Effective Aperture Distribution Research Articles

Enhanced Effective Aperture Distribution Function for Characterizing Large-Scale Antenna Arrays

Accurate characterization of large-scale antenna arrays is growing in importance and complexity for the fifth-generation (5G) and beyond systems, as they feature more antenna elements and require increased overall performance. The full 3D patterns of all antenna elements in the array need to be characterized because they are in general different due to construction inaccuracy, coupling, antenna array's asymmetry, etc. The effective aperture distribution function (EADF) can provide an analytic description of an antenna array based on a full-sphere measurement of the array in an anechoic chamber. However, as the array aperture increases, denser spatial samples are needed for EADF due to large distance offsets of array elements from the reference point in the anechoic chamber, leading to a prohibitive measurement time and increased complexity of EADF. In this paper, we present the EADF applied to large-scale arrays and highlight issues caused by the large array aperture. To overcome the issues, an enhanced EADF is proposed with a low complexity that is intrinsically determined by the characteristic of each array element rather than the array aperture. The enhanced EADF is validated using experimental measurements conducted at 27-30 GHz frequency band with a relatively large planar array.

DOA Based on Manifold Separation Technique and Dimensionality Reduction

In this paper, we investigate the high resolution of arbitrary array applied to wireless positioning system and propose a Direction of Arrival (DOA) estimation algorithm based on the Manifold Separation Technique (MST). In order to reduce the error of MST model caused by noise, this algorithm uses the MST to decompose the steering vector into sampling matrix (only describing the array itself) and Vandermonde form (only relating to the direction of arrival), the steering vector of arbitrary array is represented by combining the Effective Aperture Distribution Function (EADF). In order to reduce the complexity of Multiple Signal Classification (MUSIC) algorithm of two-dimensional array, the 2D spectral peak search is decomposed into two one-dimensional spectral peak searches using dimensionality reduction methods. Simulation results show that the algorithm not only reduces the computational complexity, but also has good performance of low signal to noise ratio (SNR).

Experimental Validation of a Wideband Metasurface for Wide-Angle Scanning Leaky-Wave Antennas

Beam scanning arrays typically suffer from scan loss; an increasing degradation in gain as the beam is scanned from broadside toward the horizon in any given scan plane. Here, a metasurface is presented that reduces the effects of scan loss for a leaky-wave antenna (LWA). The metasurface is simple, being composed of an ultrathin sheet of subwavelength split-ring resonators. The leaky-wave structure is balanced, scanning from the forward region, through broadside, and into the backward region, and designed to scan in the magnetic plane. The metasurface is effectively invisible at broadside, where balanced LWAs are most sensitive to external loading. It is shown that the introduction of the metasurface results in increased directivity, and hence, gain, as the beam is scanned off broadside, having an increasing effect as the beam is scanned to the horizon. Simulations show that the metasurface improves the effective aperture distribution at higher scan angles, resulting in a more directive main beam, while having a negligible impact on cross-polarization gain. Experimental validation results show that the scan range of the antenna is increased from $-39 {^{\circ }} \leq \theta \leq +32 {^{\circ }}$ to $-64 {^{\circ }} \leq \theta \leq +70 {^{\circ }}$ , when loaded with the metasurface, demonstrating a flattened gain profile over a 135° range centered about broadside. Moreover, this scan range occurs over a frequency band spanning from 9 to 15.5 GHz, demonstrating a relative bandwidth of 53% for the metasurface.

Quaternion-based polarimetric array manifold interpolation

In order to do direction of arrival (DoA) estimation the array manifold is needed. However, in practical scenarios the available calibration data is sampled on a finite grid only. Hence, a suitable beam pattern interpolation scheme is essential to perform high precision DoA estimation. A reasonable interpolation algorithm is present via the Effective Aperture Distribution Function (EADF). The EADF basically relies on a two-dimensional Discrete Fourier Transform of each beam pattern.Since the EADF does not inherently incorporate polarization two separate EADFs are needed to describe a single array element. Hence, we propose to use a Quaternion EADF (QEADF) that jointly interpolates both patterns. Moreover, since the QEADF is based on a Discrete Quaternion Fourier Transform it opens up some degrees of freedom with respect to the Fourier basis functions.

Unified Array Manifold Decomposition Based on Spherical Harmonics and 2-D Fourier Basis

In this paper, we derive a unified framework for orthonormal decomposition of the array manifold on scalar fields. Such fields are encountered in cases where polarization is not considered, e.g., single polarized radio waves and acoustic pressure. The results generalize and unify different decompositions of the array manifold, found in recent literature, to arrays of arbitrary geometry including conformal arrays. The concept of equivalence matrix is introduced, establishing a link between the spherical harmonics and 2-D Fourier basis functions. Under some mild assumptions that typically hold in practice, a one-to-one relationship between spherical harmonic spectra and 2-D Fourier spectra may be established. Additionally, it is shown that the rows of the equivalence matrix and the 2-D Fourier spectra of the array manifold span the same subspace. With such results the spherical harmonic and 2-D Fourier decompositions of the array manifold vector, i.e., Wavefield Modeling and 2-D Effective Aperture Distribution Function (EADF) are shown to be equivalent. Results on the modeling capabilities of both orthonormal decompositions are obtained. Moreover, the equivalence matrix is shown to facilitate noise attenuation. A fast spherical harmonic transform with complexity <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> log <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> ) can be obtained by exploiting the equivalence matrix, where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> represents the total number of points on the sphere. Finally, the equivalence matrix allows to gain more insight into the relation between rotating a function on the sphere and on the torus. These contributions facilitate high-resolution array processing both in elevation and azimuth irrespective of the array structure or imperfections.

Average Pattern and Beam Efficiency Characterization of Reflector Antennas with Random Surface Errors

Random errors on a reflector surface will result in antenna gain loss, beam efficiency reduction, and sidelobe level degradation. In this study, an improved mathematical model is presented for handling correlated random surface errors. The average power patterns of arbitrarily distorted antennas are determined by performing a complete numerical integration. Furthermore, in the case of a parabolic reflector antenna with random surface errors that have relatively short correlation length, the effective aperture distribution parameters, Be and pe, can be defined and analytically derived. Numerical data for a parabolic reflector antenna with dimensions recommended by a recent NASA study are generated to investigate the effects of uniform and linear random surface errors on power pattern, boresight gain loss, and beam efficiency. The results properly characterize the pattern degradation and the beam efficiency reduction as a function of random surface errors. For high beam efficiency and low sidelobe specifica...

Shaped reflector antenna analysis using the Jacobi-Bessel series

The physical optics approximation is employed to derive the radiation integral for a doubly curved offset reflector antenna illuminated by an arbitrary source. A novel procedure is presented for expressing the radiation integral in terms of a summation of Fourier transforms of an effective aperture distribution which includes the effect of the curvature of the surface. The Jacobi-Bessel series is used to evaluate the Fourier transforms. The vector nature of the far-field pattern is studied by evaluating its three Cartesian components in a unified fashion. The rapid numerical evaluations of the expressions obtained are demonstrated via extensive test cases. In particular, the scattering characteristics of symmetric and offset parabolic, spherical, and shaped reflectors are studied in detail, and comparisons are made with other available data.

Synthesis of a laterally displaced cluster feed for a reflector antenna with application to multiple beams and contoured patterns

When a feed is displaced from the focus of a reflector, phase distortion results in the effective aperture distribution, which in turn gives rise to secondary beam distortion. In multiple beam or contour beam antennas, the feed normally consists of an array of identical elements located on a triangular lattice. Taking advantage of this arrangement, a "cluster" of feed elements instead of a single element may be used to control each beam. By adjusting the relative excitations of the elements in a cluster, the aperture phase distortion due to the feed displacement may be partially compensated. Two general methods for synthesizing the excitations for a laterally displaced feed cluster are presented. In the first method the excitations are chosen to minimize the weighted phase error in the effective aperture by analytical means. The second method determines the excitations by a gradient optimization algorithm which minimizes the weighted error between an objective and the actual power patterns in the secondary pattern space. The first method is roughly two orders of magnitude more efficient computationally than the gradient optimization algorithm, but not as flexible in application or as precise. Numerical results are presented for cluster feed designs and their application to the synthesis of contour patterns.