Equispaced Linear Array Research Articles

Fast quasi-null-filling of radiation patterns for multiple solutions generation

Here we present an improved, rapid method for filling quasi-nulls in symmetrical radiation patterns synthesized by equispaced linear arrays, leading to the generation of multiple solutions. Considering the polynomial representation of the pattern, this null-filling is achieved by displacing the roots radially off the unit circle, keeping a constant displacement. This allows analyzing how the potential solutions vary with the quasi-uniform filling and the associated directivity loss. This method is based on the Cardano-Vieta relations, which link the coefficients of a complex Schelkunoff polynomial with its roots. As examples of application, we have considered a 20/100 element Dolph-Chebyshev pattern, with a spacing between the elements λ/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda / 2$$\\end{document}, side lobe level of − 20/− 28 dB and three inner sidelobes at − 40/− 50 dB.

On-Board Wide Broad Bandwidth Switching Linear and Planar Antenna Arrays for Industrial Use in an Era of Industrial Revolution

The paper outlines the analysis of horn antenna and arrays of microstrip antenna for onboard high data rate transmission in the X-Band ( 10 Ghz). The antenna arrays consists of eight equispaced linear array elements with beam formation and gain of 20 dB. In satellite communication, we require the transmission of waves which are circularly polarized. This is achieved by placing helical antenna elements, which has the advantage that the antenna is broadband and transmission is circularly polarized. This paper also considers method of feeding the linear array, where only a first few elements produce radiation and the pattern is highly distorted. Linear array feed from both ends will produce uniform excitation so that the entire array is excited, with low distortion of pattern.

Terahertz reflection imaging using virtual arrays and MUSIC in a synthetic aperture array

Terahertz imaging using synthetic aperture arrays (SAAs) is an attractive nondestructive measurement method, as it can increase the spatial resolution while reducing the restrictions on target placement. MUltiple SIgnal Classification (MUSIC), which is a high-resolution direction of arrival estimation method, is also attractive because it increases the resolution of terahertz imaging. However, the resolution of the MUSIC spatial spectrum deteriorates when correlated signals are received. Spatial smoothing (SS) can reduce the correlation of incoming waves; however, this technique is only applicable to equispaced linear arrays in plane wave reception environments. This paper introduces MUSIC with SS to THz imaging using an arcuate SAA by applying array interpolation using virtual arrays. The imaging results and position estimation accuracy using simulated or measured arcuate synthetic array responses of two metal wire targets demonstrate the effectiveness of the method compared with the conventional beamformer and MUSIC methods.

Multiple Solutions Starting from Real Shaped Beams in Equispaced Linear Arrays.

In the present work, the theoretical basis of the multiplicity of solutions obtained from an initial real symmetric distribution is derived. This initial solution is devoted to generating an equivalent pure real shaped-beam pattern for a concrete synthesis scenario. However, these new solutions are not based on real symmetric distributions; hence, not based on the generation of pure real patterns. The bandwidth performances and tolerance to errors provided by the multiple solutions in the array design are analyzed by considering different architectures, also including mutual coupling models and element factor expressions due to accuracy purposes. In addition, a technique to obtain efficient linear arrays by designing resonant structures is addressed. Examples involving both standard linear arrays of half-wavelength cylindrical dipoles and resonant linear arrays generating flat-top beam patterns are reported and discussed. Additionally, an extension to planar arrays performed by means of a generalisation of the Baklanov transformation through collapsed distribution techniques inspired in the well-known method devised by Tseng and Cheng is performed. In such a way, an analysis of the quality of solutions for generating circular and elliptical footprints with controlled both SLL and ripple which are highly interesting in the framework of space vehicle applications.

On bandwidth maximization of fixed-geometry arrays through convex programming

ABSTRACTWe propose a new approach to solve the problem of optimal power synthesis of array antennas, so that maximum possible bandwidth can be granted to fixed sidelobe-level performances. The proposed approach can be applied to any kind of fixed-geometry array that radiates pencil beams and to linear equispaced arrays that generate shaped patterns. The designing problem is cast as a sequence of Convex Programming optimizations. Numerous numerical experiments, including full-wave synthesis of realistic antennas, were carried out and their results discussed here to assess the array antennas’ capability of achieving ultra-wideband performances.

Physical electrostatics of small field emitter arrays/clusters

This paper aims to improve qualitative understanding of electrostatic influences on apex field enhancement factors (AFEFs) for small field emitter arrays/clusters. Using the “floating sphere at emitter-plate potential” (FSEPP) model, it re-examines the electrostatics and mathematics of three simple systems of identical post-like emitters. For the isolated emitter, various approaches are noted. An adequate approximation is to consider only the effects of sphere charges and (for significantly separated emitters) image charges. For the 2-emitter system, formulas are found for charge-transfer (“charge-blunting”) effects and neighbor-field effects, for widely spaced and for “sufficiently closely spaced” emitters. Mutual charge-blunting is always the dominant effect, with a related (negative) fractional AFEF-change δtwo. For sufficiently small emitter spacing c, |δtwo| varies approximately as 1/c; for large spacing, |δtwo| decreases as 1/c3. In a 3-emitter equispaced linear array, differential charge-blunting and differential neighbor-field effects occur, but differential charge-blunting effects are dominant, and cause the “exposed” outer emitters to have higher AFEF (γ0) than the central emitter (γ1). Formulas are found for the exposure ratio Ξ = γ0/γ1, for large and for sufficiently small separations. The FSEPP model for an isolated emitter has accuracy around 30%. Line-charge models (LCMs) are an alternative, but an apparent difficulty with recent LCM implementations is identified. Better descriptions of array electrostatics may involve developing good fitting equations for AFEFs derived from accurate numerical solution of Laplace's equation, perhaps with equation form(s) guided qualitatively by FSEPP-model results. In existing fitting formulas, the AFEF-reduction decreases exponentially as c increases, which is different from the FSEPP-model formulas. This discrepancy needs to be investigated, using systematic Laplace-based simulations and appropriate results analysis. FSEPP models might provide a useful provisional guide to the qualitative behaviour of small field emitter clusters larger than those investigated here.

Comparative Studies on Generation of Stair Step Radiation Patterns

Antenna array synthesis is usually done by controlling amplitude and phase levels or element spacing functions of the array to get the desired characteristics of the radiation pattern. In this paper, design of equispaced linear array of dipoles is presented. A new amplitude distribution is proposed for generation of stair step patterns with zero phase. These patterns are produced from dipole elements using Fourier transform method. The goal of the work is to compensate mutual coupling effects of a linear dipole array. The computed patterns are compared with those of the isotropic elements for different number of elements. The deviation in the patterns of array of isotropic radiators and the array of practical element is found to be minimum. These patterns are used to identify multiple targets moving in different altitudes and different angular regions.

Ergodic Capacity Optimization for Single-Stream Beamforming Transmission in MISO Rician Fading Channels

The maximization of the ergodic capacity for single-stream beamforming, which is a (constrained) transmission scheme referred to as “optimum beamforming,” has been extensively addressed in the open literature for multiple-input-single-output (MISO) Rayleigh fading channels and spatially uncorrelated MISO Rician fading channels with a unit transmit covariance matrix, and closed-form solutions have been derived for these cases. However, optimum beamforming for spatially correlated or uncorrelated MISO Rician fading channels with a nonunit transmit covariance matrix has received less attention and remains a complex multidimensional optimization problem. This paper first proves that this convex constrained optimization problem can be reduced to only one dimension; hence, it can be solved very fast using standard 1-D search algorithms. Then, simulations mainly performed for linear equispaced antenna arrays demonstrate that: 1) the proposed method for the calculation of the optimum beamformer has significantly lower computational complexity compared with other currently used multidimensional algorithms; and 2) the optimum beamformer further improves capacity compared with the (single-stream) beamforming transmission that maximizes the signal-to-noise ratio (SNR) at the receiver, whereas in some operational environments, it achieves ergodic capacity that is very close or equal to the maximum ergodic capacity.

FDK-Type Algorithms with No Backprojection Weight for Circular and Helical Scan CT.

We develop two Feldkamp-type reconstruction algorithms with no backprojection weight for circular and helical trajectory with planar detector geometry. Advances in solid-state electronic detector technologies lend importance to CT systems with the equispaced linear array, the planar (flat panel) detectors, and the corresponding algorithms. We derive two exact Hilbert filtered backprojection (FBP) reconstruction algorithms with no backprojection weight for 2D fan-beam equispace linear array detector geometry (complement of the equi-angular curved array detector). Based on these algorithms, the Feldkamp-type algorithms with no backprojection weight for 3D reconstruction are developed using the standard heuristic extension of the divergent beam FBP algorithm. The simulation results show that the axial intensity drop in the reconstructed image using the FDK algorithms with no backprojection weight with circular trajectory is similar to that obtained by using Hu's and T-FDK, algorithms. Further, we present efficient algorithms to reduce the axial intensity drop encountered in the standard FDK reconstructions in circular cone-beam CT. The proposed algorithms consist of mainly two steps: reconstruction of the object using FDK algorithm with no backprojection weight and estimation of the missing term. The efficient algorithms are compared with the FDK algorithm, Hu's algorithm, T-FDK, and Zhu et al.'s algorithm in terms of axial intensity drop and noise. Simulation shows that the efficient algorithms give similar performance in axial intensity drop as that of Zhu et al.'s algorithm while one of the efficient algorithms outperforms Zhu et al.'s algorithm in terms of computational complexity.

Fourier Synthesis of Linear Arrays Based on the Generalized Scattering Matrix and Spherical Modes

This paper presents a novel, simple pattern synthesis procedure for linear equispaced arrays which can be characterized by a generalized scattering matrix (GSM) and whose radiated field can be expressed as a weighted sum of shifted spherical waves. It can be viewed as an extension of the classic design techniques of the Fourier series (FS) method or the Woodward-Lawson frequency sampling method, to the case in which the individual antenna elements' patterns and all interelement couplings are taken into account. The design procedure, which yields the excitations needed to achieve the desired pattern, is based on either the FS or the discrete Fourier transform (DFT) of the spherical mode expansion of the array radiated field, as well as on various properties associated to the FS or DFT coefficients. In this work, to compute the GSM of the array and the spherical mode expansion of the field, a validated hybrid full-wave methodology, based on the finite element method and rotation and translation properties of spherical waves, is used. Numerical results of different synthesized array patterns are presented for different arrays made up of dielectric resonator antennas and cavity-backed microstrip circular patches.

Rapid Method for Finding Faulty Elements in Antenna Arrays Using Far Field Pattern Samples

A simple and fast technique that allows a diagnosis of faulty elements in antenna arrays, that only needs to consider a small number of samples of its degraded far-field pattern is described. The method tabulates patterns radiated by the array with 1 faulty element only. Then, the pattern corresponding to the configuration of failed/unfailed elements under test is calculated using the error-free pattern and the patterns with 1 faulty element. The configuration with the lowest difference between the calculated and the degraded patterns is selected. Comparison of the performance of this method using an exhaustive search and a genetic algorithm for an equispaced linear array of 100 lambda/2-dipoles is shown. Mutual coupling as well as noise/measurement errors in the pattern samples were considered in the numerical analysis.

Synthesis of a Uniformly Spaced Array with Symmetric Amplitude Excitation by a Weighted Least-Square Method

A new, non-iterative technique for synthesizing equispaced linear arrays with symmetric excitation is proposed. The methods is on the computation of an eigenvector of an appropriate real, Symmetric and positive-definite matrix. This technique can be used to determine, given a n complete description of the desired radiation pattern, the array excitation coefficients . These derived excitation will produce, either exactly or approximately, the wanted antenna radiation pattern, depending on its complexity and the number of my elements. A number of design examples are presented to illustrate the practicality and the potential of the proposed method.

Use of genetic algorithms in linear and planar antenna array synthesis based on Schelkunoff method

AbstractGenetic algorithms coupled with the Schelkunoff synthesis method are used to synthesize equispaced linear and planar arrays. The purpose is to find the different excitation amplitudes and phases to achieve good matching between the desired and calculated radiation patterns. Examples which demonstrate the versatility of the approach presented in this article are considered for various patterns including the steered pattern case. The planar array is treated as a set of two separate linear arrays upon which Schelkunoff method is applied separately. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1619–1623, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22510

Efficient computation of the 3D Green’s function for the Helmholtz operator for a linear array of point sources using the Ewald method

The Ewald method is applied to accelerate the evaluation of the Green’s function (GF) of an infinite equispaced linear array of point sources with linear phasing. Only a few terms are needed to evaluate Ewald sums, which are cast in terms of error functions and exponential integrals, to high accuracy. It is shown analytically that the choice of the standard “optimal” Ewald splitting parameter E 0 causes overflow errors at high frequencies (period large compared to the wavelength), and convergence rates are analyzed. A recipe for selecting the Ewald splitting parameter is provided.

Estimates of bio-sonar characteristics of a free-ranging Ganges river dolphin

This paper reports the first known studies of the bio-sonar characteristics of an isolated free-ranging Ganges river dolphin, Platanista gangetica. The animal preferred to roam in a deeper tract of the otherwise shallow river. The click sounds of the dolphin were recorded over a period of 2 days on a 3.2-meter-long high-frequency hydrophone array composed of three hydrophones forming an equispaced linear array and another two hydrophones in conjunction with the central hydrophone forming an SSBL triangular array in a plane perpendicular to the array axis. The array was deployed both in horizontal and vertical configurations. The array structure provided 3-D measurements of the source location through measurement of the interelement time delay. Bio-sonar characteristics such as click duration, bandwidth, and interclick intervals in click trains have been reported. Measurements of dolphin track and the relative click levels on the array hydrophones have been used to obtain a preliminary characterization of the animal’s beam pattern.

Theoretical analyses of gain and phase error calibration with optimal implementation for linear equispaced array

In array signal processing, high-resolution direction-of-arrival (DOA) estimation algorithms are known to be sensitive to system errors. In practice, the system should be properly calibrated before DOA estimation. In this paper, a calibration method of gain and phase errors of linear equispaced arrays (LEAs) is considered. A class of simplified calibration algorithms based on different diagonal lines of the covariance matrix is proposed. The statistical performance analyses of the calibration algorithms due to finite data perturbations are presented. Expressions for average bias (Abias) and square root of average variance (SRAV) of the calibration algorithms are derived using first-order approximation. These statistical and computer simulation results reveal and explain why the more diagonal lines that are used for gain and phase error estimations, the more inferior performance that may be obtained. Based on this conclusion, the simple and optimal gain and phase error calibration algorithms for such model are obtained.

Optimizing uniformly excited linear arrays through time modulation

The letter shows that, by the proper use of time modulation in equispaced linear arrays with uniform excitation distribution, it is possible to maintain the sidelobe zone of the radiated power below a certain - previously stipulated - level, whereas the undesired harmonics are minimized. In addition to that, the further extension of the technique to non-equispaced arrays permits a broadband response to be obtained, by simply searching the positions of the elements that reach the desired power pattern behavior within the required bandwidth.

A new approach for speaker tracking in reverberant environment

A scheme for detecting and locating speech signals in the presence of reverberations using a linear array is proposed. The equispaced linear array with a plurality of omni-directional microphones is decomposed into two groups. Pairs of virtual and steerable directional microphones are then generated by using the frequency invariant beamforming technique for time delay estimations. This enables the microphone array to behave like ears in a human-like fashion to enhance the likelihood of valid speaker direction estimation. Additional decision rules are incorporated to enhance the robustness of the scheme.

Linear array pattern synthesis optimizing array element excitations using the simulated annealing technique

A numerical pattern synthesis technique for equispaced linear arrays that allows us to obtain shaped patterns with a specified sidelobe and ripple level adhering to a desired array element excitation is described. The method perturbs the roots of the array factor in order to find the optimal sidelobe and null-filling topography of the pattern associated with a desired aperture distribution. Application to a shaped cosec2 θ-pattern using a cosine-type tamplitude distribution is presented. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 23: 224–226, 1999.

Phase-Only Null Fixing in Equispaced Linear Arrays Using Roots Searching

A method for fixing nulls with phase-only control in equispaced linear arrays is presented. The method uses the polynomial roots associated to the power pattern of an equispaced linear array along with the simulated annealing technique. In addition, the method minimizes the sidelobe level and can be easily modified to obtain power patterns with desired nulls depth, without fixing any null (only the sidelobe level is lowered) or patterns with fixed nulls and controlled sidelobe level without null filling. Examples of an equispaced 20-element linear array are shown.