Beam Pattern Of Array Research Articles

A Partition Spatial Filtering Method for Acoustic Array Configuration

Acoustic array is a ubiquitous tool for locating and quantifying sound sources. However, its effectiveness depends greatly on the array configuration. This paper presents an array configuration method to enhance array performance, especially on the spatial resolution and the Doppler effect correction. The problem of array configuration is formulated into a position matrix determined by introducing partition spatial filtering. Irregular coaxial ring grid spacings and partition filtering conditions are suggested to control array spatial resolution. Geometrical parameters and performance indicators are constructed to quantify the relationships between the array configuration and performance. Based on these quantitative relations, the spatial variation of the array beam pattern and the Doppler effect has got adaptive adjustment. In particular, an adaptive partition algorithm is proposed to reduce computation time. The performance of the method is examined numerically and experimentally, which is compared with the other methods. The results provide the method to guide the design of a 64‐microphone optimized array with high performance (1.8° spatial angle resolution and 40% Doppler frequency correction over the bandwidth from 800 Hz to 3000 Hz) and fast computing speed (18 s array generated time for 2000 arrays). Furthermore, an unusual feature of the method is that it can be utilized in the case when the source moves at a nonconstant velocity.

A Bayesian Compressive Sensing-Based Planar Array Diagnosis Approach From Near-Field Measurements

Array diagnosis is an important tool for detecting and correcting array antenna failures. In this letter, a high-precision planar array diagnosis method based on the Bayesian compressive sensing (BCS) theory is proposed. The model of a near-field signal with a spherical wavefront is used to acquire the measured data. Then, the difference between the beam pattern of the reference array and the array under test is obtained. The array diagnosis problem involves finding the difference between the weights of the reference and of the array under test with known differences between patterns. This problem is reformulated in a Bayesian compressive sensing framework and can be efficiently solved using a fast relevance vector machine. Numerical results confirm the superiority of the proposed method in terms of diagnostic accuracy and computational efficiency than those in previous studies.

Improving performance of three-dimensional imaging sonars through deconvolution

Three-dimensional (3D) imaging sonars are becoming increasingly important for ocean investigation and exploitation. To date, 3D imaging sonars employ a conventional beamforming technique popularly to reconstruct underwater 3D acoustical images. However, angular resolution of the conventional beamforming is limited, which is usually determined by array aperture. Sidelobe levels of the conventional beamforming are also relatively high. These two issues of the conventional beamforming: limited angular resolution and high sidelobe levels limit the performance improvement of 3D imaging sonars. High-resolution imaging algorithms with low sidelobe levels have rarely been investigated in 3D sonars. This paper applies a high-resolution imaging algorithm to improve 3D sonars. We demonstrate that the outputs of the conventional 3D beamforming in a 3D sonar can be formulated as a convolution of the beam pattern of the 2D array employed and the backscattering function of imaging objects, both in the far and near field. Based on the demonstration, the popular deconvolution algorithm in aeroacoustics is applied to deconvolve the conventional beamforming outputs in 3D sonars to improve the spatial resolution and suppress the sidelobes. Both the simulation and experiment verify that using the deconvolution algorithm help improve the angular resolution by more than two times and reduce the average sidelobe level by 20 dB.

Optimum design of both linear and planar sparse arrays with sidelobe level reduction using salp swarm algorithm

Sparse arrays play an important role in the widely used acoustic and electromagnetic applications such as sonar, radar, and satellite. In this paper, a recently proposed swarm intelligence algorithm, salp swarm algorithm (SSA), is introduced for design of both linear and planar sparse antenna arrays with optimum sidelobe level (SLL). The design of sparse antenna arrays can be regarded as a nonlinear optimization problem, which the main optimization goal is finding optimum excitations and positions for antenna elements to achieve antenna array beam pattern with desired SLL. The SSA is a new kind of swarm intelligence algorithm which inspired by the swarming behavior of salps. Compared to other evolutionary algorithms, the SSA requires few algorithm-specified tuning parameters, which makes it simple and easy to use for engineering. Illustrative examples of both linear and planar arrays are given to verify the validity of the SSA for SLL reduction of sparse arrays.

Comments on “Frequency Diverse Array Beam-Pattern Synthesis Using Symmetrical Logarithmic Frequency Offsets for Target Indication”

In recent years, the frequency diverse array (FDA) radar has gained the great interest of researchers due to its flexible scanning beam characteristics and range-angle-dependent beam pattern [1] – [5] . In contrast to the phased-array radars, the abovementioned features of FDA radars can offer potential solutions to many applications including range-interference suppression, directional communications, range ambiguity suppression, and so on [6] – [9] .

Inverse design of diffractive optical elements using step-transition perturbation approach

Abstract Diffractive optical elements are ultra-thin optical components required for a variety of applications because of their high design flexibility. We introduce a gradient-based optimization method based on a step-transition perturbation approach which is an efficient approximation method using local field perturbations due to sharp surface profile transitions. Step-transition perturbation approach be available to calculate the gradient of figure of merit straightforwardly, we implemented optimization method based on this gradient. This fast and accurate inverse design creates binary (2-level) diffractive elements with small features generating the wide angle beam arrays. The results of the experimental characterization confirm that the optimization based on the perturbation method is valid for 1-to-117 fan-out grating generating beam pattern of linear array.

Optimal Synthesis of Sum and Difference Beam Patterns With a Common Weight Vector for Symmetric and Asymmetric Antenna Arrays

To alleviate the complexity of feeding network design and reduce the dependence of sum and difference beam pattern synthesis on the central symmetric antenna arrays, a method generating a common weight vector to simultaneously produce these two beam patterns for symmetric and asymmetric antenna arrays is proposed. By considering the main-lobe radiation power of the sum beam pattern, sidelobe level (SLL), null depth of the difference beam pattern at the direction of the target, and difference-to-sum ratio as design parameters in the beam pattern synthesis, a new optimization problem with a nonconvex objective function and two quadratic fractional constraints is formulated. To tackle it, we first use the variant penalty method to convert the original constrained optimization problem into a nonsmooth unconstrained one and then adopt smooth functions to approximate the nonsmooth components to obtain a smooth unconstrained optimization problem that is then solved by steepest descent. Four representative examples, namely, symmetric linear, asymmetric linear, asymmetric rectangular, and symmetric flower arrays, are implemented to demonstrate that our algorithm can simultaneously synthesize the sum and difference beam patterns with accurately controlled SLLs even in asymmetric array configurations.

Frequency Diverse Array Beampattern Synthesis With Taylor Windowed Frequency Offsets

Frequency diverse array (FDA) is capable of generating a range-angle-dependent beampattern via adjusting the frequency offset across array elements. The classical linear FDA generates an S-shaped beampattern due to the range-angle-dependent coupling. In order to remove the coupling, and obtain a well-focused dot-shaped beampattern, several FDA frameworks are proposed via adjusting frequency offsets. It seems that the window based tapering frequency offsets are able to form a single maximum with a satisfactory mainbeam sharpness. However, most window-based FDA schemes are focused on classical fixed windows. In this letter, an FDA framework with Taylor windowed frequency offsets is first proposed. Considering that adjustable tapering windows allow adjustments by parameter manipulation, the optimized parameters of the window function are determined. The FDA beamforming results with all kinds of frequency offsets are measured, and compared. Numerical results validate the superiority of proposed FDA in terms of mainlobe width, and sidelobe level.

Efficient and Accurate Frequency-Invariant Beam Pattern Synthesis Utilizing Iterative Spatiotemporal Fourier Transform

An iterative spatiotemporal Fourier transform (STFT) method is presented to efficiently design finite-impulse-response (FIR) filter coefficients for generating a desired frequency-invariant (FI) beam pattern of an antenna array. In this method, by introducing the concepts of normalized temporal angular frequency and spatial angular frequency, the broadband pattern is treated as a spatiotemporal spectral distribution. The relationship between the FIR coefficient distribution and the spatiotemporal spectral distribution can be built as an STFT, and consequently the 2-D fast Fourier transform (2D-FFT) and inverse 2D-FFT (2D-IFFT) can be utilized to efficiently accomplish the transformation between the FIR coefficient distribution and the spatiotemporal spectral distribution. Thus, the proposed synthesis method starts from an initial spatiotemporal spectral distribution and then adopt an iterative modification-and-transformation strategy to successively update the obtained spatiotemporal spectral distribution and the corresponding FIR coefficients. Two kinds of pattern modification techniques including the mainlobe FI modification and broadband sidelobe control are adopted in each iteration. Several examples for synthesizing different FI patterns are conducted. Synthesis results show that the proposed method can obtain much better FI pattern performance in terms of both mainlobe FI property and sidelobe control than the original FT method whilst costing less CPU time than the convex optimization method especially for the case of large FI arrays.

Fast Beam Search and Refinement for Millimeter-Wave Massive MIMO Based on Two-Level Phased Arrays

In this paper, a new method of fast beam search and refinement is proposed for millimeter-wave hybrid beamforming systems. The proposed method is based on a two-level phased array approach in which the first-level phased array is formed by actual analog-domain subarrays, and the second-level phased array is virtually formed by the outputs of the first-level subarray phased combiners. Exploiting the fact that the overall beam pattern of the two-level array is the product of the beam patterns of the two levels, the proposed method searches angle-of-arrivals by sweeping coarse-resolution analog training beams at the first-level phased array and matching the first-level subarray outputs with fine-resolution digital training beams by parallel fast Fourier transform (FFT) filtering. In this way, the overall beam search resolution of the proposed method is given by the fine resolution of the second-level virtual array only with the overhead of coarse beam sweeping at the first-level subarrays. Hence, the proposed method provides a very efficient way of beam training and refinement. The performance of the proposed method including the directional ambiguity, beam search latency, and computational complexity is analyzed. Numerical results show the effectiveness of the proposed method.

Array Beampattern Synthesis Without Specifying Lobe Level Masks

In this article, we devise a novel array beampattern synthesis algorithm, namely, without lobe level mask (WLLM), to avoid specifying a possibly improper or infeasible pattern mask by minimizing the ratio of the maximal sidelobe level to the minimal mainlobe level. To solve the resultant nonconvex and nonlinear fractional programming, we introduce auxiliary exponent variables to separate the numerator and denominator, and simplify each of the corresponding subproblems as a special single-variable optimization problem with a piecewise objective function and the constraints are removed via introducing unit-step functions. We also analyze the convexity or concavity of each piecewise function to compute the corresponding local minimum from which the global minimum can be obtained. Furthermore, our developed method is extended for solving the phase-only and constant modulus pattern synthesis problems. Numerical examples show that the WLLM beampattern synthesis methods can attain sufficiently low sidelobe level relative to the mainlobe level and is suitable for arbitrary array configurations.

Reconfigurable Array Beampattern Synthesis via Conceptual Sensor Network Modeling and Computation

Reconfigurable array radiates multiple patterns with only a single array via designing multiple excitation vectors with common magnitudes for the same element-index excitation elements, so as to guarantee phase-only control. To tackle this problem, this article proposes a new reconfigurable array beampattern synthesis method. First, we borrow the concept of sensor network consensus computation and model the synthesis problem as a sensor network computation problem via imitating a virtual (conceptual) multinode sensor network, where each “node” corresponds to an individual beampattern synthesis task. More specifically, these “nodes” with the same number as those of radiated patterns share a set of common excitation magnitudes, which results in a special magnitude-consensus computation problem in the imitated sensor network. Then, via locally computing the excitation in each “node” and exchanging current computation results with neighboring “nodes,” all “nodes” obtain the magnitude-consensus excitations after the “network” is stable. Numerical examples are provided to demonstrate the validity and faster convergence speed of the proposed method.

Robust Null Broadening Beamforming Based on Covariance Matrix Reconstruction via Virtual Interference Sources.

When jammers move rapidly or an antenna platform travels at high speed, interference signals may move out of the null width in the array beampattern. Consequently, the interference suppression performance can be significantly degraded. To solve this problem, both the null broadening technique and robust adaptive beamforming are considered in this paper. A novel null broadening beamforming method based on reconstruction of the interference-plus-noise covariance (INC) matrix is proposed, in order to broaden the null width and offset the motion of the interfering signals. In the moving case, a single interference signal can have multiple directions of arrival, which is equivalent to the existence of multiple interference sources. In the reconstruction of the INC matrix, several virtual interference sources are set up around each of the actual jammers, such that the nulls can be broadened. Based on the reconstructed INC and signal-plus-noise covariance (SNC) matrices, the steering vector of the desired signal can be obtained by solving a new convex optimization problem. Simulation results show that the proposed beamformer can effectively broaden the null width and deepen the null depth, and its performance in interference cancellation is robust against fast-moving jammers or array platform motion. Furthermore, the null depth can be controlled by adjusting the power parameters in the reconstruction process and, if the direction of interference motion is known, the virtual interference sources can be set to achieve better performance.

Method to Determine the Far-Field Beam Pattern of A Long Array From Subarray Beam Pattern Measurements.

Beam pattern measurement is essential to verifying the performance of an array sonar. However, common problems in beam pattern measurement of arrays include constraints on achieving the far-field condition and reaching plane waves mainly due to limited measurement space as in acoustic water tank. For this purpose, the conventional method of measuring beam patterns in limited spaces, which transform near-field measurement data into far-field results, is used. However, the conventional method is time-consuming because of the dense spatial sampling. Hence, we devised a method to measure the beam pattern of a discrete line array in limited space based on the subarray method. In this method, a discrete line array with a measurement space that does not satisfy the far-field condition is divided into several subarrays, and the beam pattern of the line array can then be determined from the subarray measurements by the spatial convolution that is equivalent to the multiplication of beam pattern. The proposed method was verified through simulation and experimental measurement on a line array with 256 elements of 16 subarrays.

IWORMLF: Improved Invasive Weed Optimization With Random Mutation and Lévy Flight for Beam Pattern Optimizations of Linear and Circular Antenna Arrays

The beam pattern synthesis of antenna arrays is one of the most significant optimization problems in the electromagnetics community, and it affects the performance of wireless communication systems. In this article, we formulate the beam pattern optimization problems, and propose an improved invasive weed optimization with random mutation and Levy flight (IWORMLF) algorithm to synthesize the beam patterns of linear antenna arrays (LAAs) and circular antenna arrays (CAAs). IWORMLF introduces the random mutation operator and the Levy flight mechanism to enhance the efficiency and to balance the exploration and exploitation of the algorithm for optimization problems. Several simulations are conducted to evaluate the performance of the proposed approach. First, IWORMLF is tested by a variety of benchmark functions, and the results indicate that it achieves the best performance in most of the functions compared to some other algorithms. Second, IWORMLF is utilized for the maximum sidelobe level (SLL) reduction and the joint maximum SLL and mainlobe beamwidth reductions. The results show that it achieves better performances in terms of the convergence rate, stability, and accuracy compared to some evolutionary algorithms for these optimization cases. Third, the efficiencies of the improved factors are verified. Finally, electromagnetism simulations are conducted to evaluate the performance of IWORMLF for the beam pattern optimizations with considering mutual coupling.

Antenna Beampattern With Range Null Control Using Weighted Frequency Diverse Array

The range-angle-dependent beampattern of frequency diverse array (FDA) makes it capable of dealing with range-dependent interference, which cannot be handled by conventional phased array. However, current publications pay more attention to the dot-shaped beam forming, which is not suitable for the range-dependent jamming signal suppression. To address this problem, this paper proposes a weight designing method to control the nulls distribution among range bins in the mainbeam. With the additional degrees of freedom provided by FDA, it is possible to flexibly adjust the positions and notch widths of the range nulls. The performance and effectiveness of the proposed weighted FDA are validated with numerical simulations.

Information geometry resolution optimization for frequency diverse array in DOA estimation

Frequency diverse array (FDA) provides new application capabilities due to its both range and phase dependent array beampattern. In this paper, we adopt information geometry theory to study the fundamental information resolution and information theoretic frequency increment design for a general FDA system. The information resolution, associated with the waveform, measurement and noise model and characterized by the Fisher information metric, provides a statistical measure for the FDA in a given application. Moreover, an information theoretic frequency increment design approach is proposed for the FDA to achieve improved information resolution in target direction-of-arrival (DOA) applications. Numerical results verify the validity of the proposed approach and FDA indeed outperforms conventional phased-array with respect to information geometry resolution in resolving closely located targets.

Directivity of hydroacoustic systems with parametric array in marine conditions

The paper presents the results of generalization of theoretical and experimental studies of the influence of hydrophysical inhomogeneities on the directional characteristics of the parametric array in the framework of problem solution of improving the efficiency of directional properties of adaptive hydroacoustic systems with parametric emitting arrays. The results of calculations of the directional characteristics of the parametric array obtained on the basis of the Khokhlov-Zabolotskaya-Kuznetsov model are compared with the results of experimental measurements of the directional properties of the parametric array. The normalized dependence of the width of parametric array beam pattern was obtained on the reduction of the difference frequency relative to the central frequency of the pump waves from 5 to 16 times. The influence of the sound velocity change on the direction properties of the parametric array was estimated. The normalized dependence of the width of beam pattern of the parametric array on the value of the sound velocity at the surface of the pump transducer was obtained.

A Miniaturized Dual-Band Dual-Polarized Band-Notched Slot Antenna Array With High Isolation for Base Station Applications

In this article, a miniaturized dual-band dual-polarized slot antenna array is proposed for base station applications. It consists of two closely located $1 \times 4$ subarrays for the digital cellular system (DCS) and wideband code division multiple access (WCDMA) operations. The band-notched slot antenna (BNSA) is designed and adopted as the subarray element with radiation-suppression characteristic at notch frequencies. The notch frequency for one subarray is designed at the center operating frequency of the other subarray. As a result, the radiation from DCS subarray could be effectively suppressed within the WCDMA band and vice versa, resulting in high isolation between two subarrays with a small separation distance. By using the artificial magnetic conductor (AMC) reflector, the array height could be reduced by half, as compared with the perfect electric conductor (PEC) counterpart. In addition, a four-way unequal power divider is designed for the array's beam-pattern synthesis. For the demonstration, the proposed array is fabricated and measured. The measurement results show that the dual-band array achieves the impedance bandwidths of 1.65-1.88 and 1.89-2.22 GHz, the isolations over 25 dB, the realized boresight gains of 12.2-12.8 and 12.3-13.2 dBi, and the sidelobe levels below -18 dB. The results indicate that the proposed array is a promising candidate for base-station applications.

An Array Position Refinement Algorithm for Pencil Beam Pattern Synthesis With High-Order Taylor Expansion

In this letter, the array position refinement for low peak sidelobe level (PSLL) generation utilizing uniform element excitation is investigated. The array beam pattern is expressed as a polynomial function with respect to (w.r.t.) the array position variation, i.e., $\Delta {\bf x}$ , via the high-order Taylor expansion. An iterative algorithm is proposed to solve the optimization problem w.r.t. $\Delta {\bf x}$ to achieve the low PSLL. The algorithm, first, converts the original nonconvex problem into a convex one; thus, the problem can be solved efficiently by readily available tools. The array position is, thereafter, updated iteratively by adjusting $\Delta {\bf x}$ with a convex technique. Numerical simulations with both linear and planar array antennas are carried out to validate the effectiveness of the proposed algorithm. Compared with the existing algorithms, the proposed algorithm can further suppress the PSLLs with 0.9 and 0.4/1.2 dB for linear and planar array antennas, respectively.