RCS measurement standard
Pierre Massaloux, October 2017

RCS measurements are usually performed in 3 steps in an anechoic chamber. First, the reflectivity of the target is measured. Then a reference measurement (generally without the target) is performed. Finally, a calibration standard of known RCS is used as a reference target. The main goal of the calibration phase is to transform raw measurements of reflectivity (S11 parameter in dB) into RCS (in dBsm) through the determination of the inverse transfer function of the entire RCS measurement layout. This calibration process indirectly converts the received electric field into a complex scattering coefficient. Moreover, it establishes a phase reference relatively to the rotation center of the target positioning system. The most frequently used standards are metallic spheres which have advantageous characteristics: monostatic RCS is well known by Mie-Series and independent of azimuth and elevation. However, manufacturing a perfect metallic lightweight sphere using conventional techniques include many issues that can generate defects in the spherical shape. The purpose of this paper is to evaluate the geometric and RCS performances of metallic spheres obtained from metal additive manufacturing systems using Selective Laser Melting (SLM) solutions. SLM is a fast prototyping technique designed to melt and fuse metallic powders together. On the one hand, these metallic spheres were checked by a 3D scanner in order to quantify the potential shape defects and on the other hand, RCS measurements were performed in an anechoic chamber. All these results will be presented in the final paper and compared with theoretical RCS data.

Advances in SAR-ISAR Blending
Christer Larsson, Johan Jersblad, October 2017

Radar signature measurements of targets with or without camouflage in different backgrounds using airborne SAR is complicated and expensive. Measurements at many orientations as well as illumination angles have to be performed for each target for completeness. A more efficient solution is to use ground based ISAR measurements of the desired targets and then blend these images into measured SAR scenes. We are developing a SAR-ISAR blending method where the target and background are modelled by point scatterer representations. This can be formulated as an inverse problem described by the equation Ax = y, (1) where A is a forward operator describing the model, x is the image and y is the measured RCS data. The point scatterer representations for the target and the SAR background are determined by solving (1). The main contribution of this paper is that we use a combination of L1 and L2 regularization methods to solve the inverse problem. The target measured by ISAR is sparse in the image domain and (1) is therefore solved efficiently using a L1 regularization method. However, the SAR background is not sparse in the image domain and (1) is therefore solved using a L2 regularization method. We use the following procedure: Define the operators A and At, where At is the conjugate transpose of A. The same operators are used for both the target and the background. Solve (1) using L1 regularization for the target measured using ISAR. Edit the target point scatterers so that only target related scatterers are included. Solve (1) using L2 regularization for the SAR background. Edit the background point scatterers by removing the shadowed region, alternatively attenuate if there is a camouflage net. Combine the edited point scatterers for the target and background and calculate the RCS for the combination. Add estimated system noise. Create a blended SAR-image. The method is demonstrated with ISAR measurements of a full-scale target, with and without camouflage, signature extraction and blending into a SAR background. We find that the method provides an efficient way of evaluating measured target signatures in measured backgrounds.

On the Disadvantages of Tilting the Receive End-Wall of a Compact Range for RCS Measurements
Vince Rodriguez, October 2017

Abstract— Tilting the receive end wall of a compact range anechoic chamber to improve Radar Cross-Section (RCS) measurements has been a tool of the trade used since the earliest days of anechoic chambers. A preliminary analysis using geometrical optics (GO) validates this technique. The GO approach however ignores the backscattering modes from the reflected waves from a field of absorber. In this paper, a series of numerical experiments are performed comparing a straight wall and a tilted wall to show the effects on both the quiet zone and the energy reflected back towards the source antenna. Two Absorber covered walls are simulated. Both walls are illuminated with a standard gain horn (SGH). The effects of a wall tilted back 20° are computed. The simulations are done for 72-inch long absorber for the frequency range covering from 500 MHz to 1 GHz. The ripple on a 10 ft (3.05 m) quiet zone (QZ) is measured for the vertical wall and the tilted wall. In addition to the QZ analysis a time-domain analysis is performed. The reflected pulse at the excitation antenna is compared for the two back wall configurations Results show that tilting the wall improves measurements at some frequencies but causes a higher return at other frequencies; indicating this method does not provide a broadband advantage. Keywords: Anechoic Chamber Design, Radar Cross Section Measurements, Geometrical Optics

Automating RCS Measurements for High Speed Production Line In-Process Verification
Roger Richardson, Brett Haisty, October 2017

In June of this year, DSC completed the installation of a turnkey RCS measurement system that is used for in-process verification (IPV) and final component validation using standard near field QC techniques in an echoic chamber. The delivered system included a radar, antennas, shroud, ogive pylon, foam column, elevators for each – column and pylon, automated pit covers, test bodies, target transport carts, and calibration targets. The system automatically loads test objects on the correct target support system, requiring no action by the operator to connect a target onto the azimuth over elevation “tophat” positioner – it is all automatic. The user interface is designed to be operated by production line workers, greatly reducing the need for experienced RCS test engineers. Simple pass/fail indicators are shown to the test technicians, while a full detailed data set is stored for engineering review and analysis. A wall display guides users through a test sequence for target handling and starting the radar. Radar data collection of all azimuth and elevation angles and target motion are initiated from a single button push. This is followed by all data processing necessary to conduct the ATP on the parts providing a pass/fail report on dozens of parameters. The application of production line quality automation to RCS measurements improves the repeatability of the measurements, greatly reduces both measurement time as well as overhead time, and allows systems operators to become more interchangeable. This highly successful project, which was completed on-time and on-budget, will be discussed. This discussion will include radar performance, antenna and shroud design, target handling, data processing and analysis software, and the control system that automates all the functions that are required for RCS measurements.

A Radar Echo Emulator for the Evaluation of Automotive Radar Sensors
Domenic Belgiovane, Chi-Chih Chen, J. Landon Garry, November 2016

Automatic emergency braking (AEB) and collision imminent braking are beginning to be implemented by major automotive manufactures. AEB systems utilize automotive radar sensors operating in the 77 GHz frequency band for target detection. These said systems are capable of providing warning directly to the vehicle driver and when necessary apply automatic emergency braking. The effectiveness of such systems need to be accurately tested using standards and test procedures that are yet to be agreed upon among international automobile industry and government agencies. The Euro NCAP vehicle target (EVT) is the current European standard for AEB testing scenarios. The main goal of this research effort was developing a compact W-band radar echo emulator (REE) to be used for evaluating automotive pre-collision systems (PCS) operating in the 77 GHz frequency band. The proposed REE is capable of receiving radar signals from the PCS radar mounted on the vehicle under test (VUT) and then transmits modified radar signals back to PCS radar bearing the similar signatures (temporal, spectral, and pattern) as the Euro NCAP Vehicle Target (EVT). REE eliminates the need for the front vehicle target to produce radar responses which is currently accomplished with complicated arrangement of RF absorbers and reflectors as in the EVT and other vehicle surrogates. The adoption of REE means that the vehicle target only needs to bear optical signatures similar to an actual vehicle, and thus can be made with a much simpler balloon structure. Measurements present for the characterization of the Euro NCAP EVT over distance as well as the calibrated radar cross section (RCS). From this simply target model the REE echo power is empirically determined. The REE solution to PCS testing scenarios offers an easily adaptable return power various targets can be emulated with a single module.







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