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Comparison of Payload Applications in Near Field and Compact Range Facilities
Carsten Schmidt,Josef Migl, Alexander Geise, Hans-Juergen Steiner, November 2015

For satellite applications payload measurements are a crucial part of the radio frequency validation campaign before the launch. Parameters like Equivalent Isotropic Radiated Power (EIRP), Input Power Flux Density (IPFD), Gain over Noise Temperature (G/T), Gain over Frequency (G/F), Group Delay, and Passive Intermodulation (PIM) are to be measured in suitable facilities on satellite level. State-of-the-art payload measurements are conducted in compensated compact range facilities which offer a real-time test capability which is easy to setup and use. Closed link tests are straightforward to realize with two compact range feeds employing feed scanning. The measurement techniques as well as the error budgets are well known. Near-field facilities are widely used for antenna pattern measurements. However, there is not much literature available discussing in particular measurements of G/T, G/F, and Group Delay in the near field. Measurements of the above parameters in the near field seem to be feasible, however, the processing of the measured data has to be adapted and further calibration measurements are required. In this paper methodologies for payload parameter measurements in compact range and near field facilities will be described. A comparison of payload measurement campaigns in near field and compact range facilities will be drawn. The techniques will be compared in terms of measurement timing and effort, practicability for satellite applications, and achievable accuracies.

Development of a FMCW Radar Sensor For Soil Humidity Estimation
Maria C. Gonzalez,Christian Hurd, Jose Enrique Almanza Medina, Xiaoguang Liu, November 2015

To determine the proper moisture content in the soil is critical to get maximum grow in plants and crops and its estimation it is used to regulate the amount of irrigation that it is needed. For this reason, many sensors that measure water content have been developed to give the grower some feedback of the water content.   Some methods such as the ones based in gravimetric properties are accurate but labor consuming, other such as the tension meters require periodic service, the neutron probe is also accurate but expensive. The more popular sensor is based in electrical resistance measurement that gives acceptable accuracy and it is not expensive. However, this sensor has the disadvantage that needs to be buried in the soil. Here, we are exploring the characteristics of electromagnetic propagation and its scattering properties as a tool to identify the physical soil composition. The presence of water changes drastically the dielectric properties of the soil affecting the reflected signal. In this research, we are assessing the viability of a sensor based in FMCW radar technology for water detection with the advantage of being portable and low cost. The research involves the fabrication of a directive antenna operating in a broadband regimen, transmitter/ receiver circuit and the signal processing of the return signal adjusted to the detection of moisture in soil. We present the calibration methods and graphic results of the intensity of the reflected signal of dry bare soil, wet soil, and soil covered by plants.

Monostatic RCS Calibration of Radar Target Using Extrapolation Method in Millimeter-wave Frequency Band
Michitaka Ameya,Satoru Kurokawa, Masanobu Hirose, November 2015

In this paper, we propose a calibration method for monostatic radar cross section (RCS) of simple radar targets (e.g. trihedral corner reflectors and square flat-plate reflectors) using extrapolation method. By the proposed method, we can calibrate the monostatic RCS of radar targets from 1-port S-parameter measurements. In our system, the applicable size of radar targets are 75 mm to 125 mm for corner reflectors and 40 mm to 75 mm for square flat-plate reflectors, respectively. The nominal RCS of reflector targets calculated by physical optics ranges from +3 dBsm to +15 dBsm in W-band.  The measured results are agree well with simulation results calculated by method of moment (MoM).

Experimental In-Situ Antenna Array Calibration with Signals of Opportunity
Andrew L. Kintz,Inder J. Gupta, November 2015

We present experimental results for on platform (in-situ) calibration of an antenna array with signals that are treated as signals of opportunity. In-situ calibration is required for antenna arrays installed on vehicles as platform scattering significantly perturbs the radiation patterns of the antenna elements. In-situ 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 L-band 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 in-situ array calibration.

Research on Unwanted Reflections in an OATS for Precise Omni Antenna Measurement
Donglin Meng,Xiao Liu, Dabo Li, November 2015

Open-area test site (OATS) is a basic range for measuring omni antennas at VHF/HUF band. Reflections from the trees nearby, from the edge of the metal ground plane of an OATS are researched with the aid of ultra-broadband calculable dipole antennas (CDAs). Usually, these reflections are detrimental to precise antenna measurements from 20 MHz to 1 GHz; however they are very difficult to analyze accurately, since no rigorous theory exists on the relationship between the reflections and the configurations of an OATS. For this difficulty, a pair of very accurate and broadband CDAs are manufactured and verified with a slightly modified near-field method, whose site-insertion-loss deviation (?SIL) between measurements and simulation is less than 0.3 dB over 10 MHz to 340 MHz for a single pair of dipole elements resonated at 90 MHz. Based on the optimized CDAs, the effects of ground plane sizes, wire mesh shapes around the edge of the metal ground plane, trees nearby and especially masts are researched. The research shows that the reflections from the edge of an optimized ground plane is less than 0.1 dB at 10 m range. Finally, the performance of an OATS with these optimizations is verified: for 10 m separation, ?SIL is within 0.26 dB at horizontal polarization (HP) and within 0.34 dB at vertical polarization (VP) for the typical 24 frequencies from 30 MHz to 1 GHz; at 20 m separation, ?SIL is within 0.59 dB (HP) and 0.85 dB (VP) from 20 MHz to 500 MHz. An example for the uncertainty of calibration the free-space antenna factor of tuned dipole antennas are provided, too.

A Comparison of Antenna Range Polarization Correction Techniques
Justin Dobbins,Jason Jerauld, November 2015

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.

Slotted Waveguide Array Beamformer Characterization Using Integrated Calibration Channel
Akin Dalkilic,Caner Bayram, Can Baris Top, Erdinc Ercil, November 2014

In military applications, where low sidelobes and high precision in beam pointing are vital, a phased array antenna beamformer requires to be calibrated regarding the cabling that connects the beamformer to the antenna and mutual coupling between antenna elements. To avoid problems associated with mismatched phase transmission lines between the beamformer and the antenna and include the coupling effects, beamforming network characterization must be done with the antenna integrated to the beamformer. In this paper, a method to characterize the beamformer of a slotted waveguide array antenna in the antenna measurement range is introduced. The antenna is a travelling wave slotted waveguide array scanning in the elevation plane. The elevation pattern of the antenna is a shaped beam realized by a phase-only beamformer. The calibration channel includes serial cross-guide couplers fed by a single waveguide line. The channel is integrated to the waveguide lines of the antenna.  In the first phase of the characterization, the far field pattern of each antenna element is obtained from the near field measurements at the “zero” states of the phase shifters. In the second stage, all states of the phase shifters are measured automatically using the calibration channel described above. The results of calibration channel measurements are used to determine the changes in phase and magnitude for different states of phase shifters. The phase and magnitude of the peak point of the far field pattern is referenced to the zero state measurement of the calibration channel. Phase only pattern synthesis is carried out using the results of both zero-state near field and calibration channel measurements and the required phase shifter states are determined accordingly. Measured patterns show good agreement with the theoretical patterns obtained in the synthesis phase.

Computational Electromagnetic Modeling of Near-Field Antenna Test Systems Using Plane Wave Spectrum Scattering Matrix Approach
Allen Newell,Stuart Gregson, November 2014

In recent years a number of analyses and simulations have been published that estimate the effect of using a probe with higher order azimuthal modes with standard probe corrected spherical transformation software.  In the event the probe has higher order modes, errors will be present within the calculated antenna under test (AUT) spherical mode coefficients and the resulting asymptotic far-field parameters [1, 2, 3, 4] where the simulations were harnessed to examine these errors in detail.  Within those studies, a computational electromagnetic simulation (CEM) was developed to calculate the output response for an arbitrary AUT/probe combination where the probe is placed at arbitrary locations on the measurement sphere ultimately allowing complete near-field acquisitions to be simulated.  The planar transmission equation was used to calculate the probe response using the plane wave spectra for actual AUTs and probes derived from either planar or spherical measurements.  The planar transmission formula was utilized as, unlike the spherical analogue, there is no limitation on the characteristics of the AUT or probe thereby enabling a powerful, entirely general, model to be constructed.  This paper further extends this model to enable other measurement configurations and errors to be considered including probe positioning errors which can result in ideal first order probes exhibiting higher order azimuthal mode structures.  The model will also be used to determine the accuracy of the Chu and Semplak near-zone gain correction [5] that is used in the calibration of pyramidal horns.  The results of these additional simulations are presented and discussed. Keywords: near-field, antenna measurements, near-field probe, spherical alignment, spherical mode analysis. REFERENCES A.C. Newell, S.F. Gregson, “Estimating the Effect of Higher Order Modes in Spherical Near-Field Probe Correction”, Antenna Measurement Techniques Association (AMTA) 34th Annual Meeting & Symposium, Bellevue, Washington October 21-26, 2012. A.C. Newell, S.F. Gregson, “Higher Order Mode Probes in Spherical Near-Field Measurements”, 7th European Conference on Antennas and Propagation (EuCAP 2013) 8-12 April 2013. A.C. Newell, S.F. Gregson, “Estimating the Effect of Higher Order Modes in Spherical Near-Field Probe Correction”, Antenna Measurement Techniques Association (AMTA) 35th Annual Meeting & Symposium, Columbus, Ohio, October 6-11, 2013. A.C. Newell, S.F. Gregson, “Estimating the Effect of Higher Order Azimuthal Modes in Spherical Near-Field Probe Correction”, The 8th European Conference on Antennas and Propagation (EuCAP 2014) 6-11 April 2014. T.S. Chu, R.A. Semplak, “Gain of Electromagnetic Horns,’’ Bell Syst. Tech. Journal, pp. 527-537, March 1965

Investigations on Gain Measurement Accuracies at Limited Far-Field Conditions
Engin Gülten,Andreas Drexler, Josef Migl, Jürgen Habersack, November 2014

Driven by the mobile data communications needs of market broadband antennas at the upper frequency bands are already state-of-the-art, e.g. at the Ka-Band. For the characterization of an antenna the antenna gain is one of the major test parameters. This measurement task is already challenging for standard applications at the Ka-Band. However, for the calibration of remote station antennas utilized in high precision test facilities, e.g. the compact range, even higher measurement accuracies are typically required in order to fulfil the overall system performance within the later test facility. Therefore the requirement for this investigation is to improve the measurement set-up and also the steps to get a failure budget which is better than ± 0.15 dB. Every antenna gain measurement technique is affected by required changes in the measurement setup, e.g. the Device under Test (DUT) or the remote station, respectively. This results for example in a variation of mismatch with resulting measurement errors. To determine and compensate the occurred mismatches, the scattering parameters of the involved components have to be measured and be evaluated with a corresponding correction formula. To quantify the effect for the gain measurement accuracy the remaining uncertainty of the mismatch correction values is examined. Another distortion is caused by multiple reflections between the antenna apertures. To reduce this error source, four additional measurements each with a decreased free space distance should be performed. In addition to the common methods, this paper explains in detail an advanced error correction method by using the singular value decomposition (SVD) and compares this to the standard mean value approach. Finally the restricted distance between both antennas within the applied anechoic far-field test chamber has to be analysed very critically and optionally corrected for the far-field gain at an infinite distance in case the measurement distance is fulfilling the minimum distance requirement, only. The paper will discuss all major error contributions addressed above, show correction approaches and verify these algorithms with exemplary gain measurements in comparison to the expected figures.

Advantages and Disadvantages of Various Hemispherical Scanning Techniques
Eric Kim,Anil Tellakula, November 2014

When performing far field or near field antenna measurements on large antennas, it is often necessary to have various types of mechanical positioning systems to achieve the required hemispheric scans.  Measurement systems employing a single-arm gantry, a dual-arm gantry, a fixed arch moving probe, or a fixed arch multi-probe have been paired with either an azimuth positioner or a vehicle turntable to provide hemispheric scanning of the object being tested. This paper will highlight the key characteristics of various scanning methods making comparisons between the different techniques.  Positioning and system accuracy, speed, stowing ability, calibration, frequency range, upgradability, relative cost and other key aspects of the various techniques will be discussed in detail to help the end user during the system design and selection process.  In addition, the paper will highlight novel hemispheric and truncated spherical scanning approaches. In many applications, the success of the entire project often centers on the judicious selection of the positioning subsystem.  This paper will provide guidance toward making the proper selection of the scanning concept as well as of the positioning system.

Equiangular Phase Shifting Holography for THz Near-field/Far-field Prediction
Gary Junkin,Josep Parrón Granados, Pedro de Paco Sánchez, Yi Lu, November 2014

A three-step equiangular (120º) phase shifting holography (EPSH) technique is proposed for THz antenna near-field/far-field prediction. The method is attractive from the viewpoint of receiver sensitivity, phase accuracy over the entire complex plane, simplified detector array architecture, as well as reducing planarity requirements of the near-field scanner. Numerical modeling is presented for the holographic receiver performance, using expected phase shift calibrations errors and phase shift noise. The receiver model incorporates responsivity and thermal noise specifications of a commercial Schottky diode detector. Additionally, simulated near-field patterns at 372GHz demonstrate the convenience of the method for accurate and high dynamic range THz near-field/far-field predictions, using a phase-shifter calibrated to ±0.1°.

Testing of Panels And Radomes Using De-embedding To Reduce Probe Interaction Errors
Henry Burger, November 2014

Legacy methods for testing the performance of radome panels and finished radomes have always been in isolation from the system antenna, for many reasons. The legacy method of testing employed horn antennas at relatively close distances, a fixed-frequency signal source, and primitive receivers. More modern systems used much better receivers capable of measuring both phase and amplitude, and these gave way to automatic network analyzers. The network analyzer system also replaces the fixed-frequency source, because it has its own step-frequency source. The rest of the setup remains the same. A network analyzer can itself be calibrated, but that calibration cannot include the probe antennas, nor can it account for interactions, particularly at normal incidence. With increasing demands on performance, it is essential that the interaction effects of the probe antennas with the radome be removed.    The micorwave integrated circuit industry has the identical problem. The circuit probes that are used to reach into the circuit assemblies have very small tips, and the internal elements to accomplish this size reduction make probe mataching difficult. Thus the probe parameters become embedded into the overall measured response. The circuit testing community has developed a process to de-embed these probes, yielding the S-parameters of the circuit under test in isolation from surroundings.    This paper investigates a method for applying this closed-system technique to open-system testing, such as panel-measuremsnt tables, by using a secondary calibration technique that is adapted to open systems. This effectively extends the calibration of the analyzer system to encompass the probes, thus improving accuracy.

Combining Pattern, Polarization and Channel Balance Correction Routines to Improve the Performance of Broad Band, Dual Polarized Probes
Patrick Pelland,Allen Newell, November 2014

Broad band, dual polarized probes are becoming increasingly popular options for use in near-field antenna measurements. These probes allow one to reduce cost and setup time by replacing several narrowband probes like open-ended waveguides (OEWG) with a single device covering multiple waveguide bands. These probes are also ideal for production environments, where chamber throughput should be maximized. Unfortunately, these broadband probes have some disadvantages that must be quantified and corrected for in order to make them viable for high accuracy near-field measurements. Most of these broadband probes do not have low cross polarization levels across their full operating bandwidths and may also have undesirable artifacts in the main component of their patterns at some frequencies. Both of these factors will result in measurement errors when used as probes. Furthermore, the use of a dual port RF switch adds an additional level of uncertainty in the form of port-to-port channel balance errors that must be accounted for. This paper will describe procedures to calibrate the pattern and polarization properties of broad band, dual polarized probes with an emphasis on a newly developed polarization correction algorithm. A simple procedure to measure and correct for amplitude and phase imbalance entering the two ports of the near-field probe will also be presented. Measured results of the three calibration procedures (pattern, polarization, channel balance) will be presented for a dual-polarized, broad band quad-ridged horn antenna. Once calibrated, this probe was used to measure a standard gain horn (SGH) and will be compared to baseline measurements acquired using a good polarization standard open-ended waveguide (OEWG). Results with and without the various calibration algorithms will illustrate the advantage to using all three routines to yield high accuracy far-field pattern data.

Dual Polarized Near Field Probe Based on OMJ in Waveguide Technology Achieving More Than Octave Bandwidth
Lars Jacob Foged,Andrea Giacomini, Roberto Morbidini, Vincenzo Schirosi, Sergey Pivnenko, November 2014

In classical probe-corrected spherical near-field measurements, one source of measurement errors, not often given sufficient consideration is the probe [1-3]. Standard near-field to far-field (NFFF) transformation software applies probe correction with the assumption that the probe pattern behaves with a µ=±1 azimuthal dependence. In reality, any physically-realizable probe is just an approximation to this ideal case. Probe excitation errors, finite manufacturing tolerances, and probe interaction with the mounting interface and absorbers are examples of errors that can lead to presence of higher-order spherical modes in the probe pattern [4-5]. This in turn leads to errors in the measurements. Although probe correction techniques for higher-order probes are feasible [6], they are highly demanding in terms of implementation complexity as well as in terms of calibration and post-processing time. Thus, probes with high azimuthal mode purity are generally preferred.   Dual polarized probes for modern high-accuracy measurement systems have strict requirements in terms of pattern shape, polarization purity, return loss and port-to-port isolation. As a desired feature of modern probes the useable bandwidth should exceed that of the antenna under test so that probe mounting and alignment is performed only once during a measurement campaign. Consequently, the probe design is a trade-off between performance requirements and usable bandwidth. High performance, dual polarized probe rely on balanced feeding in the orthomode junction (OMJ) to achieve good performance on a wide, more than octave, bandwidth [5-7]. Excitation errors of the balanced feeding must be minimized to reduce the excitation of higher order spherical modes. Balanced feeding on a wide bandwidth has been mainly realized with external feeding network and the finite accuracy of the external components constitutes the upper limits on the achievable performance.     In this paper, a new OMJ designed entirely in waveguide and capable of covering more than an octave bandwidth will be presented. The excitation purity of the balanced feeding is limited only by the manufacturing accuracy of the waveguide. The paper presents the waveguide based OMJ concept including probe design covering the bandwidth from 18-40GHz using a single and dual apertures. The experimental validation is completed with measurements on the dual aperture probe in the DTU-ESA Spherical Near-Field facility in Denmark.       References: [1]Standard Test Procedures for Antennas, IEEE Std.149-1979 [2]Recommended Practice for Near-Field Antenna Measurements, IEEE 1720-2012 [3]J. E. Hansen (ed.), Spherical Near-Field Antenna Measurements, Peter Peregrinus Ltd., on behalf of IEE, London, UK, 1988 [4]L. J. Foged, A. Giacomini, R. Morbidini, J. Estrada, S. Pivnenko, “Design and experimental verification of Ka-band Near Field probe based on wideband OMJ with minimum higher order spherical mode content”, 34th Annual Symposium of the Antenna Measurement Techniques Association, AMTA, October 2012, Seattle, Washington, USA [5]L. J. Foged, A. Giacomini, R. Morbidini, “Probe performance limitation due to excitation errors in external beam forming network”, 33rd Annual Symposium of the Antenna Measurement Techniques Association, AMTA, October 2011, Englewood, Colorado, USA [6]T. Laitinen, S. Pivnenko, J. M. Nielsen, and O. Breinbjerg, “Theory and practice of the FFT/matrix inversion technique for probe-corrected spherical near- eld antenna measurements with high-order probes,” IEEE Trans. Antennas Propag., vol. 58, no. 8, pp. 2623–2631, Aug. 2010. [7]L. J. Foged, A. Giacomini, R. Morbidini, "Wideband dual polarised open-ended waveguide probe", AMTA 2010 Symposium, October, Atlanta, Georgia, USA. [8]L. J. Foged, A. Giacomini, R. Morbidini, “ “Wideband Field Probes for Advanced Measurement Applications”, IEEE COMCAS 2011, 3rd International Conference on Microwaves, Communications, Antennas and Electronic Systems, Tel-Aviv, Israel, November 7-9, 2011.

Polarimetric Weather Radar Antenna Calibration Using Solar Scans
Richard Ice,Adam Heck, Jeffrey Cunningham, Walter Zittel, Robert Lee, November 2014

The US NEXRAD weather surveillance Doppler radar (WSR-88D) was recently upgraded to polarimetric capability.  This upgrade permits identification of precipitation characteristics and type, thus providing the potential to significantly enhance the accuracy of radar estimated rainfall, or water equivalent in the case of frozen hydrometeors.  However, optimal benefits are only achieved if errors induced by the radar hardware are properly accounted for through calibration.  Hardware calibration is a critical element in delivering accurate meteorological information to the forecast and warning community.  The calibration process must precisely measure the gain of the antenna, the Polarimetric bias of the antenna, and the overall gain and bias of the receive path.  The absolute power measurement must be accurate to within 1 dB and the bias between the Polarimetric channels must be known to within 0.1 dB.  These requirements drive a need for precise measurement of antenna characteristics. Engineers and scientists with the NEXRAD program employ solar scanning techniques to ascertain the absolute gain and bias of the 8.53 m parabolic center fed reflector antenna enclosed within a radome.  They are also implementing use of daily serendipitous interference strobes from the sun to monitor system calibration.  The sun is also used to adjust antenna gain and pedestal pointing accuracy.  This paper reviews the methods in place and under development and identifies some of the challenges in achieving the necessary calibration accuracies.

Revising the Relationships between Phase Error and Signal-to-Noise Ratio
Ryan Cutshall,Jason Jerauld, November 2014

Within RF measurement systems, engineers commonly wish to know how much phase ripple will be present in a signal based on a given signal-to-noise ratio (SNR). In a past AMTA paper (Measurement Considerations for Antenna Pattern Accuracy, AMTA 1997), John Swanstrom presented an equation which demonstrated how the bound on the phase error could be calculated from the peak SNR value. However, it can be shown that the Swanstrom bound is broken when the signal has a peak SNR value of less than approximately 15 dB. This paper introduces a new equation that bounds the maximum phase error of a signal based on the signal’s peak SNR value. The derivation of this new bound is presented, and comparisons are made between the old Swanstrom bound and the new bound. In addition, the inverse relationship (i.e., calculating the SNR value of a signal from phase-only measurements) is investigated. In the past, analytical equations for this relationship have been presented by authors such as Robert Dybdal (Coherent RF Error Statistics in IEEE Trans. on Microwave Theory and Techniques) and Jim P.Y. Lee (I/Q Demodulation of Radar Signals with Calibration and Filtering in a Defense Research Establishment Ottawa publication). The analytical equations for calculating the SNR value using phase-only measurements are reviewed and discussed, and a brand new numerical relationship based on a polynomial curve fitting technique is proposed.

Calibration of Multi-Channel Adaptive Array Receivers
Ying Chieh Chuang,Inder Gupta, November 2014

In array signal processing; i.e. direction of arrival estimation, digital beam forming/ nulling one needs to know the antenna array manifold (relative gain and phase of individual antenna elements) as well as the relative response of RF front end of the various channels. Here the RF front end is defined as LNA, filters, various down convertors and A/Ds. Since RF front end response is highly dependent on the physical environment, in general, nearly real time calibration of the RF front end is carried out. To accomplish this, a pilot signal is injected in various channels or a strong signal is received from a known direction. The received pilot is isolated, and the isolated signal is processed for relative calibration of the various front ends. One simple processing technique is to divide the signal received at a given frequency by the channel of interest with the signal received by the reference channel at that frequency. This technique works fine when the pilot signal has high SNR (20 dB or so). For low SNR, the front end calibration will have large variance and also bias, which is undesired. One can also cross correlate the signal received by the two channels at the frequency of interest, and normalize the cross correlation with the autocorrelation of the signal received by the reference channel. We will show that for low SNR of the pilot signal, this approach can lead to bias in the estimated relative magnitude. We will also present a novel approach that leads to unbiased estimate with small variance. The approach is based on signal space idea. At the given frequency, we generate a covariance matrix that contains the correlation between the signals received by various channels. Next, the principle eigenvector (corresponding to the largest eigenvalue) of the covariance matrix is calculated. The eigenvector is adjusted such that its element corresponding to the reference channel is unity. Then the other elements of the eigenvector yield the relative response of the front end of various channels. We have applied the suggested approach to real world data with very good results. Some examples are discussed in the paper.

Gain and Phase Center Calibration of Log Periodic Dipole Arrays using Complex Fit Algorithm
Zhong Chen, November 2014

Abstract – This paper introduces a method for calibrating the gain and the frequency dependent phase center locations of Log Periodic Dipole Arrays (LPDAs).  The method builds upon the three antenna method, but is conducted over a PEC ground plane in an Open Area Test Site (OATS).   Similar to the traditional three antenna method, three pairings of transmission measurements are taken.  In each measurement, one antenna is set at a fixed height above the ground plane, while the other antenna is scanned in height over 1 to 4 m heights.  Magnitude and phase responses between the two antennas are taken at multiple heights.  Measured results are fit to a theoretical model using a complex fit algorithm.   From this process, the gain and frequency dependent phase center locations of each antenna can be solved.   Measurement data show that it is effective in reducing systematic uncertainties associated with assuming fixed phase center locations.  In addition, unlike other calibration methods over a conducting ground plane, no assumptions are made about the antenna patterns.  This method provides an accurate, versatile and fast method for calibrating LPDAs from as low as 100 MHz.

Absolute GPS Antenna Calibration at the US National Geodetic Survey
Gerald Mader,Andria Bilich, November 2013

In this paper we describe the NGS calibration facility and calibration hardware, and discuss the motivation for providing calibration services. We provide the time-difference, single-difference carrier phase observable models and estimation strategy currently used to generate NGS absolute calibrations. Calibration examples are provided in the accompanying poster presentation.
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