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To verify the proper working of a Reconfigurable Intelligent Surface (RIS), similar to antenna radiation patterns, the RIS reflection pattern has been established as key performance indicator. To overcome the necessity of a bistatic RIS qualification setup, where two antennas at different positions are used, this paper presents a novel measurement approach to obtain the RIS reflection pattern based on a monostatic indirect Far-Field (FF) Compact Antenna Test Range (CATR) setup. Due to the monostatic principle, only one antenna, which is used for transmission and reception, is required. Subsequently, the mono- static reflection patterns are transformed into bistatic reflection patterns by applying different Monostatic to Bistatic Equivalence Theorems (MBETs) known from radar-cross-section theory. With that, the required setup can be simplified in terms of mechanical complexity, setup footprint and the number of measurement scenarios, since incident and reflection angle correspond in the monostatic case. This paper analyzes three different MBETs, namely Kell, Crispin/Siegel and Falconer, with respect to their suitability for RIS reflection pattern measurements. Moreover, a monostatic CATR test environment is presented and two metal plate based RIS calibration approaches are introduced. This novel monostatic RIS measurement approach is validated with simulation and measurement data of two mmWave fixed beam RISs. Both of them are reflecting an impinging signal from broadside (θ = 0°) direction into 47° at a center frequency of 27GHz. The results prove the suitability of this approach.
Tapered anechoic ranges were introduced in the late 1960s. Since their introduction tapered anechoic chambers have become popular tools for the measurement of antenna patterns at frequencies under 1 GHz. Dating back to their first installations, several papers mention the fact that these chambers did not have a spherical wave propagation and thus, the Friis transmission equation to measure gain cannot be applied [1,2]. The array factor theory of taper chambers presented in [3] states that from the point of view of the antenna in the QZ the tapered chamber appears to be a free space environment. The phase behavior across the QZ, reported in [4] appears to agree with the theory since the phase distribution follows the far field equation. In this paper simulations for a dipole and a biconical antenna are performed that suggest that the array factor theory for the tapered ranges while not perfect provides an approximated explanation for their operation. The simulations confirm the measurements done in [2] and additionally show that at some discrete frequencies the propagation in the tapered range does follow closely the free space attenuation.
This paper extends the authors prior studies to develop a more flexible definition for the shape of a blended rolled edge compact antenna test range (CATR). This is accomplished by utilising a more sophisticated definition for the junction contour. This definition ensures the reflector surface is smooth and provides additional parameters that can be used to optimise the performance of the CATR enabling wall illumination and quiet-zone performance to be managed and balanced. As with the authors prior work, a novel, parallel, physical optics based, genetic optimisation is performed that, over subsequent generations, breeds optimal designs for each test case selecting the preferred design from many thousands of potential mutated candidates. Results are presented and discussed for several CATR designs that illustrate the concept and achievable performance highlighting the utility of a hybrid serrated blended rolled edge CATR reflector.
A low-cost, custom radar cross-section (RCS) range is designed and built to measure the RCS of wideband linear and circular retrodirective arrays over a ground plane and good accuracy over 1-4 GHz is demonstrated. The only test equipment needed is a vector network analyzer (VNA). The 3.66 m × 1.22 m ground plane is constructed from a thin aluminum foil covering a frame constructed out of plywood and foam panels with wideband probe and wideband arrays inset into the ground plane. Excellent agreement with theoretical and simulated results is demonstrated. Additionally, the measurements validate a previously proposed method for the synthesis of the antenna component of the RCS using only the scattering parameters and embedded element patterns. Extension of this synthesis method into the measurements for the case when no beamforming network is available is demonstrated as well. Time-domain RCS measurements also agree well with theoretical and simulated data, which are used to illustrate the physics of linear Van Atta arrays.
The size and optics of a Compact Antenna Test Range (CATR) determine its quiet zone and the lowest frequency at which it will meet nominal quiet zone specifications. If a reflector is not large enough to present a sufficient multi-wavelength surface at a given frequency, a plane wave is not generated. Operating compact ranges at lower and lower frequencies is a continuing desire in the measurement community. The normal solution for both instances is to increase the reflector size. This leads to larger test chambers, hence increasing cost. Collecting spherical near- field (SNF) data in a CATR within its normal operating frequency band is well known. However, this leads to collecting more data than required to obtain principal plane cuts in the CATR. This paper presents a study and empirical data on using low-frequency range antennas that operate down to one half the nominal CATR low frequency using SNF techniques to measure test articles at these frequencies with relative accuracy. The paper includes simulations of the quiet zone performance at low frequencies.
As the demand for efficient and accurate characterization of mmWave antennas grows, compact antenna test ranges (CATRs) have become preferred alternatives to traditional far-field ranges due to their smaller size requirements. CATRs transform spherical waves into planar waves at short distances using a parabolic reflector. The quality of the CATR’s quiet zone depends on minimizing edge diffractions caused by fields reflecting off the reflector’s rim. Techniques like serrated and blended rolled edges are used to reduce these diffractions. While blended edges perform better, serrated edges are more commonly used due to their ease of manufacturing and lower cost. To enhance the convenience, affordability, and performance of CATRs, this work introduces a 3D-printed blended edge reflector for a Ka-band system. Manufactured on a desktop 3D printer, this high-performing reflector shows promising results. Additionally, a surface roughness analysis of CATR reflectors quantifies the impact of surface roughness on the purity of plane waves in the quiet zone across various frequencies. Measurement results from the additive manufactured reflector align with TICRA GRASP simulations. This work aims to improve efficiency and accuracy in mmWave and sub-terahertz frequency measurements, which require high precision in antenna characterization.
Non-terrestrial networks (NTNs), including satellites, high-altitude platforms (HAPS), and unmanned aerial vehicles (UAVs), operate above the Earth’s surface. Along with ground base stations, they often require the implementation of beamforming and beam tracking techniques to achieve high-speed, low-latency transmission, thereby ensuring seamless coverage. Consequently, diagnosing the functionality of the radio units (RUs) in those network devices and verifying their beamforming patterns are critical for the effective applications of this technology. This paper presents the 3D far-field pattern measurements and calibrations of the RF carrier EIRP levels for millimeter-wave beamforming testing suites that emulate RU operations. This is achieved using a combination of the planar near-field (PNF) and compact antenna test range (CATR) measurement systems at Taiwan Tech. A side-deployed PNF scanner is used in over-the-air (OTA) scan mode for 3D antenna pattern measurement and aperture diagnosis of the RU devices in transmit mode, utilizing controlled scan beams of single-tone and modulated RF carriers. Additionally, a compact range (CR) mode is employed to calibrate the RF EIRP in the peak direction of each RU-scanned beam. Beamforming patterns obtained from the near-field measurements in the OTA scan mode demonstrate good agreements with conventional near-field tests and show reliable EIRP values at 28 GHz for 5G FR2 radio units.
The RCS of a target can be estimated using electromagnetic modeling if accurate geometries and material descriptions are available. An exact numerical calculation often requires prohibitive processing times. Moreover, numerical predictions with approximate techniques are difficult as it is challenging to consider all the physical phenomena. Therefore, a suitable RCS measurement facility adapted to the target size and specifications is required to estimate the RCS of a given target and to validate the numerical predictions. In general, the measurement of RCS takes place in anechoic chambers that simulate free-space and far-field conditions and where the unwanted reflections (walls, target mount, objects in the range, and the target interactions) are reduced. This paper presents a broadband measurement and validation of the RCS of a metallic trihedral corner reflector of 30 cm sides when fully anechoic conditions are not available, and consequently, some undesirable echoes are present in the measurements. Firstly, the measurement facility calibration and the target calibration are outlined. A single target reference approach is performed using a sphere as a reference, and its scattering response is shortly described. Then, the measurement of the target is performed. After these steps, a processing procedure is applied to isolate the target response from the background and the close responses due to unwanted reflections. The post-processing technique and the acquisition system are presented and discussed. The measurements are performed at X band as a function of the viewing angle for vertical transmit and receive polarization. To validate the technique, the RCS of the trihedral corner reflector is numerically simulated using the Integral Solver (I-Solver) of CST, with a Gaussian excitation, for vertical transmit and receive polarization. Measurements are compared with results obtained from CST software and show a good agreement with the numerical simulations. This setup will be used for RCS measurement of different complex targets and compared with measurements from other facilities to analyze and evaluate the RCS measurement uncertainty.
5G communications have supported the deployment of millimeter-wave beam-steering technologies at an unprecedented commercial scale. Mobile phones operating in frequency ranges above 20 GHz integrate antenna arrays and radiofrequency front-ends which control magnitudes and phases of signals to enable adaptive beam-steering. As per the 3GPP Test Specifications, a large number of tests covering the various operational modes of such devices are required in order to establish that the performance is adequate for guaranteeing the integrity of the mobile network. The defined measurement methodology relies on Over-The-Air (OTA) evaluations in Compact Antenna Test Ranges (CATR). As mobile wireless user equipment are practically utilized in diverse environmental conditions, a part of the test plan imposes spherical OTA measurements at extreme temperature conditions ranging from -10 to +55° C. Such temperatures indeed influence the active electronics in the device under test (DUT) and hence the beam-forming performance. This paper presents an innovative realization of a CATR with embedded thermal chamber supporting the above-described test capabilities. Inventive steps are introduced to solve the complex engineering problem of allowing fast temperature ramps to go through the complete range in a few minutes, while allowing two-axis rotations of the DUT, and all of this with preventing damages from the anechoic chamber and positioner and limiting the radiofrequency impact of the thermal testing chain. Thermal and air flow simulation and measurement results are presented, establishing how the design allows sustaining high pressure with low air leakage. Measurements of the quality of quiet zone with and without thermal enclosure demonstrate the limited RF impact of the introduced materials encapsulating the DUT. The derived solution is applied to measurements of a commercial 5G mobile phone, illustrating the influence of the environment on the DUT operation and corroborating the need for such test scenarii.
Over the past decades, near-field (NF) measurements have been established as a reliable alternative to direct far-field (FF) or compact-range measurements for the verification of radiation properties of antennas. Quantities of interest typically include the FF characteristic obtained by means of an NF FF transformation (NFFFT), which is a computational post-processing step applied to the NF data. Common NFFFTs work with time-harmonic data and require the acquisition of magnitudes and phases of the NF samples with respect to a common reference signal. In other words, classical NFFFTs require the observed magnitude and the observed phase data to be drift-free during the time span of the complete measurement. With increasing measurement frequency and exposed or complex measurement setups in uncontrollable environments, e.g., as encountered in outdoor NF antenna measurements with unmanned aerial vehicles (UAVs), phase stability quickly becomes a limiting factor. Therefore, nonlinear phaseless NFFFTs have been developed that do not require any phase information, which, however, heavily rely on accurate and globally consistent magnitude information and are notorious for their unreliable behavior. Recently, a linearized and reliable NFFFT operating on locally consistent, i.e., relative, phase information has been reported. By using local phase differences within the NF data, the method becomes immune to phase drifts of the reference signal. However, in real-world measurements in uncontrolled environments, drifts in the measured power or magnitude may occur as well, e.g., caused by temperature variations during UAV flights, which render common phaseless NFFFTs useless. In particular, this prevents the use of the otherwise reliable linearized transformation. We investigate NFFFTs requiring a variable degree of global synchronization. In particular, a linearized transformation utilizing only relative, i.e., locally synchronized, information, both in magnitude and phase, is presented. It is shown that the transformation yields similarly accurate results as transformations employing global data, while being immune to magnitude and phase drifts. Furthermore, we compare the overall benignancy of a complete set of retrieval problems: completely phaseless, magnitudeless and mixed relative/global magnitudes and phases. Transformation results for simulation data illustrate the accuracy and suitability of the transformations with relative data, even for electrically large problems.
Progressing towards highly automated vehicles, radar systems have been developed into reliable assistance systems of environmental perception for a wide spectrum of mobile applications in air, on sea and rails, and especially on roads. This success as well as further improvements necessitate the precise characterization of radar objects with radar cross-section (RCS) measurements throughout the manifold parameter space, including frequency, aspect angles or even illumination and observation angles in bi-static radar constellations. According to the IEEE RCS standard 1502-2020, parasitic effects from ground reflections have to be taken into account in the test setup in almost all RCS measurement systems. In ground-plane ranges, multipath signal propagation is even considered intentionally. In this paper, the influence of ground reflections on bi-static radar measurements has been investigated both analytically and experimentally. A geometry-based analytical model was applied to calculate interference and the resulting small-scale fading of the electric field strength at the receiver. The geometry consists of independently arranged transmitter, receiver, and scatterer. The model includes antenna crosstalk, ground reflections for different relative heights of transmitter and receiver, and the scattered signal contributions. As a result, six paths are considered in terms of their time delays and phases, resulting from the classical two-way propagation model in a point-to-point link plus the four-way radar propagation model including ground reflections. The model yields interference gains between 0 and 4, where the maximum value is uniquely obtained at equal distances between transmitter and scatterer, and between scatterer and receiver, respectively. The variations of the bi-static angle lead to further fluctuations, which confirm to expectation and will be described in the full paper. The analytical model was validated with bi-static radar measurements in a semi-anechoic chamber with a metallic ground floor. As a canonical radar target, a metal sphere was measured in the frequency range between 1GHz and 10GHz at different heights and distances. The measurement results confirm the analytical model and provide the basis for further extensions of practical relevance, e.g., the reflectivity parameters of the ground (e.g., dry and wet road surfaces). Funded by: Federal Ministry of Education and Research (BMBF), grant number 16ME0164K
The near-to-far-field transformation (NTFFT) technique adopting the plane-rectangular (PR) scanning is the most simple one from the analytical and computational points of view and can be suitably employed when characterizing antennas which exhibit pencil beam radiation patterns. In recent years, NTFFTs using the nonconventional planar wide-mesh scanning (PWMS) have been developed. They allow a remarkable measurement time saving with respect to that adopting the classical PR scanning, since their raster grid is characterized by meshes which become larger and larger as their distance from the scanning plane center increases. These NTFFTs have been obtained by applying the non-redundant sampling representations of the electromagnetic fields to the voltage detected by the scanning probe and adopting suitable AUT modellings for volumetric and quasi-planar AUTs. The evaluation of the AUT far field is then got by applying the PR NTFFT, whose input data are accurately recovered through optimal sampling interpolation expansions from the collected PWMS samples. In both the conventional and non-conventional scannings, the sampling points are reached through an x-y scanner. However, the finite resolution of the probe positioners and/or their imprecise control can prevent to exactly collect the near-field samples at the prescribed sampling points and imperfections in the mechanical rails driving the motion of the probe can cause a deviation from the considered measurement plane. Accordingly, 3-D positioning errors, which can be revealed via laser interferometric techniques, affect the acquisition. The aim of this work is to develop an effective NTFFT with PWMS from 3-D probe positioning error affected near-field measurements. To this end, the so named k-correction (Joy and Wilson, AMTA Proceedings 1982) will be used to compensate the positioning error related to the deviation from the considered measurement plane. Then, an iterative procedure (D’Agostino et al., International Journal of Electronics and Communications 2020) will be applied to retrieve the near-field samples at the points specified by the non-redundant sampling representation from those obtained at the previous step and affected by 2-D positioning errors. Numerical tests will show the capability of the procedure to fully compensate the 3-D positioning errors affecting the acquisition of the PWMS samples.
With the growing of vehicular communication technologies, the need for performing radiated measurements accounting for the full vehicle is becoming increasingly important. In modern cars, antennas are an integral part of the vehicle which is too complex to be represented by a simple ground plane during the tests. 5GAA test report [1] unifies measurement procedures for vehicle mounted antennas for both passive (at the antenna level) and Over-the-Air (OTA - at the modem level) measurements. Both Far-Field (FF) and Near-Field (NF) measurement systems are considered for testing of the full vehicle. In NF systems the radiated signals are measured on a closed surface at reduced distance, and a NF-to-FF transformation is applied. Since the transformation requires phase coherence between the transmitter and the receiver, NF systems are suited for passive tests. On the other hand, FF ranges are more suited for OTA tests, but requires large measurements distances, and hence expensive testing environments. OTA testing at reduced distances offers several advantage including the possibility to consider smaller and cost-effective anechoic chambers and the reduction of the system path losses (improved dynamic range). Moreover, the use of multi-probe systems dramatically reduces the testing time. The possibility of performing automotive OTA tests in spherical multiprobe systems at a reduced distance will be investigated in this paper. Simulations of a realistic vehicle with antennas installed in different locations will be considered to assess the uncertainty introduced by the reduced measurement distance. Figure of merits like different partial radiated powers [1] will be considered. Experimental automotive OTA measurements of a monopole-like antenna, installed on the roof of a vehicle will also be presented. These measurements have been performed at LTE bands in a spherical multiprobe system with a 4m radius. The measurements will be analysed comparing direct OTA measurement with a two-stage method, where passive antenna measurements and a few sampled OTA measurement points are combined. The outcome of the simulated analysis and experimental tests will be used to preliminary assess the uncertainty of automotive OTA measurements at reduced distance considering metrics relevant to automotive technologies [1].
Measurements of modern multi-service antenna systems require ever increasing bandwidths of the measurement equipment. The main bandwidth limiting factor of traditional Spherical Near Field (SNF) systems is mainly the probe as it should radiate only first-order azimuthal spherical modes to apply the first-order Probe Compensation (PC). Even though full PC techniques are becoming standard, enabling the use wideband antennas with more than 10:1 bandwidth as probes, high-purity first-order probes are still required in many applications, because of the simplification of data processing and calibration. Conventional dual-polarized first-order probes are based on Ortho-Mode Junctions (OMJ) with externally balanced feeding. The OMJ is fully symmetrical using two pairs of excitation pins fed by high precision 3dB, 0º/180º hybrid couplers to achieve good matching and maximize the cx-polar performance. Unfortunately, realistic couplers provide some excitation errors which are one of the main contributors of the generation of unwanted higher order spherical modes. Even a small unbalancing in amplitude or phase of the coupler will excite higher order modes at frequencies where these modes are allowed to propagate. Beside the possibility to compensate the effect of the higher-order modes in post-processing (e.g. full PC), the propagation of the spurious spherical modes can be controlled directly on the probe with improved designs of the feeding mechanism or considering ad-hoc designed hybrid couplers. In this paper, two innovative and high performance SNF probes will be presented. Both probes are based on an inverted quad-ridge waveguide technology. An advanced feeding mechanism allows the first probe to provide a high modal purity in the 617-960 MHz band, rejecting errors introduced by the external coupler. In the second one, a highly accurate coupler has been designed to minimize the higher order modes on a large bandwidth, 1427-4200 MHz. The two probes have been designed as part of the upgrade of a gantry arm system used to test modern base station antennas. The same measurement system has been used to calibrate the two probes and to verify the expected performance both in terms of radiation pattern and spherical modal content. The achieved measurement results will be shown in this paper.
The Field Strength Metrology Project at the National Institute of Standards and Technology (NIST) in Boulder, CO has restarted field probe calibration services from 10 kHz to 40 GHz, after a renovation of ouranechoic chamber. WhileNISThas long served as the nation’s link to the SI for radiated field measurements, in 2014, the anechoic chamber used for generating standard electromagnetic fields from 0.5 – 40 GHz was renovated. The positioning system was upgraded with a new rail, motion control, and a robotic arm. New absorber was installed in the main section of the chamber. During the renovation, Field Strength services were unavailable. In order to resume operation in the chamber, several tests were done to validate the chamber. We show the results of a thorough comparison of three facilities, the anechoic chamber, a TEM cell and a GTEM cell. Measurements of electric field probes in the new chamber were also compared with past measurements in the chamber before renovation. The Electromagnetic Field Strength special test services are now operational.
This paper is an extension of a 2020 AMTA paper [1] in which we simulated (with added noise) an older, and seemingly forgotten, technique for processing three-antenna polarization data that employs well known signal processing methods. In this paper we analyze actual measured data. Topics to be explored include: (1) Time-domain gating to mitigate antenna-antenna multiple reflection and room-reflection error signals, (2) Bi-directional S-parameter measurements, (3) a scheme [2] (based on the geometric mean of the S-parameters S_pq and S_qp) to mitigate calibration drift errors, (4) Fourier filtering. We plan to demonstrate a robust method that is effective and easy to implement. [1] R. C. Wittmann and M. H. Francis, "Three Antenna Polarization Measurement Revisited," Proc. AMTA, Virtual, pp. 3–6, Nov. 2–5, 2020. [2] D. R. Novotny, A. J. Yuffa, R. C. Wittmann, M. H. Francis, and J. A. Gordon, "Some advantages of using bi-directional s-parameters in near-field measurements," Proc. AMTA, Williamsburg, VA, pp. 327–332, Nov. 4–9, 2018.
Abstract. In order to characterize the Boeing 9-77 compact range, the empty chamber background was measured as a function of frequency, polarization, and the azimuth angle of the upper turn-table (UTT). The results exhibited a diffraction pattern with enlarged hot-spots on a 4-fold symmetry [1]. A 2-D FFT on the diffraction pattern yielded a mapping on the relative arrangement of the very weak absorber tips on the UTT [2]. Here, we take a closer look at the scattering geometry of the UTT as illuminated by the residual field above and beyond the quiet zone (QZ). The different responses in VV and HH are discussed. The enhanced diffraction due to a “blazed grating” condition is identified and analyzed. Some interesting physics are discussed. An extended long object usually gives rise to a strong reflection (glint) when viewed near its surface normal. To take advantage of this phenomenon, a discrete Fourier transform (DFT) on RCS measurements taken within a small angular range would yield a spectrum of incident wave distribution along that object [3]. Some results along the horizontal direction have been reported [4]. As a complementary, we present and discuss the results in the vertical direction. References [1]. P. S. P. Wei, A. W. Reed, and C. N. Ericksen, “Radar cross section measurements amid interfering backgrounds,” Proc. 22nd AMTA, pp. 99-104 (2000). [2]. P. S. P. Wei, “Scattering of the residual field above and beyond the quiet zone of a compact range,” Proc. 35th AMTA, Columbus, OH (2013). [3]. P. S. P. Wei, “Measurements on long and rigid objects for radar field probes" Proc. 34th AMTA, pp. 195-200 (2012); Also in ACES Journal 28, 1228-1235 (2013). [4]. P. S. P. Wei, “Measurements on extended objects for radar field probes," Proc. 41st AMTA, pp. 199-204 (2019); Also presented at ICECOM-2019 (23rd International Conf. on Applied Electromagnetics & Communications), paper S_16_3, Dubrovnik, Croatia, Sept. 30, 2019.
Electromagnetic materials characterization at UHF and VHF frequencies is typically done with laboratory fixtures such as the coaxial airline or rectangular waveguide. These conventional methods require material specimens to be cut or machined to precision tolerances for insertion within the transmission line fixture. Measurement accuracy dictates there should be little or no air gaps between the specimen and the transmission line walls. Transmission line methods also require significant handling and multi-step calibration procedures to characterize a material specimen. This paper describes a new handheld measurement device that overcomes these limitations with a simple calibration and non-destructive measurement procedures. This new method applies an open-ended stripline sensor tuned to maximize measurement sensitivity in the 100 to 1000 MHz range. The sensor footprint is approximately 100 mm square and utilizes an integrated one-port vector network analyzer. It operates by measuring the amplitude and phase of the reflection coefficient when placed adjacent to a material specimen. While traditional transmission line methods employ analytical expressions to relate scattering parameters to intrinsic properties, The open-ended stripline sensor geometry and its interaction with the material cannot be easily modeled with an analytical approximation. Instead, it is modeled with a full-wave Finite Difference Time Domain (FDTD) code to develop the relationship between measured reflection and complex permittivity. This inversion method precomputes a translation table by iteratively modeling the measurement fixture across a range of complex permittivities and specimen thicknesses. From this inversion database, interpolation is then used to calculate the frequency dependent complex permittivity or sheet impedance of a given specimen. This paper provides details about the calibration and use of this new device as well as the material property inversion algorithm. Measurement examples of low-loss and lossy materials as well as resistive sheets are also presented and compared to more conventional transmission line results, and are discussed in relationship to measurement uncertainties.
Modern design of phased array apertures typically begins with unit-cell design relying on an extensive use of full-wave simulations. The waveguide simulator is an equivalent, experimental simulator that allows for measurement of the active impedance of radiating elements at a prescribed pair {frequency, scan angle} in an infinite array environment. Therefore, the waveguide simulator offers a means of real-world verification of a unit-cell design before proceeding with finite array design or realization. In its simplest form, the waveguide simulator is constructed through placing an element within the walls of a rectangular waveguide. The natural imaging of the waveguide walls acts to emulates an infinite array environment. The multielement waveguide simulator described first by Gustincic (J. J. Gustincic, IEEE Trans. Antennas Propagat., vol. 20, no. 5, pp. 589–595, 1972), allows for experimental determination of the active reflection coefficient of an embedded array element for a discrete set of scan conditions corresponding to a given waveguide mode excitation. Though the theory behind the waveguide simulator is well documented in the literature, there is scant discussion of the effect of configuration on the number of and distribution of valid scan pairs. The number of valid scan pairs is proportional to the number of modes that are excited within a waveguide, which is set by the element spacing and size of the waveguide. It is desirable, for a given number of elements constituting a waveguide simulator, to maximize the number of valid scan pairs and simultaneously the information content that can be obtained from a single experimental setup. The number of valid modes for a square waveguide with half-wavelength element spacing is found to reduce to the well known Gauss circle problem. For the general case in which the element spacings are arbitrary and the waveguide is rectangular the problem is reduced to Hardy’s generalization of the Gauss circle problem (G. H. Hardy, Proceedings of the Royal Society of London. vol. 107, (744), pp. 623-635, 1925). The herto unrecognized connection to an existing and widely developed mathematical theory gives insight into the fundamental sampling limitations of the waveguide simulator.
Diagnostic and verification testing of Low Observable (LO) platforms and components requires an Ultra-Wideband (UWB) Inverse Synthetic Aperture Radar (ISAR) imaging capability. A Compact Range (CR) is a test instrument that, when fitted with an instrumentation radar and target positioner, can efficiently produce ISAR images and other Radar Cross Section (RCS) data products required for LO research, design and production programs. Key limiting factors for the instantaneous radar imaging bandwidth of a CR is the feed antenna, where the criteria of a good feed is frequency bandwidth and illumination pattern shape. Maintaining a relatively constant reflector illumination characteristic typically requires several feeds with constant patterns functioning over smaller operating bandwidths, to be mechanically sequenced in the measurements. These feed limitations increase operational costs and complexity for LO measurements, driving a need for improved illumination sources providing constant reflector illumination for UWB collections. Focal Plane Arrays (FPAs) can be utilized to resolve these issues while increasing instantaneous bandwidth and measurement quality while reducing operational costs. This paper presents a procedure for defining complex weights of an FPA aperture to optimize radiation pattern matching to the reflector. A simulated plane wave arriving from the CR quiet-zone impinges on a model of the reflector. The FPA is placed in a region near the focal point and contained within the beam waist envelope, and the FPA weights are computed using a Computed Electromagnetic (CEM) techniques. The computational complexity of CEM simulations of electrically large CRs are usually prohibitive, however this method exploits the large focal lengths of CRs to sparsely model reflectors, and produces a tractable solution even at millimeter wavelengths. Practical aspects of FPA designs are presented and discussed as applied to the large outdoor CR at the US Army, Electronic Proving Ground (EPG), Fort Huachuca, Arizona.