Rectangular Planar Array Research Articles

Minimal mean‐square error for 3D MIMO beamforming weighting

The 3D MIMO beamforming system needs a weighting method to determine the direction of beam whist reducing the interference for other beam areas operating at the same carrier frequency. The challenge is to determine the weights of the 3D MIMO beams to direct each beam towards its cluster of user terminals while placing its nulls at undesired user directions to minimise undesired interference. Therefore, the signal-to-interference-plus-noise ratio should be increased while the interference from the side lobes of the other beams reduced. A weight determining method is presented that constructs horizontal and vertical array weights, respectively, by minimising the mean-square error between the array pattern vector and the unit vector, where the unit vector expresses the desired direction for the array pattern and zero vector expresses the undesired direction. Since the rectangular planar array can be viewed as M linear arrays of N elements, the weight of the M–Nth element can be obtained based on the horizontal and vertical array weights.

A three-dimensional image reconstruction algorithm for electrical impedance tomography using planar electrode arrays

We present a three-dimensional non-iterative reconstruction algorithm developed for conductivity imaging with real data collected on a planar rectangular array of electrodes. Such an electrode configuration as well as the proposed imaging technique is intended to be used for breast cancer detection. The algorithm is based on linearizing the conductivity about a constant value and allows real-time reconstructions. The performance of the algorithm was tested on numerically simulated data and we successfully detected small inclusions with conductivities three or four times the background lying beneath the data collection surface. The results were fairly stable with respect to the noise level in the data and displayed very good spatial resolution in the plane of electrodes.

Synthesis of Sparse Planar Arrays Using Matrix Mapping and Differential Evolution

This letter proposes a differential evolution (DE) with matrix mapping for sparse rectangular planar array synthesis technique with multiple constraints. The multiple constraints include the number of elements, the planar array aperture, and the minimum spacing of adjacent elements. By introducing a novel matrix mapping between the element spacing and the variables of DE, the strong constrained optimization problem is transformed to a nonconstrained problem with only lower and upper limits, and the infeasible solutions are naturally avoided during the optimization process. The simulation results show the high efficiency and the robustness of the proposed method and indicate that our method can achieve better results than existing methods.

Analysis of Rectangular Planar Array with Different Distributions and Optimization of Sidelobe Level using GA and PSO

Analysis of Rectangular Planar Array with Different Distributions and Optimization of Sidelobe Level using GA and PSO

Strategy for realizing magnetic field enhancement based on diffraction coupling of magnetic plasmon resonances in embedded metamaterials.

We have demonstrated a straightforward strategy to realize magnetic field enhancement through diffraction coupling of magnetic plasmon (MP) resonances by embedding the metamaterials consisting of a planar rectangular array of U-shaped metallic split-ring resonators (SRRs) into the substrate. Our method provides a more homogeneous dielectric background allowing stronger diffraction coupling of MP resonances among SRRs leading to strong suppression of the radiative damping. We observe that compared to the on-substrate metamaterials, the embedded ones lead to a narrow-band hybridized MP mode, which results from the interference between MP resonances in individual SRRs and an in-plane propagating collective surface mode arising from light diffraction. Associated with the excitation of this hybridized MP mode, a twenty-seven times enhancement of magnetic fields within the inner area of the SRRs is achieved as compared with the pure MP resonance. Moreover, we also found that besides the above requirement of homogeneous dielectric background, only a collective surface mode with its magnetic field of the same direction as the induced magnetic moment in the SRRs could mediate the excitation of such a hybridized MP mode.

A Virtual Subarray Architecture for Imaging Radar

In this paper, an architecture for imaging systems employing a smart subarray design to reduce the number of control points as much as possible is proposed. The radar consists of two linear arrays, orthogonally orientated to achieve the same response of a full planar rectangular array, while the feeds are realized by means of properly designed subarrays, that cancel out the grating lobes of the array factor. In the proposed architecture, the role of the subarrays is interchanged: The subarray that cancels out the grating lobes of the vertical array is used as the element of the horizontal array, and vice-versa, so that there is no feed overlapping. A synthesis strategy for the optimization of subarray and array excitations, based on generalized alternate projections, is also presented and validated by means of a number of simulations. The proposed radar is compared with other existing radar architectures, showing good performances with a very limited number of control points.

Fanolike resonance in light transmission through a planar array of silver circular disks

We studied theoretically light transmission through a planar rectangular array of silver circular disks. An asymmetric lineshape, which is characteristic of the Fano resonance, has been found in a narrow frequency range of the spectrum. The effect can be attributed to the strong coupling between localized particle plasmon resonances excited on individual silver circular disks and an in-plane propagating collective surface mode arising from the array periodicity, as indicated by the anticrossing behavior of the resonance positions in the transmission spectra. More importantly, it was found that a fifty-two fold enhancement of electric field was achieved as compared with the purely resonance at the excitation of this Fanolike resonance; and only a collective surface mode with its electric field parallel to the array plane can mediate the excitation of such a Fanolike resonance.

Combination of fast Fourier transform and self-adaptive differential evolution algorithm for synthesis of phase-only reconfigurable rectangular array antenna

Reconfigurable antenna arrays are often capable of radiating multiple patterns by altering the excitation phases of the array elements. In this paper, an efficient method based on FFT is presented for generating dual-radiation pattern from a single rectangular planar array by modifying the excitation phases of the array elements while sharing common amplitudes. The common amplitudes shared by both the patterns and the phases which play the role of turning between the two patterns when updated over zero phase among the elements are computed using Self-adaptive Differential Evolution (SaDE) algorithm. Two different beam-pairs of pencil/pencil and pencil/flat-top are generated from the proposed array while maintaining precise design specifications. The proposed method greatly reduces the computational time as compared with the conventional method for calculating beam patterns. The dynamic range ratio of the excitation amplitudes are kept below a threshold level to reduce the design complexity of the attenuators at the feed network level and to minimize the effect of mutual coupling among the array elements. To illustrate the effectiveness of SaDE, the fitness functions associated with the two beam-pairs are minimized individually using differential evolution (DE) algorithm and particle swarm optimization (PSO) algorithm. Results clearly show the superiority of SaDE over DE and PSO to handle the proposed problem.

Synthesis of satellite footprint patterns from rectangular planar array antenna by using swarm‐based optimization algorithms

SUMMARYA pattern synthesis method based on Firefly Algorithm (FA) and Artificial Bee Colony (ABC) optimization has been presented to generate satellite footprint patterns from a rectangular planar array of isotropic antennas by modifying the amplitude, phase, and the state of the array elements. Three cases comprising three different footprints of rectangular, square, and circular boundary are generated from the same array by using two different swarm‐based optimization algorithms FA and ABC. Both the algorithms, following the proposed procedures are able to generate the three different footprint patterns while maintaining a satisfactory lower peak side lobe level and ripple. A comparative analysis has been carried out between FA, ABC, and Genetic Algorithm (GA) for the presented problem in terms of fitness value for the three different cases. The superiority of FA and ABC over GA has been established in terms of finding better solutions for all the three cases of the proposed problem. Copyright © 2013 John Wiley & Sons, Ltd.

LPA 2D-DOA Estimation for Fast Nonstationary Sources Using New Array Geometry Configuration

This paper proposes a new array geometry configuration to improve the two dimensional direction of arrival (2D-DOA) estimation of narrowband moving sources with less complexity. This new array is denoted by verticircular configuration, which is composed of both Uniform linear array (ULA) and Uniform Circular array (UCA) to avoid too much computation for 2D-DOA estimation. The proposed verticircular array is applied with the LPA nonparametric estimator to estimate multiple rapidly moving sources’ parameters (angles and angular velocities) for both azimuth as well as elevation directions. Simulation results show that this nonparametric technique is capable of resolving closely spaced sources provided that their velocities are sufficiently different with decreased computational complexity when using the verticircular array. Different scenarios are used to show the efficient LPA beamformer to distinguish sources that can have the same angles using their different angular velocities. In addition, this paper is to compare the performance of the 2DLPA DOA estimation algorithm when using verticircular array (proposed array geometry) or rectangular planar array geometry. Simulation results show that the performance of the proposed method with less complexity than that obtained when using rectangular planar array.

Combination of differential evolution algorithm and fast fourier transform for synthesis of footprint patterns from rectangular planar array

ABSTRACTAn FFT‐based footprint pattern synthesis from a rectangular planar array of isotropic antennas by modifying the amplitude, phase and the state (‘on’/‘off’) of the array elements using differential evolution algorithm has been presented. Three different footprints of rectangular, square and circular boundaries are generated from the array while maintaining a satisfactory lower peak sidelobe level and ripple. The method greatly reduces the computational time than the conventional method of calculating beam patterns. The dynamic range ratio of the excitation amplitudes are kept below a threshold level to reduce the design complexity of the attenuators at the feed network level and to minimize the effect of mutual coupling among the array elements. Copyright © 2013 John Wiley & Sons, Ltd.

FAST SYNTHESIS OF LARGE PLANAR ARRAYS USING ACTIVE ELEMENT PATTERN METHOD AND FINE-GRAINED PARALLEL MICRO-GENETIC ALGORITHM

A radiation pattern synthesis technique for large planar arrays with active element pattern (AEP) method and flne-grained parallel micro-genetic algorithm (FGPMGA) is presented. Based on the AEP method, the mutual coupling between array elements can be taken into account. Analysis problems of large rectangular and triangular grid planar arrays are divided into small linear array problems. And for a multiple concentric circular ring array, we only need to obtain one-sixth of all AEPs. So computational cost is greatly reduced. Large planar arrays with low side lobe level (SLL) can be achieved via optimizing the excitation amplitudes and phases. In order to reduce the global optimization time, the FGPMGA is used. This technique is applied to design 256-element rectangular grid, 200- element triangular grid and 4-circle 60-element concentric circular ring E-shaped patch antenna arrays. The radiation patterns calculated by the AEP method show good agreements with those by using CST Microwave Studio.

Magnetic field enhancement at optical frequencies through diffraction coupling of magnetic plasmon resonances in metamaterials

We studied theoretically the diffraction coupling of magnetic resonances in metamaterials consisting of a planar rectangular array of metal rod pairs with a dielectric spacer. A narrow-band mixed mode was observed due to a strong interaction between magnetic resonances in individual pairs of metal rods and an in-plane propagating collective surface mode arising from the array periodicity. Upon the excitation of this mixed mode, a five-fold enhancement of magnetic field in the dielectric spacer was achieved as compared with the purely magnetic resonance. It was also found that only a collective surface mode with its magnetic field parallel to the array plane could mediate the excitation of such a mixed mode.

SYNTHESIS OF PLANAR ARRAYS USING A MODIFIED PARTICLE SWARM OPTIMIZATION ALGORITHM BY INTRODUCING A SELECTION OPERATOR AND ELITISM

A modifled particle swarm optimization (PSO) algorithm applied to planar array synthesis considering complex weights and directive element patterns is presented in this paper. The modern heuristic classical PSO scheme with asynchronous updates of the swarm and a global topology has been modifled by introducing tournament selection, one of the most efiective selection strategies performing in genetic algorithms the equivalent role to natural selection, and elitism. The modifled PSO proposed combines the abilities of the classical PSO to explore the search space and the pressure exerted by the selection operator to speed up convergence. Regarding the optimization problem, the synthesis of the feeds for rectangular planar arrays consisting of microstrip patches or subarrays of microstrip patches is considered. Results comparing the performance and limitations of classical and modifled PSO-based schemes are included considering both test functions and planar array complex synthesis to best meet certain far-fleld radiation pattern restrictions given in terms of 3D-masks. Finally, representative synthesis results for sector antennas for worldwide interoperability for microwave access (WiMAX) applications are also included and discussed.

Antenna array design for low earth observation satellites

Abstract:A rectangular planar array antenna design using thinning technique and GeneticAlgorithm (GA) optimization technique are used to minimize the gain variation for LowEarth Orbit (LEO) satellites antenna. This design controls the feeding amplitude throughthinning without requirements to control the phases which yields to simplify the feedingnetwork.Two antenna elements are proposed, cos1.5 􀈙 radiation pattern element and therectangular patch element.A simple genetic algorithm optimizer is used to get the optimum excited elements onthe array.

Antenna gain optimization for LEO satellites using a genetic algorithm

Abstract:A rectangular planar array antenna synthesis technique based on Genetic Algorithmoptimization is used to achieve sufficient link margin for low earth orbit (LEO) satellitesantenna, by adjusting the antenna gain.A genetic algorithm (GA) is used to optimize the array excitation. Thinning [1] ofelements is used with different excitation techniques.A phased array antenna with rectangular aperture and cos1.5 􀈙 elements power pattern isassumed.

A hybrid spectral/spatial method to evaluate the active Green's function of large planar rectangular arrays: a combined asymptotic/numerical algorithm

The article illustrates a formulation to evaluate the array Green's function (AGF) of large finite planar phased array for observation points on the array plane, possibly close to the array contour. The procedure is based on the AGF representation in terms of a double spectral integral, whose integration paths are properly deformed to have an exponential attenuation of the integrand. The diffraction integral is evaluated numerically for point close to the array edges while an asymptotic treatment is proposed far from the edges. This latter comprises higher order contributions. Thanks to the convergence properties, the final algorithm is numerically accurate, stable and more efficient with respect to the individual element summation for large arrays. It also constitutes the basic step for the efficient evaluation of the AGF of a multilayer environment

Asymptotic high-frequency Green's function for a large rectangular planar periodic phased array of dipoles with weakly tapered excitation in two dimensions

This paper deals with the derivation and physical interpretation of a uniform high-frequency representation of the Green's function for a large planar rectangular phased array of dipoles with weakly varying excitation. Thereby, our earlier published results, valid for equiamplitude excitation, and those for tapered illumination in one dimension are extended to tapering along both dimensions, including dipole amplitudes tending to zero at the edges. As previously, the field obtained by direct summation over the contributions from the individual radiators is restructured into a double spectral integral whose high-frequency asymptotic reduction yields a series of propagating and evanescent Floquet waves (FWs) together with corresponding FW-modulated diffracted fields, which arise from FW scattering at the array edges and vertexes. To accommodate the weak amplitude tapering, new generalized periodicity-modulated edge and vertex slope transition functions are introduced, accompanied by a systematic procedure for their numerical evaluation. Special attention is given to the analysis and physical interpretation of the complex vertex diffracted ray fields. A sample calculation is included to demonstrate the accuracy of the asymptotic algorithm. The resulting array Green's function forms the basic building block for the full-wave analysis of planar weakly amplitude-tapered phased array antennas, and for the description of electromagnetic radiation and scattering from weakly amplitude-tapered rectangular periodic structures

Efficient hybrid discrete Fourier transform-moment method for fast analysis of large rectangular arrays

A novel approach combining the moment method (MoM) and the discrete Fourier transform (DFT) is developed for the fast analysis of electromagnetic (EM) radiation/scattering from electrically large, finite, planar rectangular arrays. In particular, the unknown array distribution to be solved is represented in terms of the DFT within the MoM for a given array excitation. The proposed DFT-MoM approach for large arrays has the advantage that it can overcome the inefficiency of the conventional MoM approach by drastically reducing the number of unknowns. The latter is possible because only a relatively few DFT terms are significant in this DFT-MoM. A useful criterion to select significant DFT terms is described. Numerical results are presented to indicate the efficiency and accuracy of the DFT-MoM analysis for determining the array distribution and the radiation pattern of large rectangular arrays with uniform excitation. It is found that the efficiency and accuracy of the DFT-MoM increases dramatically with an increase in array size. Furthermore, the DFT representation employed within the MoM can provide an asymptotic closed form solution for both the near and far fields of the array, which can be described in the ray format of the uniform geometrical theory of diffraction (UTD).

Null steering in rectangular planar arrays by amplitude control using genetic algorithms

Null steering in rectangular planar arrays has been achieved when only the amplitudes of the array elements are perturbed. Genetic algorithms were employed to solve the problem of null steering in uniform and Chebyshev planar arrays. Mathematical expressions for the planar array factor were derived from the linear array factor expression. The results show that nulls can be accurately steered to the required real space directions with the minimal disturbance to the other array parameters and at the same time achieve any prescribed null depth.