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Experimental InSitu Antenna Array Calibration with Signals of Opportunity
We present experimental results for on platform (insitu) calibration of an antenna array with signals that are treated as signals of opportunity. Insitu calibration is required for antenna arrays installed on vehicles as platform scattering significantly perturbs the radiation patterns of the antenna elements. Insitu measurement of the array response requires: determining location of the unknown signals; determining the array’s response in the direction of the signals; and synthesizing the array pattern from the measured data. For this work, a seven element Lband antenna array was mounted on a generic aircraft platform. The platform was mounted on a dual rotator setup and emitters were placed nearby. The platform was then rotated while the emitters transmitted, and the signals received by the antenna elements were digitized. The collected data was then post processed to obtain the array calibration. We found that the calibrated array manifold enables more accurate direction of arrival estimation and provides additional gain in direction constrained beamforming. The present work serves as experimental verification of earlier simulation studies on insitu array calibration.
EarthFacing Antenna Characterization in Complex Ground Plane/Multipath Rich Environment
The Space Communications and Navigation (SCAN) Testbed was a Software Defined Radio (SDR)based payload launched to the International Space Station (ISS) in July of 2012. The purpose of the SCAN Testbed payload was to investigate the applicability of SDRs to NASA space missions in an operational space environment, which means that a proper model for system performance in said operational space environment is a necessary condition. The SCAN Testbed has lineofsight connections to various ground stations with its SBand Earthfacing NearEarth Network Low Gain Antenna (NENLGA). Any previous efforts to characterize the NENLGA proved difficult, therefore, the NASA Glenn Research Center built its own SBand ground station, which became operational in 2015, and has been successfully used to characterize the NENLGA’s insitu pattern measurements. This methodology allows for a more realistic characterization of the antenna performance, where the pattern oscillation induced by the complex ISS ground plane, as well as shadowing effects due to ISS structural blockage are included into the final performance model. This paper describes the challenges of characterizing an antenna pattern in this environment. It will also discuss the data processing, present the final antenna pattern measurements and derived model, as well as discuss various lessons learned.
CATR Quiet Zone Modelling and the Prediction of "Measured" Radiation Pattern Errors: Comparison using a Variety of Electromagnetic Simulation Methods
The singleoffset compact antenna test range (CATR) is a widely deployed technique for broadband characterization of electrically large antennas at reduced range lengths [1]. The nature of the curvature and position of the offset parabolic reflector as well as the edge geometry ensures that the resulting collimated field is comprised of a pseudo transverse electric and magnetic (TEM) wave. Thus, by projecting an image of the feed at infinity, the CATR synthesizes the type of wavefront that would be incident on the antenna under test (AUT) if it were located very much further away from the feed than is actually the case with the coupling of the planewave into the aperture of the AUT creating the classical measured “farfield” radiation pattern. The accuracy of a pattern measured using a CATR is primarily determined by the phase and amplitude quality of the pseudo planewave with this being restricted by two main factors: amplitude taper (which is imposed by the pattern of the feed), and reflector edge diffraction, which usually manifests as a high spatial frequency ripple in the pseudo plane wave [2]. It has therefore become customary to specify CATR performance in terms of amplitude taper, and amplitude & phase ripple of this wave over a volume of space, termed the quietzone (QZ). Unfortunately, in most cases it is not directly apparent how a given QZ performance specification will manifest itself on the resulting antenna pattern measurement. However, with the advent of powerful digital computers and highlyaccurate computational electromagnetic (CEM) models, it has now become possible to extend the CATR electromagnetic (EM) simulation to encompass the complete CATR AUT pattern measurement process thereby permitting quantifiable accuracies to be easily determined prior to actual measurement. As the accuracy of these models is paramount to both the design of the CATR and the subsequent determination of the uncertainty budget, this paper presents a quantitative accuracy evaluation of five different CEM simulations. We report results using methods of CATR modelling including: geometricaloptics with geometrical theory of diffraction [3], planewave spectrum [4], KirchhoffHuygens [4] and current element [3], before presenting results of their use in the antenna pattern measurement prediction for given CATRAUT combinations. REFERENCES [1]C.G. Parini, S.F. Gregson, J. McCormick, D. Janse van Rensburg “Theory and Practice of Modern Antenna Range Measurements”, IET Press, 2014, ISBN 9781849195607. [2]M. Philippakis, C.G. Parini, “Compact Antenna Range Performance Evaluation Uging Simulated Pattern Measurements”, IEE Proc. Microw. Antennas Propag., Vol. 143, No. 3, June 1996, pp. 200206. [3]G.L. James, “Geometrical Theory of Diffraction for Electromagnetic Waves”, 3rd Edition, IET Press, 2007, ISBN 9780863410628. [4]S.F. Gregson, J. McCormick, C.G. Parini, “Principles of Planar NearField Antenna Measurements”, IET Press, 2007.
Error of Antenna Phase Pattern Measured by NFTR and Correction Technique
Abstract Antenna far field phase pattern is important for some applications. It can be directly obtained in pattern measurement by far field test range (FFTR) or compact range (CR). However, it is found that the antenna far field phase pattern measured by current near field test range (NFTR) is not correct. For a uniform phase feeding plane array, its far field phase pattern should be near constant in 3dB beam width. However, the antenna phase pattern measured by current NFTR looks square curve vs angle. This paper found out that the root cause of the error is due to different reference planes. Both the amplitude pattern and the phase pattern obtained by current NFTR, in fact, refer to the probe scanner plane, not the antenna plane. This shifting of the reference plane has no effect on amplitude pattern, but has effect on phase pattern. After that, a correction method is proposed. One example is used for the root cause finding and correction technique explanation. According to this paper, if one wants to get phase pattern using NFTR, it is necessary to measure the distance between AUT and probe aperture accurately so as to correct it accurately after measurement and obtain accurate phase pattern.
Effect of Higher Order Modes in Standard Spherical NearField Probe Correction
Within the standard scheme for probecorrected spherical dataprocessing, it has been found that for an efficient computational implementation it is necessary to restrict the characteristics of the probe pattern such that it contains only azimuthal modes for which µ = ±1 [1, 2, 3]. This firstorder pattern restriction does not however extend to placing a limit on the polar index mode content and therefore leaves the directivity of the probe unconstrained. Clearly, when using this widely utilized approach, errors will be present within the calculated probecorrected test antenna spherical mode coefficients for cases where the probe is considered to have purely modes for which µ = ±1 and where the probe actually exhibits higher order mode structure. A number of analysis [4, 5, 6, 7, 8] and simulations [9, 10, 11, 12] can be found documented within the open literature that estimate the effect of using a probe with higher order modes. The following study is a further attempt to develop guidelines for the azimuthal and polar properties of the probe pattern and the measurement configuration that can be utilized to reduce the effect of higher order spherical modes to acceptable levels. ? [1] P.F. Wacker, ”Nearfield antenna measurements using a spherical scan: Efficient data reduction with probe correction”, Conf. on Precision Electromagnetic Measurements, IEE Conf. Publ. No. 113, pp. 286288, London, UK, 1974. [2] F. Jensen, ”On the probe compensation for nearfield measurements on a sphere”, Archiv für Elektronik und Übertragungstechnik, Vol. 29, No. 7/8, pp. 305308, 1975. [3] J.E. Hansen, (Ed.) “Spherical nearfield antenna measurements”, Peter Peregrinus, Ltd., on behalf of IEE, London, 1988. [4] T.A. Laitinen, S. Pivnenko, O. Breinbjerg, “Oddorder probe correction technique for spherical nearfield antenna measurements,” Radio Sci., vol. 40, no. 5, 2005. [5] T.A. Laitinen, O. Breinbjerg, “A first/thirdorder probe correction technique for spherical nearfield antenna measurements using three probe orientations,” IEEE Trans. Antennas Propag., vol. 56, pp. 1259–1268, May 2008. [6] T.A. Laitinen, J. M. Nielsen, S. Pivnenko, O. Breinbjerg, “On the application range of general highorder probe correction technique in spherical nearfield antenna measurements,” presented at the 2nd Eur. Conf. on Antennas and Propagation (EuCAP’07), Edinburgh, U.K. Nov. 2007. [7] T.A. Laitinen, S. Pivnenko, O. Breinbjerg, “Theory and practice of the FFT/matrix inversion technique for probecorrected spherical nearfield antenna measurements with highorder probes”, IEEE Trans. Antennas Propag., vol. 58,, No. 8, pp. 2623–2631, August 2010. [8] T.A. Laitinen, S. Pivnenko, “On the truncation of the azimuthal mode spectrum of highorder probes in probecorrected spherical nearfield antenna measurements” AMTA, Denver, November 2012. [9] A.C. Newell, S.F. Gregson, “Estimating the effect of higher order modes in spherical nearfield probe correction”, AMTA 34th Annual Meeting & Symposium, Seattle, WA, October. 2012. [10] A.C. Newell, S.F. Gregson, “Higher Order Mode probes in Spherical NearField Measurements”, EuCAP, Gothenburg, April, 2013. [11] A.C. Newell, S.F. Gregson, “Estimating the Effect of Higher Order Modes in Spherical NearField Probe Correction”, AMTA 35th Annual Meeting & Symposium, Seattle, WA, October. 2013. [12] A.C. Newell, S.F. Gregson, “Estimating the Effect of Higher Order Azimuthal Modes in Spherical NearField Probe Correction”, EuCAP, The Hague, April, 2014.
Characterization of an InSitu Ground Terminal via a Geostationary Satellite
In 2015, the Space Communications and Navigation (SCaN) Testbed project completed an SBand ground station located at the NASA Glenn Research Center in Cleveland, Ohio. This SBand ground station was developed to create a fully characterized and controllable dynamic link environment when testing novel communication techniques for Software Defined Radios and Cognitive Communication Systems. In order to provide a useful environment for potential experimenters, it was necessary to characterize various RF devices at both the component level in the lab and at the system level after integration. This paper will discuss some of the lab testing of the ground station components, with a particular focus / emphasis on the nearfield measurements of the antenna. It will then describe the methodology for characterizing the installed ground station at the system level via a TDRS satellite, with specific focus given to the characterization of the ground station antenna pattern, where the max TDRS transmit power limited the validity of the nonnoise floor received power data to the antenna main lobe region. Finally, the paper compares the results of each test as well as provides lessons learned from this type of testing methodology.
Determining Measurement Uncertainty in a CATR using Quiet Zone Spherical NearField Scanning.
Measurement uncertainty is a vital parameter when assessing the performance of an antenna. Common measurement procedures such as fieldprobing give performance parameters of the quiet zone, such as amplitudetaper and ripple. However, relating these measurements to the actual measurement uncertainty is difficult at best. Furthermore the gain of the used probe has large influence on the outcome of the performance parameters, making measurement chamber intercomparison based on these parameters difficult. Quiet zone spherical nearfield scanning fully describes the field distribution inside the quiet zone. Probe correction can be applied to compensate for the probe influence on the spherical modes. The mode spectrum consists of all electric waves propagating into the quiet zone. From the mode spectrum several performance parameters of the quiet zone can be derived. As an example the main beam power is concentrated in the m=±1 spectrum when aligned with the zaxis. Since other sources, having a different angle, have their mode spectrum spread over the mspectrum, the power in m=±1 can be divided by the power in m?±1. This provides a signaltonoise ratio which can be directly related to measurement uncertainty. Using the signaltonoise ratio a new determination of the measured pattern uncertainty is found. In contrast to parameter derived from fieldprobing the new parameter is more general and comprehensive. In the paper we will derive new performance parameter and apply them to measured data in a CATR.
Methods of Shaping Directional Characteristics of Microstrip Antenna Arrays
In the contemporary world there is high demand for mutual communications and data transmissions. More and more new radio communication systems are developed that require to prepare new types of antennas. Such requirements are satisfied by microstrip antennas. These antennas are characterised by many interesting features, both positive and negative, these attributes have to be taken into account in the design process. These antennas allow to miniaturise antenna system, and by this its highest density. It causes appearance of mutual couplings changing fields distributions on aperture antennas as well currents distributions in linear antennas. A methodology of shaping directional characteristics of microstrip antenna arrays will be presented in the article using phase shifters. Basing on the CST Microwave Studio software, two models of microstrip antenna arrays were designed and done using a method of radiation patterns shaping as well as real models that were put on measurements. Shapes of radiations patterns optimised according to the effects of signal amplitude and phase of particular antenna array radiators were presented in the article. The results were also presented in the tables taking into account values of phase shifts and amplitudes of power supplying system. The results achieved were compared with the results of measurements done on a special measuring position at the anechoic chamber.
Interplanetary Communications from Mars: Development and Testing of a Novel Compact Circularly Polarized Subarray
Mars rover DirecttoEarth (DTE) communication is an exciting new development that can maintain transfer of high volumes of scientific data from Mars to Earth. Currently, large orbiting assets are used as a relay to return scientific data, often containing higher data rates than current DTE systems. Therefore, the goal of this paper is to investigate antenna array topologies to augment DTE systems to support high data rates. The antenna design is complex, having to simultaneously support dualband, high gain, high power handling, and circular polarization capabilities. An exhaustive study of patch elements in literature shows that current geometries are infeasible for a Mars rover DTE system. A CP Half Eshaped patch element is developed, containing important dual band S11/AR performance in the required RX and TX bands while featuring a singlefeed singlelayer design. Moreover, various subarray architectures are evaluated to determine if the gain requirements can be achieved. To meet this gain requirement, a 4x4 subarray topology is designed which allows a modular, scalable, and high gain design. To feed each of the 4x4 element subarrays, a stripline feed network is developed, consisting of a binomial impedance transformer and a four stage 1:2 power divider. This feed network supported a broadside radiation pattern for the subarray topology. These components are then integrated, first through a full wave simulation in HFSS. This rigorous study showed support for Mars rover DTE communications systems. The integrated subarray design is then fabricated and measured using a spherical nearfield chamber in the UCLA Center for High Frequency Electronics (CHFE) facilities where measurements showed a very good comparison to the simulation results. Overall this integrated subarray design was successful, showing dualband, high gain, high power handling, and CP performance.
Computation of the Far Field Radiated by Aperiodic Sampled Planar Fields by Means of NUFFT
It is a common practice when computing radiation patterns from nonuniformly sampled planar fields to interpolate the samples into a regular grid [1], although it might cause inaccuracies due to the interpolation process. The nonuniform fast Fourier transform (NUFFT) has been applied to process near field measurements in nonuniform planar grids with arbitrary precision [2], and also to analyze aperiodic arrays [3]. However, samples are usually treated as punctual sources. In this contribution, an efficient and accurate method to calculate the far field radiated by nonuniformly sampled planar fields which comply the Nyquist theorem using the nonuniform fast Fourier transform (NUFFT) is shown. The method takes into account the amplitude of the unit cell radiation pattern, which allows to compute more accurately the copolar and crosspolar components of the far field with regard to the array factor [3], which models the samples as punctual sources. For measured fields it is assumed that postprocessing has been done, for instance, taking into account probe corrections. Because the NUFFT is precisiondependent, a discussion of how its accuracy can affect the computed radiated fields will be carried out. Numerical examples will be provided to show the accuracy and performance of the NUFFT with regard to the FFT and direct evaluation of the far fields. Finally, a study of computing times comparing the FFT, NUFFT and direct evaluation will be presented. References [1] Y. RahmatSamii, L. I. Williams, and R. G. Yaccarino, “The UCLA bipolar planarnearfield antennameasurement and diagnostics range,” IEEE Antennas Propag. Mag., vol. 37, no. 6, pp. 16–35, Dec. 1995. [2] R. C. Wittmann, B. K. Alpert, and M. H. Francis, “Nearfield antenna measurements using nonideal measurement locations,” IEEE Trans. Antennas Propag., vol. 46, no. 5, pp. 716–722, May 1998. [3] A. Capozzoli, C. Curcio, G. D'Elia, and A. Liseno, “Fast phaseonly synthesis of conformal reflectarrays,” IET Microw. Antennas Propag., vol. 4, no. 12, Dec. 2010.
Optimization of the Reflectarray Quiet Zone for use in Compact Antenna Test Range
Reflectarrays have been widely studied in the past 3 decades and several techniques have been developed for the synthesis of shapedbeam farfield radiation patterns [1]. Also, some nearfield applications have been studied, such as imaging [2] or RFID [3]. In this contribution, a nearfield synthesis technique is proposed for the reflectarray quiet zone optimization, which can be of interest in the design of probes for compact antenna test ranges (CATR) at high frequencies. The nearfield of the reflectarray is characterized by a simple radiation model which computes the near field of the whole antenna as farfield contributions of each element. The reflectarray unit cell is considered the unit radiation element and its far field is computed employing the second principle of equivalence. Then, at each point in space, all contributions from the elements of the reflectarray are added in order to obtain the near field [4]. This simple model has been validated through simulations with GRASP [5] and also through nearfield measurements. Then it has been used to optimize the near field of the reflectarray. The Intersection Approach algorithm is used to optimize both amplitude and phase of the near field radiated by the antenna, and uses the LevenbergMarquardt algorithm [6] as backward projector. This optimization increases the size of the quiet zone generated by the reflectarray. References [1] J. Huang and J. A. Encinar, Reflectarray Antennas WileyIEEE Press, 2008. [2] H. Kamoda et al., "60GHz electronically reconfigurable large reflectarray using singlebit phase shifters," IEEE Trans. Antennas Propag., vol. 59, no. 7, pp. 2524–2531, July 2011. [3] HsiTseng Chou et al., "Design of a nearfield focused reflectarray antenna for 2.4 GHz RFID reader applications," IEEE Trans. Antennas and Propag., vol. 59, no. 3, pp. 1013–1018, March 2011. [4] D. R. Prado, M. Arrebola, M. R. Pino, F. LasHeras, "Evaluation of the quiet zone generated by a reflectarray antenna," International Conference on Electromagnetics in Advanced Applications (ICEAA), pp. 702–705, 27 Sept. 2012. [5] "GRASP Software", TICRA, Denmark, http://www.ticra.com. [6] J. Álvarez et al., “Near field multifocusing on antenna arrays via nonconvex optimisation,” IET Microw. Antennas Propag., vol. 8, no. 10, pp. 754–764, Jul. 2014.
Review of CrossEye Jamming
This paper gives a review of crosseye (CE) jamming using the retrodirective channel implementation. CE jamming is an electronic warfare selfprotection technique in which the phasefront of an electromagnetic wave, transmitted towards a threat radar, is distorted in a way similar to radar glint. A retrodirective channel is used in the implementing of the CE jammer to avoid prohibitive tolerance requirements on the electronic warfare (EW) system. In a practical implementation of the CE jammer in an EW system, active electronically scanned array antennas (AESA) can be used to fulfil effective radiated power requirements. The achievable reciprocity i.e. similarity between the transmission and reception radiation patterns in the AESA is central to the performance of the CE jammer system. Effects of the CE jammer on monopulse radar are presented and described. The effects include the mixing of a CE jammer signal and a target echo. The CE jammer can induce false target angles and prevent the radar from finding a stable settling angle. The origin of CE jamming is in the field of radar multipath phenomenon such as glint and reflections from water surfaces. The CE jamming technique has previously been described and analyzed in various literature. This paper summarizes the most recently published results and gives references to the publications.
A Comparison of Antenna Range Polarization Correction Techniques
Antenna range calibration is commonly performed with the goal of obtaining the gain of an antenna under test. The most straightforward calibration procedure makes assumptions about the polarization properties of the range illumination, which can lead to both polarization and gain errors in the measured patterns. After introducing the concept of polarization correction we describe three published range polarization correction techniques and provide an example of polarization correction applied to a compact antenna test range measurement. We then discuss the practical aspects of incorporating polarization correction into the range calibration workflow.
Experimental Measurements Using the Uniform, Latitude, and EquallySpaced Spherical NearField Measurement Grids
Comparisons are made between farfield patterns of an Xband polarization reference horn obtained using the equallyspaced, latitude, and uniform nearfield measurement grids. All of the farfields were obtained by transforming the measured nearfield data. Measurement and data processing times are also presented, such that the reader can understand the benefits and drawbacks of the equallyspaced, latitude, and uniform grids. In addition to these comparisons, the sampling requirements of the latitude grid are investigated. In the past, it has been recommended to thin the uniform grid near the poles of the measurement sphere, which is referred to as latitude sampling. The typical method is to multiply the number of sample points required on the equator by a sin(theta) weighting function to obtain the number of sample points required near the poles. However, it will be shown that the sin(theta) weighting function may lead to aliasing in certain cases, and a new method is proposed which is guaranteed to minimize aliasing for any antennaundertest. We refer to this new grid as the Maximum Fourier Content (MFC) latitude grid.
Reduction of the Cross Polarization Component in the Quiet Zone of a Single Reflector CATR
A single reflector CATR exhibits certain depolarizing properties, as any other offset reflector antenna, when illuminated by a linearly polarized feed in its focal point. One way to improve the polarization purity in the Quite Zone (QZ) is to use a feed antenna which aperture fields provide a conjugate match to the electricfield distribution in the reflector’s focal plane when illuminated with a linearly polarized plane wave. MVG developed and built a proofofconcept demonstrator in the form of a 3x1 array of linearly polarized elements, exited to match the focal plane distribution as predicted by a fullwave simulation of the specific range. This demonstrator has been installed in the CATR at RWTH Aachen University, which is a cornerfed serrated edge reflector system with a 1.2 m diameter QZ and a specified maximum cross polarization level of 30 dB (edge of QZ) due to the offset geometry. In this paper we will show measurement results for planar co and crosspolar probing of the QZ in Xband, using the demonstrator and compare it to the respective results using the range’s conventional, low cross polarization, corrugated feed horn. The measured data will also be crosschecked against the fullwave simulation results for the fields in the QZ. Furthermore, we will compare 0°, 90°, ±45° pattern cuts of a demanding Antenna Under Test, a 40 cm x 40 cm offset reflector antenna with a wide band dual ridge horn as a feed, again using the demonstrator and the conventional feed. This is to show the potential improvement in measurement quality by using a matched feed in a single reflector CATR.
The effect of the receivingantenna pattern on the results of the freespace VSWR technique
The freespace VSWR technique as the standard method to extract the quietzone reflectivity in anechoic chambers has been explained in short. Among different uncertainty factors, the effect of pattern of the probe/receiving antenna has been investigated and some points how to reduce this effect has been suggested.
Determination of the Far Field Radiation Pattern of an Antenna from a Set of Sparse Near Field Measurements
This work introduces a new technique in electromagnetic antenna nearfield to farfield transformation (NF/FF). The NF/FF transformation is based on the solution of an inverse problem in which the measured NF and predicted FF values are attributed to a set of equivalent electric and magnetic surface currents which lie on a convex arbitrary surface that is conformal to the antenna under test (AUT). The NF points are conformal to the AUT, reducing the number of samples and relaxing positioning requirements used in conventional spherical, cylindrical and planar NF/FF geometries. A pseudo inversion of the matrix representing the mapping of the equivalent sources into the nearfield samples is obtained by using the singular value decomposition (SVD). The SVD is used to form an approximation of the inverse of the matrix. This inverse, when multiplied by the NF measurement vector, solves for the efficiently radiating components of the current, and not the essentially nonradiating components of current which are not visible in the measurements. The inversion technique used is robust in the presence of measurement noise and provides a stable solution for the unknown currents. The FF is computed from the currents in a straightforward manner. The work develops the theoretical foundation for the approach and investigates the FF reconstruction accuracy of the technique for a test case. Approved for Public Release; Distribution Unlimited. Case Number 160884 The author's affiliation with The MITRE Corporation is provided for identification purposes only, and is not intended to convey or imply MITRE's concurrence with, or support for, the positions, opinions or viewpoints expressed by the author.
Practical Considerations for Coordinate System Rotations in ModeSpace
Rotating the coordinate system of an antenna pattern can be problematic due to the need to interpolate complex data in spherical coordinates. Common approaches to 2D interpolation often introduce errors because of polarization discontinuities at the spherical coordinate system poles. To overcome these difficulties, it is possible to transform an antenna pattern from fieldspace into spherical modespace, perform the desired coordinate system rotation in modespace, and then transform the modes in the rotated coordinate system back into fieldspace. This method, while more computationally intensive, is exact and alleviates all of the interpolationrelated issues associated with rotations in fieldspace. Although rotations in modespace have been implemented in commercially available software (e.g., the ROSCOE algorithm provided by TICRA), these algorithms may not be well understood by the general antenna measurement community. Therefore, the first goal of this paper is to present an easytounderstand algorithm for performing rotations in modespace. Next, the paper will address the challenge of computing the rotation coefficients, which are required by the modespace coordinate system rotation algorithm. Although J. E. Hansen presented a method for recursively computing the rotation coefficients, this method is numerically unstable for large values of N (where N is the upper limit of the polar index). Therefore, this paper will present a numerically stable method for the recursive computation of the rotation coefficients. Finally, this paper will show the relationships between Euler angles and both AzoverEl angles and EloverAz angles. These relationships are quite useful because it is often desired to rotate an antenna pattern based on Elevation and Azimuth angles, whereas the inputs for the modespace rotation algorithm are Euler angles. Knowing these relationships, the Euler angles may be computed from the Azimuth and Elevation angles, which can then be used as the inputs to the modespace rotation algorithm.
A Radar Echo Emulator for the Evaluation of Automotive Radar Sensors
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 Wband radar echo emulator (REE) to be used for evaluating automotive precollision 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.
Far Field Uncertainty due to Noise and Receiver Nonlinearity in PlanarNear Field Measurements
The uncertainty of the far field, obtained from antenna planar near field measurements, against the dynamic range is investigated by means of statistical analysis. The dynamic range is usually limited by the noise floor for low level signals and by the receiver saturation for high level signals. The noise level could be important for high measurement rate, which requires the usage of a high signal level to ensure a sufficient signal to noise ratio. As a result the nonlinearities are increasing, thus a compromise must be accomplished. To evaluate the effects of the limited near field dynamic range on the far field, numerical simulations are performed for dipoles array. Initially, the synthetic near field data corresponding to a given antenna under test were generated and directly processed to yield the corresponding far field patterns. Many far field parameters such as gain, beam width, maximum sidelobe level, etc. are determined and recorded as the errorfree values of these parameters. Afterwards, the synthetic near field data are deliberately corrupted by noise and receiver nonlinearities while varying the amplitude through small, medium and large values. The errorcorrupted near field data are processed to yield the far field patterns, and the errorcorrupted values of the far field parameters are calculated. Finally, a statistical analysis was conducted by means of comparison between the errorcorrupted parameters and the errorfree parameters to provide a quantitative evaluation of the effects of near field errors on the different far field parameters.

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