Arbitrary Linear Array Research Articles

Grid-free compressive beamforming for arbitrary linear microphone arrays

Grid-free compressive beamforming is a new attractive method for acoustic source identification based on compressive sensing theory, which extracts the source information from the microphone array measurements without discretizing the target source region. In the framework of linear microphone array measurements, many studies have been carried out around this method. They have strict requirements on the distribution of microphones. Specifically, only the uniform arrays with equally spaced microphones and sparse arrays consisting of a selection of microphones from uniform arrays are available. In this paper, based on the prolate spheroidal wave functions, we propose a grid-free compressive beamforming method compatible with arbitrary linear microphone arrays. Some examples are conducted to demonstrate the correctness and superiority of the proposed method. Plenty of Monte Carlo simulations are performed to reveal the effects of source coherence, source separation, noise, and number of snapshots. This study helps to promote the popularization and application of grid-free compressive beamforming method and offers the possibility to improve the acoustic source identification performance by optimizing microphone distribution.

PSWF-based decoupled atomic norm minimization for DOD and DOA estimation in MIMO radar with arbitrary linear arrays

Decoupled atomic norm minimization (D-ANM) is a computationally-efficient gridless two-dimensional parameter estimation method via dividing the two-level Toeplitz matrix into two one-level matrices, and can be applied to the one-snapshot direction-of-departure (DOD) and direction-of-arrival (DOA) estimation in bistatic multiple-input multiple-output (MIMO) radar with uniform linear arrays (ULAs). Nevertheless, in actual applications, the transmitting and receiving arrays are not always ULAs, which leads to the Toeplitz structure not satisfied and the regular D-ANM algorithm not available. In this work, the one-snapshot DOD and DOA estimation in bistatic MIMO radar with arbitrary linear arrays (ALAs) is investigated. The Prolate spheroidal wave functions (PSWFs) are utilized to express such a D-ANM problem followed by a semi-definite programming (SDP) solution. The PSWF-based method can extend the application of D-ANM from ULAs to ALAs, and avoid the grid partition of the conventional sparse representation methods. The numerical experiments are conducted to verify the proposed method.

Robust Low Sidelobe Synthesis for Arbitrary Arrays Based on Gradient Ascent With Min-Oracle

This article studies the robust pattern synthesis of a narrow main beam and low sidelobes of arbitrary arrays, which represents a classical but challenging problem for array antennas. In addition, pattern synthesis for a given sidelobe envelope is discussed. The synthesis problem is formulated as a nonconvex–nonconcave minimax problem with nonconvex constraints, which avoids the design of the optimal desired pattern and ensures the robustness of pattern synthesis for arbitrary arrays by nonconvex constraints. An algorithm named gradient ascent with min-oracle (GAmin) is proposed to address the considered minimax problem. Furthermore, the majorization–minimization algorithmic framework is used to reduce computational complexity. It is shown that for arbitrary linear and planar arrays, the proposed GAmin-based pattern synthesis method can perform well for pattern synthesis both without and with a given sidelobe envelope. A variety of numerical examples are provided to demonstrate the superior performance of the proposed method.

An efficient synthesis method for large unequally spaced sparse linear arrays based on surrogate models of subarrays

The synthesis of large arrays with optimization of element locations including mutual coupling effects is always known as a computationally cost task. In this article, an efficient synthesis method for large unequally spaced sparse linear arrays in the presence of coupling effects based on artificial neural network (ANN) surrogate models of subarrays is presented. High-quality ANN surrogate models of arbitrary large linear arrays are built by grouping the surrogate models of subarrays together to tackle the “curse of dimensionality” of ANNs caused by the large number of array elements. The surrogate models of a complete group of subarrays with the given physical structures are built by several independent ANNs which are used to characterize the effects of mutual coupling on the active element patterns (AEPs) with variable element location distributions. After training, the surrogate models of subarrays can be called by an alternating convex optimization (ACO) method, so that arbitrary large arrays can be quickly synthesized including mutual coupling effects. Numerical experiments are conducted to determine the suitable parameters of subarray partition and build surrogate models of subarrays. The results of four examples for synthesizing unequally spaced linear arrays are demonstrated to validate the effectiveness of the proposed method.

Half-Dimension Subspace Decomposition for Fast Direction Finding With Arbitrary Linear Arrays

It is well-known that the multiple signal classification (MUSIC) algorithm is computationally time-consuming because it requires a complex-valued full-dimension eigenvalue decomposition (EVD) and a complex-valued spectral searching. In this paper, we exploit the virtual signal model of forward/backward average of array covariance matrix (FBACM) to show that its real part (R-FBACM) is a real symmetric matrix. Based on that, we prove that by evaluating two half-dimension EVD after an orthogonally similar transformation performed on the estimated R-FBACM, we are able to reconstruct the original eigenspace whereas the maximum number of estimated sources is reduced as compared to the upper limit <inline-formula><tex-math notation="LaTeX">$\mathit{M}-\text{1}$</tex-math></inline-formula> for original MUSIC. Numerical results show that the proposed method provides satisfactory estimation accuracy and improved resolution with reduced complexity.

DOA estimation using sparse array with gain-phase error based on a novel atomic norm

Sparse arrays have attracted great attention in the field of direction-of-arrival (DOA) estimation due to the extended degrees of freedom (DOFs). Nevertheless, the traditional DOA estimation methods for sparse arrays suffer from degraded performance when sensor elements are uncalibrated. This paper presents a novel atomic norm-based algorithm for source localization with arbitrary sparse linear array (SLA) in the scenario with gain-phase uncertainties. Our proposed approach defines a new atomic norm for second order virtual signal by taking model errors into consideration. Then, the dual problem corresponding to original optimization problem is formulated to recover the DOAs by defining the dual atomic norm. We further present the corresponding semidefinite program characteristic that can be solved. The proposed method avoids iterations and restrictions on array configuration. It makes full use of all the DOFs provided by difference coarray of arbitrary SLA to estimate more sources and to provide high accuracy. Besides, compared with the existing coarray-based calibrated algorithms, the proposed algorithm does not need discretization on spatial domain. Computer simulations are carried out to demonstrate the superiority of the proposed algorithm.

Real-Valued Sparse Bayesian Learning for DOA Estimation With Arbitrary Linear Arrays

Sparse Bayesian learning (SBL) has become a popular approach for direction-of-arrival (DOA) estimation, but its computational complexity for Bayesian inference is quite high because calculating inverse of a large complex matrix per iteration is required. It is known that the computational load can be reduced by transforming the complex-valued problem into a real-valued one. However, the commonly used real-valued transformation works for uniform linear arrays (ULAs) only. In this paper, we propose a new real-valued transformation for DOA estimation with arbitrary linear arrays by exploiting the virtual steering of linear arrays. Then, we introduce an alternating optimization algorithm based on the variational Bayesian inference (VBI) methodology to iteratively obtain a stationary solution to the real-valued sparse representation problem. Because of utilizing the additional real-valued structure, the VBI scheme can achieve a better performance in terms of both estimation accuracy and computational complexity. Moreover, we embed the generalized approximate message passing (GAMP) into the VBI-based method for further complexity reduction. Although there may be a performance loss for the GAMP variant, simulation results reveal its substantial performance improvement over existing methods.

Optimal Pattern Synthesis of Linear Array and Broadband Design of Whip Antenna Using Grasshopper Optimization Algorithm

Antenna arrays with high directivity, low side-lobe level, and null control in desired direction and whip antenna with wider bandwidth both need to be optimized to meet different needs of communication systems. A new natural heuristic algorithm simulating social behavior of grasshoppers, grasshopper optimization algorithm (GOA), is applied to electromagnetic field as a new effective technology to solve the antenna optimization problem for the first time. Its algorithm is simple and has no gradient mechanism, can effectively avoid falling into local optimum, and is suitable for single-objective and multiobjective optimization problems. GOA is used to optimize the side lobe suppression, null depth, and notch control of arbitrary linear array and then used to optimize the loading and matching network of 10-meter HF broadband whip antenna compared with other algorithms. The results show that GOA has more advantages in side-lobe suppression, null depth, and notch control of linear array than other algorithms and has better broadband optimization performance for HF whip antenna. The pattern synthesis and antenna broadband optimization based on GOA provide a new and effective method for antenna performance optimization.

An Optimum Volumetric Array Design Approach for Both Azimuth and Elevation Isotropic DOA Estimation

In this study, a new volumetric array design approach is presented for both azimuth and elevation isotropic direction of arrival (DOA) estimation. The presented method uses a minimum number of additional sensors to extend the given arrays to a volumetric array which has equal values for the Cramér-Rao lower bound (CRLB) for the entire azimuth and elevation angles. This approach can be applied to all arbitrary linear and planar arrays. Moreover, the design approach also takes into account the electromagnetic mutual coupling (MC) effect between the array elements and both the azimuth and elevation angular ambiguity uncertainties in an optimum manner while extending the array. It has been verified both analytically and with simulations that the designed volumetric arrays satisfy the two dimensional (2-D) isotropic DOA estimation conditions. The proposed approach is applied to Uniform Linear Arrays (ULA), Uniform Circular Arrays (UCA), V-shaped Arrays, and an arbitrary planar array to extend to optimum volumetric arrays with considerable results.

Manifold studies of FDA geometries for joint angle and range estimation

Different from traditional phased-array, frequency diverse array (FDA) provides an angle-range-dependent and time-variant transmit beampattern that can be utilized for many promising applications. Since array manifold is critical in various array applications, this paper studies the FDA manifold properties including manifold surface and manifold curve for joint range and angle estimation. We prove that the shape of FDA manifold surface is either parabolic or planar, and the families of θ-curves and r-curves lying on FDA manifold surface are geodesic curves. It is shown that, for a symmetric linear array, FDA manifold curve provides longer arc length than that of a phased-array. More generally, we prove that, for an arbitrary linear array, FDA also outperforms phased-array in producing longer arc length and larger rate-of-change of the arc length in some condition. Furthermore, the Cramér-Rao lower bounds (CRLBs) for both angle and range estimation under the FDA manifold geometry framework are also derived, which indicate that FDA achieves lower CRLB than phased-array for an arbitrary linear array. All theoretical analysis are verified by numerical results.

Improved localization of near-field sources using a realistic signal propagation model and optimally-placed sensors

In this paper we analyze the estimation of the angle and the range of a narrow-band source located in the near-field of an arbitrary centro-symmetric linear array (CSLA). This analysis deals with the Cramer Rao bound (CRB) on both angle and range, obtained thanks to an exact expression of the source-to-sensor delay and a realistic (range-dependent) model of source-to-sensor attenuation, ultimately achieving two objectives. On the first hand, closed-form approximate expressions of the CRB are developed and compared to those obtained assuming (unrealistically) that sensors perceive the same power despite being at different distances from the source. While the impact on angle estimation is negligible, range CRB significantly decreases if one incorporates the more appropriate range-dependent power model (except for sources at broadsides). An important consequence is that localization algorithms taking this range-dependent modelization of the apparent source power into account in their signal modeling should have much better range performance. On the second hand, the obtained CRBs are used to design nonuniform CSLA taking into account the ambiguities, with improved angle and range estimation, comparatively to uniform linear arrays (ULA). Finally, we show that our optimized CSLA for a single source also brings some benefits for two closely-spaced sources.

CRB-Based Design of Linear Antenna Arrays for Near-Field Source Localization

This paper is devoted to the Cramer Rao bound (CRB) on the angle and range of a narrow-band near-field source localized by means of an arbitrary linear array using the exact expression of the time delay parameter. First, we prove that the conditional and unconditional CRBs are proportional for an arbitrary parametrization of the steering vector (that may include, but is not limited to, the source DOA, range or polarization). Then, a Taylor expansion of the CRB is conducted to obtain accurate nonmatrix closed-form expressions of the CRB on angle and range. In contrast to the existing expressions, our expressions are simple, interpretable and more general because the sensors are only constrained to be placed along some axis. Our analysis leads to the characterization and design of a class of centro-symmetric linear arrays with improved near-field angle and range estimation capabilities.

PENALTY FUNCTION SOLUTION TO PATTERN SYNTHESIS OF ANTENNA ARRAY BY A DESCENT ALGORITHM

In this paper, an algorithm based on penalty cost function for synthesizing ∞at-top patterns is proposed. A descent algorithm (DA) as its optimizing approach is proposed in this paper as well. Apparently, whole algorithm e-ciency totally depends on the DA. Unlike traditional descent method, the DA deflnes step length by solving a inequality, instead of Wolf or Armijo-type search rule, stimulation results indicate that it can improve the computational e-ciency. Under mild conditions, we prove that the DA has strong convergence properties. Several numerical examples are presented to illustrate the efiectiveness of the proposed algorithm. The results indicate that the approach is efiective in the pattern shape precisely in both mainlobe and sidelobe region for arbitrary linear arrays.

Near-Field Analysis of Electromagnetic Interactions in Antenna Arrays Through Equivalent Dipole Models

This paper presents an analysis of the near fields of antenna arrays using an alternative approach taking into account field variations due to mutual coupling. The method does not require solving Maxwell's equations under the customary boundary condition, but is based instead on searching for equivalent dipole models that are capable of reproducing the same radiated fields of the actual array (ideally obtained through accurate measurement.) We treat mutual coupling between array elements as essentially a multiple scattering effect and propose a method to calculate the near field of arbitrary linear arrays with significant electromagnetic coupling. It is found that a single (analytical) dipole model obtained under certain circumstances, which are detailed in the paper, can be used to predict correctly the near field radiated by arbitrary-size antenna arrays. The paper ends by developing an application of the equivalent dipole method by expanding the near fields into a sum of propagating and nonpropagating parts. It is shown that the 3-D spatial Fourier transform required in this expansion can be eliminated when the dipole model is used in computing the near field in the domain of the validity of the model.

Near-field light focusing by a slit array in a planar metal film with nonuniform slit dielectric material

We study the interference of evanescent electromagnetic waves generated from multi-slits in a metal film and demonstrate the anomalous bending of light at infrared frequencies due to negative refraction. We also calculate the diffraction of an incident plane electromagnetic waves by a metallic film with an arbitrary linear array of slits, slit separation, and slit dielectric material. In contrast to a double-convex shaped quartz lens, we show that a planar metallic film with a one-dimensional slit array can also focus polarized light in the near-field region when either the slit width or the slit dielectric material becomes spatially nonuniform.

Developing pattern recognition systems based on Markov models: The ESMERALDA framework

In this paper we describe ESMERALDA—an integrated Environment for Statistical Model Estimation and Recognition on Arbitrary Linear Data Arrays—which is a framework for building statistical recognizers operating on sequential data as, e.g., speech, handwriting, or biological sequences. ESMERALDA primarily supports continuous density Hidden Markov Models (HMMs) of different topologies and with user-definable internal structure. Furthermore, the framework supports the incorporation of Markov chain models (realized as statistical n-gram models) for long-term sequential restrictions and Gaussian mixture models (GMMs) for general classification tasks. ESMERALDA is used by several academic and industrial institutions. It was successfully applied to a number of challenging recognition problems in the fields of automatic speech recognition, offline handwriting recognition, and protein sequence analysis. The software is open source and can be retrieved under the terms of the LGPL.

Minimum Sidelobe Levels for Linear Arrays

A method of finding the optimum sidelobe-minimizing weights for an arbitrary linear array is derived that holds for any scan direction, beamwidth, and type of antenna element used. Optimum linear array positions are then determined via the particle swarm optimization method. Hence, the two together can give a global bound on antenna array performance with regards to sidelobe minimization. Results are presented for linear arrays of 2-6 elements for different scan angles, beamwidths and antenna elements.

Nonlinear least-square solution to flat-top pattern synthesis using arbitrary linear array

This paper presents a new approach for synthesizing flat-top patterns, based on the least-square error criterion. The cost function is formulated according to the amplitude approximation error without phase constraint. The optimal array weight is obtained by using the Levenberg–Marquardt nonlinear optimization algorithm. Simulations are performed to compare the proposed approach with the Woodward–Lawson method and two recent methods using minimax and adaptive array techniques, respectively. The results indicate that the approach is effective in sidelobe control and synthesizing prespecified patterns for arbitrary linear arrays.

Parallel computation of symbolic robot models of pipelined processor architectures

SUMMARYIncreased speed of inverse dynamics computation is essential for improving the characteristics of robot control systems. This is achieved by reducing the numerical complexity of the models and by introducing parallelism in model computation. In this paper customized symbolic models with a near minimum numerical complexity will be used as a basis for the examination of parallelism in inverse dynamic robot models. A scheduling algorithm for the distribution of computational load onto an arbitrary linear array of pipelined processors will be developed. The proposed algorithm is experimentally evaluated on a transputer network.

In Situ Optimal Reshading of Arrays With Failed Elements

An algorithm is presented which computes optimal weights for arbitrary linear arrays. The application of this algorithm to in situ optimal reshading of arrays with failed elements is discussed. It is shown that optimal reshading can often regain the original sidelobe level by slightly increasing the mainlobe beamwidth. Three examples are presented to illustrate the algorithm's effectiveness. Hardware and software issues are discussed. Execution time for a 25-element array is typically between 1 and 2 min on an HP9836C microcomputer.