An analysis of the complex fit normalized site attenuation method

For decades, site validation measurements below 1 GHz have been framed within the concept of Normalized Site Attenuation (NSA) proposed by Smith et al. in 1982. Conceptually, measured results are compared to a theoretical model, which is derived based on a raytracing model between two antennas over a conducting ground plane. It was quickly realized that the theoretical model cannot fully encompass the complexity of real antennas in geometries needed for site validation, and the individual antenna effects cannot be “normalized” entirely from the site attenuations by a simple subtraction (in dB) of the antenna factors. For dipole antennas, correction factors have been included to amend the errors (derived from numerical simulations). For broadband antennas, there had been no simple solution until Geometry-Specific Correction Factor (GSCF) was introduced in ANSI C63.5 in 2000. It may not have been immediately clear to users of the standards that since the introduction of GSCF, the Smith model NSA has been essentially bypassed. Of the two prescribed methods for site validations, the biconical GSCF provided in the form of correction values is based on a numerical model, while the measurement GSCF is a site-to-site comparison method. ANSI C63 can benefit significantly in clarity by removing the pretence of a simple theoretical dipole NSA model, and rewrite the site validation requirements directly in terms of either the numerical or the site-to-site comparison methods.

Complex Fit Normalized Site Attenuation (CFNSA) is an improved theoretical model for transmission between broadband antennas over a conducting ground plane. The CFNSA model overcomes the limitations of the original NSA model proposed by Smith, German and Pate, by allowing variable radiation pattern and variable phase center positions as a function frequency. The CFNSA model is well suited for log periodic dipole arrays (LPDAs) from 200 MHz to 1000 MHz because the variable phase centers and antenna pattern deviations relative to dipoles are the dominant source of errors. CFNSA has been shown to be effective to reduce systematic errors in the theoretical NSA model for LPDAs by up to 1 dB per antenna factor (or 2 dB in a site attenuation measurement). Antenna calibration and site validations above 1 GHz are increasingly addressed by using fully anechoic rooms (FAR). This makes earlier efforts to improve the CFNSA model above 1 GHz to be of limited application at present. This paper concentrates on improving the model for below 1 GHz. In this study, the antenna patterns are shown to be better represented by a piecewise function versus radiation angle, as compared to the earlier proposed functions, such as cosn θ, or polynomial functions. Efforts are also made to clarify the mathematical process, so that CFNSA can be adopted by the antenna calibration standards, e.g. ANSI C63.5.

In the ANSI C63.4 development of normalized site attenuation (NSA) for vertical polarization the E-field sine pattern generated by short dipoles was used to account for the additional attenuation that occurs as a function of the antenna patterns. A pattern dependent NSA equation is developed incorporating antenna pattern factors for any types of antennas for which mathematical expressions of the patterns exist. For resonant dipoles, biconicals and log-periodics the decibel differences from the existing standard have been found to be small, leading to increased confidence in the utility of the present standard.

For the validation of an open area test site usually the normalized site attenuation (NSA) is considered. However, the model for the calculation of the NSA in the various standards is a point dipole. While this may be a correct assumption for biconical antennas or reference dipoles with a well-defined phase center, it is wrong for the antennas used in an automotive antenna test setup. Measurements of automotive antennas for radio and TV reception generally are done on a dedicated test range consisting of a turntable that can bear the weight of the vehicle and a test antenna that is placed in a considerable distance in order to ensure far field conditions. For broadband measurements often log-periodic antennas are used. In these antennas the phase center is not known exactly for all frequencies. The phase center of the automotive antenna is not known either. This uncertainty in the position of the phase centers in combination with the ground reflection occurring between object under test and test antenna results in a measurement error that cannot be neglected. In this work we show how this error can easily be calculated for all test site geometries and give an exemplary calculation for the test site used at our company.

This paper describes an analysis methodology that implements the theoretical normalized site attenuation (NSA) model into a standard electronic spreadsheet program, such as Microsoft Excel, that can calculate and plot the exact theoretical NSA value for any given frequency of interest. The theoretical NSA is referenced in ANSIC63.4(1992) and is discussed in numerous papers in the open literature. The mathematical model for the theoretical NSA consists of a set of complex equations for horizontal and vertical polarization and is best suited for calculation via computer automation. The spreadsheet analysis technique addressed in this paper has several advantages: (1) the popularity of spreadsheets today provides an easy to use software platform that can be utilized to fully automate the complex theoretical NSA calculations,( 2) the spreadsheet provides an open framework whereby all areas of the model are open for visual inspection, and (3) the spreadsheet model can be used for "what-if" scenarios whereby the test site input parameters are easily modified and the calculations re-pun for new test site configurations.

The phase center location and the phase pattern for a 110 GHz corrugated horn were measured by a novel differential phase method. This method makes it possible to overcome problems associated with the complexity of the measurement setup and errors caused by the flexible cable or rotary joint required in the system. The phase center at 110 GHz is 2.7+or-0.3 mm from the aperture. The measurements agree very well with the results given by the modal matching technique. This technique predicts very accurately both the phase center position and the phase pattern.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The phase pattern of an antenna can be expressed with reference to an arbitrary point in space such that the phase over the range of directions of interest becomes constant. This point is called the phase center of the array, from where the antenna radiation appears to emanate. In general, an antenna does not have a unique phase center for all the directions of observation. This is due to the fact that theoretically a point emanates a spherical wavefront and the radiated wavefront from the array antenna, which has some finite dimensions, will not be therefore purely spherical with fixed curvature in all the direction of observations. The location of the phase center is a function of observation angle. An array antenna can be focused at some finite distance by moving the phase center of antenna and a flat-top beam can be obtained. This paper describes the effects of moving the phase center of an array antenna to change the shape of the beam by changing its beamwidth. It also discusses the movement of phase center in a planar array.

For a synthetic aperture radar (SAR) system, the platform attitude drift will affect the image qualities. During SAR system design computer simulation can be used to determine the attitude stability which can satisfy the users' demands. In the computer simulation, the first step is to create the mathematic model. General models of platform attitude drift are usually created in the time domain, such as the sinusoid one, and the model presented is done in the frequency domain. For each attitude angle (roll, yaw, pitch), the amplitude and phase values are first generated in the frequency domain. Because the attitude parameters are sampled with PRF (pulse repetition frequency) in SAR system, the maximum frequency is set to PRF/2. The amplitude may be changed with the frequency (for example, inversely proportional to the square of frequency), while the phase may be uniformly distributed between 0 to 2/spl pi/. Then the inverse Fourier transformation converts this data into the time domain. Because the phase center of the SAR's antenna is usually offset from the platform center, the attitude drift will change the slant range between the antenna's phase center and the target on the ground. These changes will affect the Doppler history in azimuth direction for the SAR. After these changes are simulated, the SAR raw data of a point target can be generated. With the general SAR procession, the simulated image is obtained. Using the analysis software, the authors can get the effects on the image qualities of the attitude drift. At last, the simulation steps and an example are also presented.

Using a very short baseline interferometer, the relative stability of the YEBE and YEB1 GPS stations at the Yebes Observatory (Spain) is assessed. A baseline length bias of 1 mm was found between estimates from different observed frequencies due most likely to phase center errors resulting from antenna calibration uncertainties and/or phase center migrations caused by the electromagnetic coupling of antenna and monument. Also a bias of 0.5 mm in the vertical component of the baseline length was found between estimates from different cut-off elevation angles due to elevation-dependent errors as phase center and multipath. In addition to these biases, significant variations in the horizontal component of the baseline length were found, mostly in the form of a trend of −0.45 ± 0.10 mm/yr and an annual oscillation of amplitude 1 ± 0.1 mm and phase 155 ± 5 (beginning of June). The annual oscillation showed a high correlation with ambient temperature variations. Bedrock thermal expansion seems not to be a significant contributor to the annual variation due to the excellent agreement between the phases of the baseline and temperature annual signals. Thermoelastic expansion of the station monuments, which are comprised of concrete pillars and buildings, driven by the sunshine heating, is likely the origin of this oscillation. Near-field multipath and phase center errors are also rejected as being the main contributor to the annual signal. Conversely, near-field multipath and phase center errors may significantly contribute together to the time-correlated noise content of the baseline time series at long periods (flicker noise amplitude of 1.2 ± 0.1 mm). This research provides thus an assessment of the GPS station stability at the Yebes Observatory, which may be extended to the level of station-dependent contamination of geophysical and geodetic studies (e.g., plate tectonics, surface loadings, local ties) when similar station installations on top of buildings are used.

The determination of multi-GNSS Differential Code Biases (DCBs) is crucial for improving both precise positioning and ionospheric modeling. While frequency-specific antenna phase center (APC) information for multi-GNSS is available, the IGS Analysis Centers have not yet fully incorporated APC calibrations into their DCB products. This study evaluates the effect of Antenna Phase Center (APC) corrections, specifically satellite Phase Center Offset (PCO) corrections, on multi-GNSS DCB estimation. Two correction strategies are proposed: (1) a rigorous approach applied during DCB estimation, and (2) an approximate approach that adjusts existing DCB products using z-PCO corrections. Through a six-month analysis, i.e., July–December 2022, we show that PCO-corrected DCB products exhibit high consistency, with root mean square differences of less than 0.1 ns compared to DLR's PCO-corrected DCB products. Positioning tests with 20 MGEX stations demonstrate notable accuracy improvements for SF-PPP when applying PCO-corrected DCBs, including a 20.3% increase for GPS and a 13.1% improvement for BDS-3. SFIC-PPP results further show convergence time reductions of 54.9% for GPS and 10.7% for BDS-3. Since June 2022, the newly generated CAS PCO-corrected DCB products have been routinely provided to the International GNSS Service (IGS).

The anti-jamming antenna is one of the most efficient ways to resist the adversary effect of the interference signal in GNSS positioning. Most anti-jamming antennas can adaptively adjust the radiation figure of the antenna to minimize the interference impact. A side effect of changing the radiation figure is that the antenna phase center (APC) is also changed accordingly. Meanwhile, a stable phase center is a prerequisite for high precision GNSS positioning, thus the anti-jamming and high-precision becomes a dilemma for the GNSS antenna design. This study proposed an efficient antenna phase center variation (PCV) compensation algorithm for the anti-jamming antennas which enables real-time high-precision applications with the anti-jamming antennas. The performance of the algorithm is evaluated with the short baseline tests, and the results indicate that the proposed algorithm can reduce the carrier phase residuals by compensation of the anti-jamming antenna PCV and consequently, the 3D root mean squares (RMS) of real-time kinematic (RTK) positioning in two experiments is improved by 42.3% and 9.7% respectively. After PCV correction, the RTK positioning with the anti-jamming antennas achieves better than 4 cm accuracy.

Initiating an error budget of the DORIS ground antenna position: Genesis of the Starec antenna type C

This paper presents a novel polarimetric near-field two-dimension (2D) synthetic aperture focusing technique (SAFT) suitable for ground penetrating radar (GPR) application. The imaging algorithm is intended for locating metallic and non-metallic anti-personnel (AP's) mines using an ultra-wide-band stepped frequency radar. A radar image can be formed by coherently integrating the backscattered field over the measured frequency spectrum and cross-range scan. The coherent integration is essentially a convolution of the collected data and a focusing (test) function, which only depends on the geometry of the measurement. Wavefront curvature must be taken account of when attempting to image an object within 1-2 wavelengths off an antenna(s) phase center. Applying conventional far-field SAR imaging using a direct Fourier inversion may result in images which are increasingly blurred and shifted at points more distant from the point of rotation of the focusing function. Here, a focusing function is first derived based on a conventional far-field geometrical optic propagator for a two-media problem. Then to correct for geometric distortion in the focusing function when applied in the near-field zone we introduce higher order terms to the range function. In order to verify and augment the technique described two field studies were conducted, over different frequency spectrums, the finding of which demonstrates the utility of the technique and the experimental practices.

Three major GPS antenna calibration methods are available toda: the relative field calibrations using the GPS data collected on short baselines, the absolute field calibrations, where the GPS antenna is rotated and tilted by a robot, and calibration measurements in an anechoic chamber. Mean antenna offsets and the elevation-dependent phase center variations of GPS antennas determined by all three techniques are compared to assess their accuracy. The analysis of global GPS data with these sets of calibration values reveals that the offsets and variations of the satellite antenna phase centers have to be considered, too, to obtain a consistent picture. © 2001 John Wiley & Sons, Inc.

This paper expatiates on the definition and solution of antenna phase center in planar near field. It provides the method of error analysis modeling and the 18 error items of phase pattern. And the final boundary of the error is obtained by error synthesis method. Based on error matrix, Monte Carlo method is employed for error analysis of phase center.