Superdirective Array Research Articles

Superdirective Wideband Array of Circular Monopoles with Loaded Patches for Wireless Communications.

A wideband superdirective array, composed of a two-element circular monopole configuration, is introduced. The monopoles are placed in close proximity, facing each other on a metal ground. To ensure good matching at high frequencies, two pairs of elliptical patches are added to the sides of the monopoles, enhancing the surface current of the circular patch for wideband performance. To achieve equal amplitude excitation and the desired phase difference, a wideband power divider with a phase shifter is designed to feed the antenna array. Simulation and measurement results demonstrate that the proposed wideband antenna array, operating within the frequency range of 2.94-7.93 GHz, exhibits a maximum directivity of 8.36-10 dBi, with an antenna efficiency ranging from 47.86 to 83.18% across the bandwidth. The proposed array has the advantages of miniaturization, high directivity and wideband operation and can be widely used in various portable wireless communication systems, including WLAN (5.05-5.9 GHz), ISM (5.725-5.875 GHz), 5G communication (3.3-3.8 GHz), etc.

Compact and High-gain Magnetic Dipole Antennas Utilizing Superdirective Array Excitation Condition

Compact and High-gain Magnetic Dipole Antennas Utilizing Superdirective Array Excitation Condition

The Statistics of Superdirective Beam Patterns

Superdirective arrays have been extensively studied because of their considerable potential accompanied, unfortunately, by a high sensitivity to random errors that affect the responses and positions of array elements. However, the statistics of their actual beam pattern (BP) has never been systematically investigated. This paper shows that the Rician probability density function (PDF), sometimes adopted to study the impact of errors in conventional arrays, is a valid approximation for superdirective BP statistics only where some mathematical terms are negligible. The paper also shows that this is the case for all linear end-fire arrays considered. A similar study is proposed concerning the correlation between BP lobes, showing that for the superdirective arrays considered the lobes, especially non-adjacent ones, are almost independent. Furthermore, knowledge of the PDF of the actual BP allows one to define quantile BP functions, whose probability of being exceeded, at any point, is fixed. Combining the lobes’ independence with quantile BP functions, an empirical equation for the probability that the entire actual BP will not exceed a quantile function over an interval larger than a given size is obtained. This new knowledge and these tools make it possible to devise new methods to design robust superdirective arrays via optimization goals with clearer and more relevant statistical meaning.

Superdirective dimers of coupled self-resonant split ring resonators: Analytical modelling and numerical and experimental validation

Superdirective antennas developed over the last century have received renewed interest in recent years from the development of metamaterials. These arrays of electromagnetic resonators (or meta-atoms) carrying short wavelength electro- and/or magneto-inductive waves support current distributions with very high spatial frequency as required by the classical conditions for superdirectivity. As meta-atoms can have both electric and magnetic dipole characteristics (and hence radiation properties), developing antennas exploiting these distributions can challenge conventional intuitions regarding the optimal configurations required. In this work we are reporting the development of a genuinely superdirective array using split ring resonators (SRRs). We provide a comprehensive analytical model characterizing the radiation from SRR dimers in which excitation of only one split ring leads to superdirective radiation via mutually coupled modes. Our model exploits simple circuit descriptions of coupled resonant circuits, combined with standard radiation formulae for curvilinear current distributions. Using this simple model we are able to map directivity against possible SRR locations and orientations in two dimensions and identify the unique optimal configuration which meets the requirements for superdirective emission. We validate the theoretical findings by comparison to both full wave simulations and experiments showing that our SRR dimer achieves endfire directivity very close to the maximum theoretical value.

A Correlation Theory of Antenna Directivity With Applications to Superdirective Arrays

We develop a general approach to antenna directivity by combining the infinitesimal dipole model (IDM) and the cross-correlation Green's function (CGF) in a new formulation. The theory is deployed for the analysis and synthesis of antenna systems via the proposed IDM-CGF method after integration with global optimization algorithms. The IDM-CGF theory opens the door for hitherto unexplored connections between applications involving antenna gain engineering on one side, and multiple-input–multiple-output (MIMO) and diversity methods on the other, helping to devise new techniques for applications like massive MIMO and millimeter-wave beamforming algorithms, wireless power transfer, in-package antennas, and full three-dimensional isotropicity.

Incoherent Synthesis of Sparse Arrays for Frequency-Invariant Beamforming

Frequency-invariant beamformers are used to prevent signal waveform distortions in real world applications like audio, underwater acoustics, and radar. Most of existing methods assume uniform arrays, and only few consider sparse designs, which may lead to higher performance in terms of robustness and directivity factor. We propose an incoherent approach that first determines for each frequency bin a sparse set of sensors positions. Subsequently, by using tools of dimensionality reduction and clustering, these selections are merged together yielding the optimal sensors on a sparse array layout. We present design examples of sparse linear and planar superdirective array designs. We show that the proposed incoherent sparse design obtains superior performance in terms of white noise gain, directivity factor, and computational load compared to a uniform array design and compared to a coherent sparse approach, where the sensors’ locations and the beamformer coefficients are optimized simultaneously for all frequencies.

Superdirective beamforming applied to SWellEx96 horizontal arrays data for source localization.

Arrays employing superdirective beamforming can provide the same directivity and directivity index (or array gain) with less aperture as a large size array using conventional beamforming (CBF). Superdirective arrays offer a practical and significant improvement in the reception of low frequency signals and is useful for many applications where the array size is limited, such as a miniature microphone array or an underwater acoustic array with a limited aperture. Deconvolving the CBF is a method of superdirective beamforming. The improvement in directivity (beam width) and array gain is studied/illustrated using the SWellEx96 horizontal array data where only sub-arrays are used.

Characteristic Modes Approach to Design Compact Superdirective Array With Enhanced Bandwidth

Superdirective arrays have become the key technique in enhancing the directivity of electrically small antennas. By forming an array of closely spaced unit elements, a high directivity can be achieved. Despite the high directivity, these arrays suffer from narrow bandwidth and low efficiency. In this paper, we present an approach to enhance the bandwidth of superdirective arrays using the network characteristic modes. The key step is to use an internally loaded compact wideband unit element. The loads inside the unit element are used to manipulate the characteristic modes in order to optimize its impedance bandwidth. A two-element endfire array is then formed. The modal coefficients of the characteristic fields are then optimized at multiple frequency points in order to radiate a maximal directivity in the endfire direction. The best current excitation that can maintain a constant directivity as a function of frequency is then deduced. Finally, a feeding network that can provide the desired excitation at the array ports is designed and integrated on the array system, where the 1 dB directivity bandwidth is about 23% with $D_{max}=7.1$ dBi. The antenna impedance bandwidth is equal to 15%.

Synthesis of Sparse Linear Array for Directional Modulation via Convex Optimization

The design of a directional modulation (DM) signal by a phased array is one of the important topics in the field of physical layer security communication. In this paper, we synthesize a sparse array for DM based on convex optimization. The main idea is that a nonconvex optimization problem associated with $\ell _{0}$ -norm is formulated for synthesizing a sparse array. To solve this nonconvex optimization problem, two different solutions are employed to relax the nonconvex optimization problem in a convex way: one is based on iterative reweighted $\ell _{1}$ -norm resulting in a superdirective array, the other is based on mixed integer programming resulting in a nonsuperdirective array. Furthermore, multiple important metrics of a DM transmitter, such as power efficiency, information beamwidth, and dynamic DM signal, are also considered in the optimization problem to achieve better performance of the DM signal via a sparse array. Simulation results show that the proposed synthesis method provides greater flexibility of controlling the security performance, power efficiency, and static or dynamic DM signal while the number of excitations is less than the uniformly spaced linear array in the benchmark problems.

Second-order cone programming with probabilistic regularization for robust adaptive beamforming.

Probabilistic regularization (PR) is introduced to make superdirective array beamforming robust against sensor characteristic mismatches. The objective is to enlarge the directivity while ensuring robustness with high probability. The PR problem is solved via the second-order cone programming where the regularization parameter is chosen through a statistical analysis of the system perturbations, based on Monte Carlo simulations. Experiments are carried out on a miniaturized 3 × 3 uniform rectangular array without calibration. The results show that for this particular array, the PR method is robust to sensor mismatches and achieves a higher level of directivity compared with other robust adaptive beamforming approaches.

Existence of Superdirective Radiation Modes in Thin-Wire Nanoloops

The problem of obtaining broadband superdirective radiation from an electrically small, easy to manufacture antenna is among the most challenging and elusive problems in electromagnetics. Superdirective arrays tend to be narrowband and sensitive to tolerancing, while a single superdirective radiator typically requires a very complicated and difficult to manufacture design. In this Article, we report on a new and transformative discovery, the fact that broadband superdirectivity naturally occurs for a single thin-wire nanoloop of the appropriate material composition and size. Full-wave simulations have revealed end-fire directivity of above 4.0 (6 dBi) for a nanoloop with radius less than 0.2 wavelength. This surprising phenomenon is explained in two ways: by comparison with two-element superdirective arrays and via a spherical multipole decomposition. This finding offers a solution to the problem of the inherently short-range communication of nanodevices and thus had the potential to strongly impact the f...

Design of a Super Directive Four-Element Compact Antenna Array Using Spherical Wave Expansion

In this paper, a super directive four-element compact parasitic antenna array has been designed and optimized using an ad hoc procedure based on the Harrington maximum directivity definition and spherical wave expansion. The complete design procedure (i.e., calculation of the optimum excitation coefficients and equivalent impedance loads associated to each parasitic element) is presented and validated through full-wave electromagnetic simulations. The proposed array has been designed at 868 MHz; its electrical size is $0.45 \lambda_0 \times 0.36 \lambda_0$ (diameter of minimum sphere circumscribing the antenna equal to $0.57 \lambda_{\bm{0}}$ ). A prototype has been built and tested to demonstrate the effectiveness of this design. A maximum directivity of 11.7 dBi has been measured at 871 MHz in satisfactory agreement with theoretical results and electromagnetic simulations.

Small aperture microphone arrays

Superdirectional microphone arrays are arrays that are typically smaller than the acoustic wavelength and attain directional gains that exceed those of a classical delay-sum beamformer. Early superdirectional microphones utilized a combination of a velocity microphone along with a pressure microphone. Later, a single sensor superdirectional microphone was discovered that utilized the combination of pressure and pressure-difference (which is proportional to the acoustic particle velocity) through appropriate porting of the incident acoustic field to both sides of the microphone diaphragm. In the early 1980s, with the advent of multichannel FFT analyzers, there was a renewed interest in using superdirectional microphone arrays to estimate the acoustic intensity and to calculate the acoustic power flow from sources. The estimation of the vector acoustic intensity led to many transducer designs that utilized up to 6 pressure microphones and commensurate signal processing. In this talk we will show some of the early acoustic intensity probes that were designed to estimate the acoustic intensity. These small arrays have been utilized in many other beamforming applications. We will show one where a superdirectional beamformer is also capable of source direction finding by utilizing some simple adaptive beamformer implementations.

Maximum directivity of arbitrary dipole arrays

A fully analytical form, more general than any reported previously, for the optimum current distribution and maximum directivity of an arbitrary array consisting of dipoles parallel with each other, is derived. For an array configuration consisting of several hundred elements, a calculation takes a fraction of a second making many-element superdirective arrays candidates for adaptive antenna applications. Examples for two-dimensional (2D) and 3D arrays are given and some earlier superconductive arrays are revisited. It is also shown in further examples that superconductivity is not incompatible with moderate values of the quality factor.

Design of an Optimum Superdirective Beamformer Through Generalized Directivity Maximization

Maximization of the directivity with a constraint on the lower bound of the white noise gain is a typical strategy used to attain robust performance in superdirective arrays. However, array imperfections and sensor mismatches significantly reduce the nominal directivity, even in robust designs. We focus on the generalized directivity (i.e., the directivity of the mean beam power pattern, computed using the probability density functions of the array errors) as a reliable metric to assess the average performance. We show that the generalized directivity is an extension of the nominal directivity, corresponds to the array gain when the array errors are considered, and is strictly related to the mean directivity. We demonstrate that, unlike the mean directivity, the generalized directivity of a linear array (under fair assumptions for gain, phase, and position errors) can be computed in closed form. Starting from this result, we propose a method to analytically compute, through the generalized eigenvalues, the weight vector that maximizes the generalized directivity. The numerical results confirm that maximizing the performance by setting a lower bound for the white noise gain a priori is a critical operation. Differently, maximization of the generalized directivity directly provides the optimum average performance. Notable advantages in designing maximum directivity arrays and in achieving the maximum degree of superdirectivity are reported, particularly for linear arrays steered at end-fire.

Optimal beamformer designed for robustness against channel mismatch based on Monte Carlo Simulation

Design of beamformers that withstand mismatch in channel characteristics of gain, phase, and position has been a key issue in array signal processing. These mismatch factors are random in nature and generally intractable by deterministic approaches. This paper examines the effects of channel mismatch on beamformer performance from a statistical perspective. The aim of this work is twofold: analysis and synthesis. In the analysis phase, the mismatch factors of microphone characteristics are assumed to be random variables following either uniform or Gaussian distribution. In the light of the Monte-Carlo Simulation (MCS), statistics including the mean, maximum, minimum, and the probability density function (pdf) of Directivity Factor (DF) can be efficiently obtained with random sampling. This provides useful information for choosing performance measures in the next synthesis phase. Optimal parameters of superdirective array designed using least squares (LS) and convex optimization (CVX) are determined based on the preceding performance measures. Simulation results have shown that the proposed statistical approach with different performance measures provided various performance-robustness tradeoffs in terms of parameter range for optimal beamformers.

Reply to “Comments on `Superdirective-Type Near Fields in the Method of Auxiliary Sources'”

Summary form only given, as follows. We would like to Dr. Skobelev for bringing to the authors' attention the paper by N.P. Malakshinov and V.G. Yerikhov: On one numerical method for solving diffraction problems in Antennas, no. 25, pp. 53-65, 1977 (in Russian), which, to the best of their knowledge, has not been translated into English. Having now located and read the interesting paper by N.P. Malakshinov and V.G. Yerikhov the authors' of the above-named article (ibid., vol. 60, no. 6, pp. 3056-3060, June 2012) agree with Dr. Skobolev that the IEEE article discusses relations between the Method of Auxiliary Sources (MAS) and superdirectivity in more detail than in the Russian article. In the IEEE article the authors go beyond the rather obvious similarity that both MAS and superdirective arrays exhibit oscillating currents. Rather, they focus on developing asymptotic formulas for the near field that allow one to distinguish the superdirective-type behaviors in MAS from effects due to roundoff. They cannot agree with Dr. Skobelev's comment ... creates the impression that its authors were the first and only ones who detected the indicated analogy; in fact, in the Acknowledgment of the Russian article Malakshinov and Yerikhov thank Professor Ramakrishna Janaswamy for first suggesting the relationship between MAS and superdirectivity.

Comments on “Superdirective-Type Near Fields in the Method of Auxiliary Sources”

Summary form only given. The authors of [1] have pointed out some analogies taking place between auxiliary currents and near fields in the method of auxiliary sources (MAS) from one side and the currents and near fields of superdirective antennas from another side. Their observations are based on the results obtained in the previous papers published by G. Fikioris and his coauthors since 2006. The paper [1] creates the impression that its authors were the first and only ones who detected the indicated analogy. In fact, that analogy has been known since the second half of 1970s when the first papers introducing the MAS started to appear in the literature. In particular, the authors of [2] were probably the first ones who paid attention that the oscillatory behavior of the auxiliary currents is similar to that of the currents in radiators of superdirective arrays, although they did not discuss that issue in detail as it is done in [1].

ON THE EFFICIENCY AND GAIN OF ANTENNAS

The fundamental limits of the gain and e±ciency of an antenna are explored. These are very important quantities for, e.g., superdirective arrays. The antenna is in this paper con¯ned in a sphere and all of the currents are assumed to run in a material with a given conductivity. It is shown that one can ¯nd the current distribution in the sphere that optimizes the gain, given the frequency and the radius of the sphere. The results indicate the distribution of antenna elements in an antenna array in order to maximize gain, or e±ciency. The analysis is based on the expansion of the electromagnetic ¯elds in terms of vector spherical harmonics. Explicit expressions for the limits of gain and e±ciency, and the corresponding current densities, are derived for di®erent types of antennas. (Less)

Superdirective Magnetic Dipole Array as a First-Order Probe for Spherical Near-Field Antenna Measurements

The theory as well as numerical and experimental results are presented for a superdirective array composed of closely spaced electrically small resonant magnetic dipole elements. The array operates on a metal ground plane and can exhibit a maximum directivity of 11.5 dBi, 15.2 dBi, and 17.8 dBi (including 3 dB due to the ground plane), for 2, 3, and 4 magnetic dipoles, respectively. The array is self-resonant and is directly excited by a 50-ohm coaxial cable through the ground plane. The array radiates essentially the |μ| = 1 spherical modes, which, despite a narrow bandwidth, makes it an excellent first-order probe for spherical near-field antenna measurements at low frequencies.