Non-uniform Planar Array Research Articles

Joint 3D coordinate and wave-speed estimation with nonuniform planar array: Multi-leak localization in gas pipe buried in sandy soil

The acoustic-based methods enable remote detection of gas pipeline leaks and provide the leak area. However, accurate localization of buried leaks within the leak area requires further investigation. In this scenario, the unknown wave speed in soils and the computational complexity associated with three-dimensional (3D) localization in underground spaces pose challenges. Therefore, a joint estimation method based on a specially-designed nonuniform planar array is proposed to determine both the leak position and wave-speed. Specifically, a small-aperture uniform subarray is embedded into the large-aperture nonuniform array. By utilizing the small-aperture subarray, we can solve for the relationship between wave-speed and direction of arrival (DOA) of far-field waves. Subsequently, two-dimensional spectrum estimation is performed using the large-aperture array to obtain estimates for both wave-speed and near-field source distance. Finally, without resorting to 3D spectrum estimation, the 3D coordinates of the leak are determined. Experimental results conducted on buried pipes demonstrate that the proposed method effectively works across three soil types at varying burial depths. Notably high accuracy is achieved using a large-aperture array expended from the uniform L-shaped array with RMSE less than 0.1 m at SNR of 15 dB. Both experimental validations and simulations confirm that the novel approach can be successfully applied in various scenarios.

Optimizing Antenna Topology for Massive MIMO Planar Arrays With Line-of-Sight Deterministic Channels

Utilizing the classical uniform arrays in massive multi-input multi-output (MIMO) communications will lead to rank-deficiency of channel matrix under line-of-sight (LOS) propagation scenarios, which can be further manifested as the uneven distribution of channel eigenvalues, resulting in the inability to support multi-stream data transmissions. In this paper, we are committed to addressing this problem by the topology design of non-uniform planar array (NUPA) under a generalized scene where the receiving and transmitting arrays are misaligned placed with certain placement angles and a relative rotation offset angle. Specifically, the geometric structure relationship of the arrays must be investigated to derive a general expression for the channel capacity with this NUPA deployment. By applying the singular value decomposition (SVD) method and analyzing the relationship between the eigenvalues and the misaligned angles, the impact of misaligned angles on channel capacity can be disclosed, i.e., channel capacity under specific transmission distance is related to the offset angle but irrelevant to the placement angles. The NUPA design guidelines can then be acquired by using the Kronecker product. Numerical results confirm our theoretical analysis and demonstrate the superiority of the proposed NUPA topology in promoting channel capacity.

Low-Complexity Sparse Array Synthesis Based on Off-Grid Compressive Sensing

In this letter, a novel sparse array synthesis method for nonuniform planar arrays is proposed, which belongs to compressive sensing (CS) based synthesis. Particularly, we propose an off-grid refinement technique to simultaneously optimize the antenna element positions and excitations with a low complexity, in response to the antenna position optimization problem that is difficult for standard CS. More importantly, we take into account the minimum interelement spacing constraint for ensuring the physically realizable solution. Specifically, the off-grid orthogonal match pursuit algorithm is first proposed with low complexity and then off-grid look ahead orthogonal match pursuit is designed with better synthesis performance but higher complexity. In addition, simulation results have shown that the proposed schemes have more advantages in computational complexity and synthesis performances compared with the related method.

Multiple Angles of Arrival Estimation Using Broadband Signals and a Nonuniform Planar Array

As the requirements related to resolution or the data rate increase, most angle-of-arrival (AoA) estimation problems can be assumed to be under a broadband signal model. In this paper, AoA estimation using a nonuniform planar array (NUPA), which aims to resolve more signals and reduce mutual coupling, is considered under a broadband signal model. The analysis is conducted in both the space and frequency domains, and a broadband co-array is proposed to improve the performance of the AoA estimation. The broadband co-array is generated as follows: First, the received broadband signal is decomposed into several narrowband signals, and the samples from different frequency bins are transformed to space-domain samples to generate a virtual array. Then, the second-order statistics of the virtual array are used to generate the broadband co-array. The virtual array can decrease the number of element pairs with small interelement spacing to reduce mutual coupling in AoA estimations. With the help of the virtual array, the following broadband co-array can greatly increase the degrees of freedom, resulting in more resolvable signals and lower Cramer-Rao bounds of AoA estimation. An optimization method based on sparse recovery is proposed to locate the array. The simulation results confirm the AoA estimation performance achieved by the designed NUPA.

Constant-Beamwidth Kronecker Product Beamforming With Nonuniform Planar Arrays

In this paper, we address the problem of constant-beamwidth beamforming using nonuniform planar arrays. We propose two techniques for designing planar beamformers that can maintain different beamwidths in the XZ and YZ planes based on constant-beamwidth linear arrays. In the first technique, we utilize Kronecker product beamforming to find the weights, thus eliminating matrix inversion. The second technique provides a closed-form solution that allows for a tradeoff between white noise gain and directivity factor. The second technique is applicable even when only a subset of the sensors is used. Since our techniques are based on linear arrays, we also consider symmetric linear arrays. We present a method that determines where sensors should be placed to maximize the directivity and increase the frequency range over which the beamwidth remains constant, with a minimal number of sensors. Simulations demonstrate the advantages of the proposed design methods compared to the state-of-the-art. Specifically, our method yields a 1000-fold faster runtime than the competing method, while improving the wideband directivity factor by over 8 dB without compromising the wideband white noise gain in the simulated scenario.

Synthesis of Planar Arrays Based on Fast Iterative Shrinkage-Thresholding Algorithm

In this communication, a pattern synthesis method based on fast iterative shrinkage-thresholding algorithm (FISTA) is proposed for nonuniform planar arrays. In the proposed method, the array synthesis problem is first expressed as a weighted least absolute shrinkage and selection operator (LASSO) problem. Then, the weighted LASSO problem is solved iteratively by FISTA to acquire the locations of reconstructed array elements. At last, two kinds of methods are given to acquire the excitations of the reconstructed array elements. The first kind of method to obtain the excitations is based on the least-squares method. Another way to calculate the excitations is based on convex optimization. The characteristics of these two methods are discussed in this communication. A series of numerical examples are introduced to show the effectiveness and robustness of the proposed method.

Millimeter-Wave Beamformed Full-Dimensional MIMO Channel Estimation Based on Atomic Norm Minimization

The millimeter-wave (mmWave) full-dimensional (FD) MIMO system employs planar arrays at both the base station and user equipment and can simultaneously support both azimuth and elevation beamforming. In this paper, we propose atomic-norm-based methods for mmWave FD-MIMO channel estimation under both uniform planar arrays (UPA) and non-uniform planar arrays (NUPA). Unlike existing algorithms such as compressive sensing (CS) or subspace methods, the atomic-norm-based algorithms do not require to discretize the angle spaces of the angle of arrival (AoA) and angle of departure (AoD) into grids, thus provide much better accuracy in estimation. In the UPA case, to reduce the computational complexity, the original large-scale 4D atomic norm minimization problem is approximately reformulated as a semi-definite program (SDP) containing two decoupled two-level Toeplitz matrices. The SDP is then solved via the alternating direction method of multipliers (ADMM) where each iteration involves only closed-form computations. In the NUPA case, the atomic-norm-based formulation for channel estimation becomes nonconvex and a gradient-decent-based algorithm is proposed to solve the problem. Simulation results show that the proposed algorithms achieve better performance than the CS-based and subspace-based algorithms.

DIRECTION OF ARRIVAL ESTIMATION FOR NONUNIFORM PLANAR ARRAY BASED ON PIECEWISE INTERPOLATION METHOD

The problem of direction-of-arrival (DOA) estimation by using spectral search for a non-uniform planar array is addressed. New search methods for DOA estimation based on piecewise interpolation are proposed. The relationships between these methods and Fourier-Domain (FD) root-MUSIC are discussed. The proposed methods are based on dividing the multiple signal classiflcation (MUSIC) null-spectrum function into a number of equal subintervals. These subintervals are interpolated by using low-degree polynomials. Piecewise interpolation methods based on elementary functions are used to reduce the required computations of MUSIC null-spectrum function. This property reduces the computational complexity compared with line-search methods for DOA estimation. The Cramer Rao Lower Bound (CRB) is used as a benchmark to check the accuracy and validity of the proposed methods.

Design of Scannable Non-uniform Planar Array Structure for Maximum Side-Lobe Reduction

In this letter, we propose a novel design scheme for an optimal non-uniform planar array geometry in view of maximum side-lobe reduction. This is implemented by a thinned array using a genetic algorithm. We show that the proposed method can maintain a low side-lobe level without pattern distortion during beam steering.

A numerical and experimental investigation of the interactions between a non‐uniform planar array of incompressible free jets

AbstractThe interaction between multiple incompressible air jets has been studied numerically and experimentally. The numerical predictions have been first validated using experimental data for a single jet configuration. The spreading features of five unequal jets in the configuration of one larger central jet surrounded by four smaller equi‐distant jets, have been studied, for different lateral spacing ratios of 1.5, 2.0 and 2.5 and a central jet Reynolds number of 1.24×105 (corresponding to a Mach number of 0.16). Flow of five equal jets has also been simulated, for the sake of comparison. The jet interactions commence at an axial distance of about 3–4 diameters and complete by an axial distance of about 10 diameters for the lowest spacing ratio of 1.5. For larger spacing ratios, the length required for the start and completion of jet interaction increase. Peripheral jets bend more towards the central jet and merge at a smaller distance, when their sizes are smaller than that of the central jet. The entrainment ratio for multiple jets is higher than that for a single jet. Excellent agreement is observed between the experimental data and theoretical predictions for both mean flow field and turbulent quantities, at regions away from the jet inlet. The potential core length and initial jet development, however, are not predicted very accurately due to differences in the assumed and actual velocity profiles at the jet inlet. Copyright © 2004 John Wiley & Sons, Ltd.