Sparse Array Configurations Research Articles

New sparse array for non‐circular sources with increased degrees of freedom

Recently, sparse arrays have received considerable attention as they provide larger array aperture and increased degrees-of-freedom (DOFs) compared to uniform linear arrays. These features are essential to enhance the direction-of-arrival estimation performance. However, most of the existing sparse arrays are mainly designed for circular sources and realize limited increment in DOFs for non-circular sources. In this letter, a new sparse array configuration for non-circular sources is presented, which significantly increases the achievable DOFs and improves the direction-of-arrival estimation performance. The proposed geometry comprises two effectively configured uniform linear arrays that exploit the characteristics of non-circular sources and extend the array aperture. For a given number of sensors, its virtual array is advantageously a hole-free uniform linear array. Moreover, the precise sensor locations, achievable DOFs, and optimal distribution of physical sensors are determined analytically by closed-form expressions. Owing to these benefits, the proposed array efficiently resolve multiple sources in under-determined conditions and achieves better direction-of-arrival estimation performance than its counterpart structures. Simulation results validate the superiority of the proposed configuration.

Sparse Symmetric Linear Arrays With Low Redundancy and a Contiguous Sum Co-Array

Sparse arrays can resolve significantly more scatterers or sources than sensor by utilizing the co-array - a virtual array structure consisting of pairwise differences or sums of sensor positions. Although several sparse array configurations have been developed for passive sensing applications, far fewer active array designs exist. In active sensing, the sum co-array is typically more relevant than the difference co-array, especially when the scatterers are fully coherent. This paper proposes a general symmetric array configuration suitable for both active and passive sensing. We first derive necessary and sufficient conditions for the sum and difference co-array of this array to be contiguous. We then study two specific instances based on the Nested array and the Kl{\o}ve-Mossige basis, respectively. In particular, we establish the relationship between the minimum-redundancy solutions of the two resulting symmetric array configurations, and the previously proposed Concatenated Nested Array (CNA) and Kl{\o}ve Array (KA). Both the CNA and KA have closed-form expressions for the sensor positions, which means that they can be easily generated for any desired array size. The two array structures also achieve low redundancy, and a contiguous sum and difference co-array, which allows resolving vastly more scatterers or sources than sensors

Fast Underdetermined DOA Estimation Based on Generalized MRA via Original Covariance Vector Sparse Reconstruction

Minimum redundancy array (MRA) has the maximum aperture with continuous difference co-array among various sparse arrays with same number of physical sensors, but it is hard to calculate the sensor position of MRA and realize array design by using MRA. To solve those problem, generalized MRA is proposed with mutual coupling limitation and easy calculation method of sensor position. Based on proposed array configuration, a high-precision underdetermined direction of arrival (DOA) estimation method is proposed with reduced computational complexity. In this method, fast covariance matrix reconstruction is achieved by trace norm minimization with more accurate covariance estimation. Based on the Toeplitz property of covariance matrix in uniform array, a new sparse representation model is established with reduced dimension of covariance vector and faster DOA estimation is achieved via convex optimization. In addition, the proposed method can also be used for underdetermined DOA estimation of other sparse arrays. Using simulation experiments, we demonstrate that the proposed sparse array configuration has superiority over other sparse arrays and the proposed method can outperform most existing methods in terms of underdetermined DOA estimation accuracy and efficiency.

Simulated Annealing Assisted Sparse Array Selection Utilizing Deep Learning

This paper proposes simulated annealing (SA) assisted deep learning (DL) based sparse array selection approach. Conventional DL-based antenna selectors are primarily data-driven techniques. As a result, the required dataset is generated by listing all possible combinations of selecting M sensors given N uniform array, which is computationally expensive. A simulated annealing algorithm is proposed to assist dataset generation as an initializer to circumvent the above limitation. The SA algorithm sequentially samples and optimizes the subarrays that constitute the training data samples while retaining specific array characteristics. Hence, it simplifies the dataset annotation as most array configurations generated contain desired properties, thereby reducing the computation complexity of the overall data annotation processes. Therefore, the initializer reduces computation costs related to data generation considerably. Simulation examples show that using the dataset generated by the proposed method improves the DL-based array selector’s accuracy compared to the one generated by the conventional random sampler. Moreover, the realized sparse arrays show better sparse array configuration characteristics and enhanced DOA estimation performance.

Sparse Array Beamforming Design for Wideband Signal Models

We develop sparse array receive beamformer design methods achieving maximum signal-to-interference plus noise ratio (MaxSINR) for wideband sources and jammers. Both tapped delay line (TDL) filtering and the DFT realizations to wideband array processing are considered. The array sparsity stems from the limited number of available RF transmission chains that switch between the sensors, thereby configuring different arrays at different times. The sparse array configuration design problem is formulated as a quadratically constraint quadratic program (QCQP) and solved by using SDR (semidefinite relaxation). A computationally viable approach through SCA (successive convex relaxation) is also pursued. In order to realize an implementable design, in presence of missing autocorrelation lags, we propose parameter-free block Toeplitz matrix completion to estimate the received data correlation matrix across the entire array aperture. It is shown that the optimum wideband sparse array effectively utilizes the array aperture and provides considerable performance improvement over suboptimal array topologies.

Optimal Design of Improved L-shaped Coprime Array Based on Difference and Sum Co-array

The concept of difference and sum co-array(DSCA) has become a new design idea for planar sparse arrays. Inspired by the shifting invariance property of DSCA, a specific configuration named here as the improved L-shaped array is proposed. Compared to other traditional 2D sparse array configurations such as 2D nested arrays and hourglass arrays, the proposed configuration has larger central consecutive ranges in its DSCA, thus increasing the DOF. At the same time, the mutual coupling effect is also reduced due to the enlarged spacing between the adjacent sensors. Simulations further demonstrate the superiority of the proposed arrays in terms of detection performance and estimation accuracy.

Design of 2D Sparse Array Transducers for Anomaly Detection in Medical Phantoms.

Aperiodic sparse 2D ultrasonic array configurations, including random array, log spiral array, and sunflower array, have been considered for their potential as conformable transducers able to image within a focal range of 30–80 mm, at an operating frequency of 2 MHz. Optimisation of the imaging performance of potential array patterns has been undertaken based on their simulated far field directivity functions. Two evaluation criteria, peak sidelobe level (PSL) and integrated sidelobe ratio (ISLR), are used to access the performance of each array configuration. Subsequently, a log spiral array pattern with −19.33 dB PSL and 2.71 dB ISLR has been selected as the overall optimal design. Two prototype transducers with the selected log spiral array pattern have been fabricated and characterised, one using a fibre composite element composite array transducer (CECAT) structure, the other using a conventional 1–3 composite (C1–3) structure. The CECAT device demonstrates improved coupling coefficient (0.64 to 0.59), reduced mechanical cross-talk between neighbouring array elements (by 10 dB) and improved operational bandwidth (by 16.5%), while the C1–3 device performs better in terms of sensitivity (~50%). Image processing algorithms, such as Hough transform and morphological opening, have been implemented to automatically detect and dimension particles located within a fluid-filled tube structure, in a variety of experimental scenarios, including bespoke phantoms using tissue mimicking material. Experiments using the fabricated CECAT log spiral 2D array transducer demonstrated that this algorithmic approach was able to detect the walls of the tube structure and stationary anomalies within the tube with a precision of ~0.1 mm.

Regular and Irregular-on-Grid Sparse Array Comparison of Connected Aperture Arrays

For square kilometer array (SKA) mid-frequency aperture arrays, dense connected aperture arrays such as Vivaldi antenna arrays are being considered, but to achieve the required system sensitivity for radio astronomical observations, this would mean a large number of antenna elements particularly in the order of millions. Two concepts of regular-on-grid and irregular-on-grid sparse array configuration are introduced for these connected arrays to reduce the number of antenna elements and the sensitivity performance of the two concept arrays is compared. Comparing the effective area of these two configurations, it is shown that a regular-on-grid sparse configuration achieves slightly larger effective area than an equivalent irregular-on-grid sparse configuration. Using the regular-on-grid sparse configuration as a case study, the effect that terminating impedance of the inactive antennas has on the receiver noise temperature of a connected array of Vivaldi antennas is investigated.

Diversely polarised sparse array design with minimum interelement spacing constraint for polarised pattern synthesis

The problem of optimised design of diversely polarised sparse array for joint synthesis of spatial and polarisation beampattern is addressed in this Letter. Two kinds of polarised array configurations, cocentred and non-cocentred crossed-dipole arrays, are considered. Minimum interelement spacing constraint along with non-cocentred constraint are involved in the design methods by using two discrete linear operators. The optimisation process can be formulated as a mixed-integer quadratically constrained programming problem which guarantees the optimal solution of the sparse array configuration. Comparison examples with state-of-the-art method validate the advantages of the proposed method in terms of the reduction of required element number and the enlargement of adjacent element spacing.

Optimum sparse array configuration for DOA estimation on moving platforms

Sparse array motion can efficiently expand the numbers of achievable degrees of freedom (DOFs) and consecutive lags, improving direction-of-arrival (DOA) estimation. Sparse arrays on a moving platform benefit from motion translation that introduces new sensor positions, which collectively with the original positions can increase the number of spatial autocorrelation lags and lead to full array augmentability. This property has been recently used for the case of environment-independent sparse array configurations, such as those defined by nested and co-prime arrays. In this paper, we consider environment-dependent sparse arrays (EDSAs) design using Cramer-Rao bound (CRB) as the metric of optimality for DOA estimation. The CRB is derived for a sparse array on a moving platform, where the number of identifiable uncorrelated sources exceeds the number of sensors. The CRB expression is used to solve for the sparse array configuration by applying the Genetic algorithm. Simulation results are provided to validate the effectiveness of the proposed EDSA design.

Sparse array design for multiple switched beams using iterative antenna selection method

Digital beamforming (DBF) arrays with a large number of small antennas are extensively employed in millimeter-wave (mmWave) sensing systems. Sparse arrays have been posed as an attractive solution to mmWave systems due to their capability of striking the best compromise between performance and complexity. We propose two iterative antenna selection strategies, referred to as deterministic selection and adaptive selection, to design sparse DBF arrays in this paper. The first strategy assumes a common sparse array associated with different beamforming weights for multiple switched beams, while the other exploits switching networks to adaptively change the sparse array configuration with different beams. To counteract hardware-related issues that arise in practical realizations, we then propose guided adaptive selection and regularized adaptive selection to impose additional constraints for different switching networks. The optimality of sparse DBF arrays is defined in terms of both transmit and receive patterns. Taking that into account, an iterative re-weighted l1-norm is modified to promote boolean sparsity of the selection vector in this work. Simulation results validate the effectiveness of proposed antenna selection methods.

L-Shaped Sparse Array Structure for 2-D DOA Estimation

In order to improve the performance of two-dimensional (2-D) direction-of-arrival (DOA) estimation, an L-shaped sparse array structured by two new sparse linear arrays is proposed. Each part of the proposed L-shaped array is used for one-dimensional (1-D) azimuth and elevation estimation, respectively. The new sparse linear array configuration is consisted of two subarrays which have N and M physical sensors, respectively. Owing to the advantages of the proposed sparse linear array configuration, higher degrees-of-freedom (DOF) and larger array aperture can be achieved when the second-order statistics of the received data is used. To match the azimuth and elevation angles automatically, the cross-covariance matrix of the two parts of the proposed L-shaped array is used to estimate the paired DOA angles. Based on the proposed L-shaped array configuration, (M +1)(N -[M/2]) signal directions can be estimated with M +N sensors in each part and totally 2M + 2N - 1 sensors. Through the comparative analysis of the parameters with other sparse planar arrays, the proposed L-shaped array can achieve better performance due to its higher DOF and larger array aperture. Finally, numerical simulation results verify the superiority of the 2-D DOA method based on the proposed L-shaped array.

Padded Coprime Arrays for Improved DOA Estimation: Exploiting Hole Representation and Filling Strategies

As a generalized coprime array structure, the coprime array with displaced subarrays (CADiS) allows a large minimum inter-element spacing by introducing a specific displacement between two sparse subarrays. While this structure can effectively reduce mutual coupling, the holes in its difference co-array greatly decrease the achievable number of uniform degrees of freedom (DOFs). In this paper, we first provide a complete characterization for the hole locations in the difference co-array generated by a tailored CADiS (tCADiS) as the union of four subsets of locations related via simple symmetry properties. We then introduce two representation approaches for the hole locations, revealing that the latter can be generated from the differences between sensor locations in the subarray of tCADiS and a small uniform linear array, referred to as a padded subarray. Subsequently, we propose novel padded coprime arrays (PCAs) by incorporating the padded subarray into tCADiS to enlarge the consecutive segments in the difference co-array. This not only contributes to increase the number of available uniform DOFs, but also helps mitigating the mutual coupling by limiting the number of sensor pairs with small separations. Finally, numerical simulation results are provided to demonstrate the superiority of PCAs over existing sparse array configurations in terms of DOF, mutual coupling and DOA estimation accuracy.

Hybrid Beamforming for Active Sensing Using Sparse Arrays

This paper studies hybrid beamforming for active sensing applications, such as millimeter-wave or ultrasound imaging. Hybrid beamforming can substantially lower the cost and power consumption of fully digital sensor arrays by reducing the number of active front ends. Sparse arrays can be used to further reduce hardware costs. We consider phased arrays and employ linear beamforming with possibly sparse array configurations at both the transmitter and receiver. The quality of the acquired images is improved by adding together several component images corresponding to different transmissions and receptions. In order to limit the acquisition time of an image, we formulate an optimization problem for minimizing the number of component images subject to achieving a desired point spread function. Since this problem is not convex, we propose algorithms for finding approximate solutions in the fully digital beamforming case, as well as in the more challenging hybrid and analog beamforming cases that employ quantized phase shifters. We also determine upper bounds on the number of component images needed for achieving the fully digital solution using fully analog and hybrid architectures, and derive closed-form expressions for the beamforming weights in these cases. Simulations demonstrate that a hybrid sparse array with very few elements, and even fewer front ends, can achieve the resolution of a fully digital uniform array at the expense of a longer image acquisition time.

Audio enhancement and intelligent classification of household sound events using a sparsely deployed array

A household sound event classification system consisting of an audio localization and enhancement front-end cascaded with an intelligent classification back-end is presented. The front-end is composed of a sparsely deployed microphone array and a preprocessing unit to localize the source and extract the associated signal. In the front-end, a two-stage method and a direct method are compared for localization. The two-stage method introduces a subspace algorithm to estimate the time difference of arrival, followed by a constrained least squares algorithm to determine the source location. The direct localization methods, the delay-and-sum beamformer, the minimum power distortionless response beamformer, and the multiple signal classification algorithm are compared in terms of localization performance for sparse array configuration. A modified particle swarm optimization algorithm enabled an efficient grid-search. A minimum variance distortionless response beamformer in conjunction with a minimum-mean-square-error postfilter is exploited to extract the source signals for sound event classification tasks that follow. The back-end of the system is a sound event classifier that is based on convolutional neural networks (CNNs), and convolutional long short-term memory networks Mel-spectrograms are used as the input features to the CNNs. Simulations and experiments conducted in a live room have demonstrated the strength and weakness of the direct and two-stage methods. Signal quality enhancement using the array-based front-end proves beneficial for improved classification accuracy over a single microphone.

Enhanced Nested Array Configuration With Hole-Free Co-Array and Increasing Degrees of Freedom for DOA Estimation

In this letter, we propose an enhanced nested array (ENA) configuration consisting of two uniform linear arrays (ULAs) with different separations and an additional sensor, whose resulting difference co-array (DCA) is hole-free. As compared with most of the existing sparse array configurations, the proposed ENA has simple closed-form expressions for array geometry and degrees of freedom (DOF), and also can provide more consecutive DOF and larger array aperture. Based on the above good properties of the ENA, compressive sensing (CS) approach is employed for direction-of-arrival (DOA) estimation by solving an ${l}1$ -norm minimization problem. The theoretical propositions are proved and numerical simulations are performed to demonstrate the superior performance of the proposed ENA.

Joint Inversion for Sound Speed Field and Moving Source Localization in Shallow Water

This paper develops a joint approach for time-evolving sound speed field (SSF) inversion and moving source localization in shallow water environment. The SSF is parameterized in terms of the first three empirical orthogonal function (EOF) coefficients. The approach treats both first three EOF coefficients and source parameters (e.g., source depth, range and speed) as state vectors of evolving with time, and a measurement vector that incorporates acoustic information via a vertical line array (VLA), and then the inversion problem is formulated in a state-space model. The processors of the extended Kalman filter (EKF) and ensemble Kalman filter (EnKF) are used to estimate the evolution of those six parameters. Simulation results verify the proposed approach, which enable it to invert the SSF and locate the moving source simultaneously. The root-mean-square-error (RMSE) is employed to evaluate the effectiveness of this proposed approach. The interfile comparison shows that the EnKF outperform the EKF. For the EnKF, the robustness of the approach under the sparse vertical array configuration is verified. Moreover, the impact of the source-VLA deployment on the estimation is also concerned.

Extended Coprime Array Configuration Generating Large-Scale Antenna Co-Array in Massive MIMO System

Generally, massive multiple-input multiple-output (MIMO) system incorporates hundreds of antennas at the base station for various attractive merits, whereas severe mutual coupling arises in the dense structure. In this paper, we introduce the sparse array configuration, coprime array, into the massive MIMO system to alleviate mutual coupling, increase the degrees of freedom (DOFs) and enhance the spatial resolution. Specifically, we propose the extended coprime array structures through two systematical schemes. One scheme is to slide one subarray of the typical augmented coprime array to decompose the interleaved subarrays and the resulting sliding extended coprime array (SECA) produces weaker mutual coupling than the traditional dense uniform linear array, especially the newly proposed super nested array and augmented nested array. Meanwhile, SECA can produce an augmented co-array with more antennas than the physical array and resultantly increase the available DOFs as well as the array aperture. The other scheme is to relocate a proper number of antennas in the generalized coprime array composed of two subarrays with a displacement, namely coprime array with displaced subarrays (CADiS), and the resulting relocating extended coprime array can further alleviate mutual coupling and enhance the consecutive co-array. Furthermore, we provide the closed-form expressions of the co-array, sliding factor, the minimum number of relocating sensors, and their corresponding positions.

Dual-Function MIMO Radar Communications System Design Via Sparse Array Optimization

Spectrum congestion and competition over frequency bandwidth could be alleviated by deploying dual-function radar-communications systems, where the radar platform presents itself as a system of opportunity to secondary communication functions. In this paper, we propose a new technique for communication information embedding into the emission of multiple-input multiple-output (MIMO) radar using sparse antenna array configurations. The phases induced by antenna displacements in a sensor array are unique, which makes array configuration feasible for symbol embedding. We also exploit the fact that in a MIMO radar system, the association of independent waveforms with the transmit antennas can change over different pulse repetition periods without impacting the radar functionality. We show that by reconfiguring sparse transmit array through antenna selection and reordering waveform-antenna paring, a data rate of megabits per second can be achieved for a moderate number of transmit antennas. To counteract practical implementation issues, we propose a regularized antenna selection based signaling scheme. The possible data rate is analyzed and the symbol/bit error rates are derived. Simulation examples are provided for performance evaluations and to demonstrate the effectiveness of proposed DFRC techniques.

DOA Estimation Exploiting Sparse Array Motions

This paper utilizes sparse array motion to increase the numbers of achievable both degrees of freedom (DOFs) and consecutive lags in direction-of-arrival (DOA) estimation problems. We use commonly employed environment-independent sparse array configurations. The design of these arrays is not dependent on the sources in the field of view, but rather aims at achieving desirable difference co-arrays. They include structured coprime and nested arrays, minimum redundancy array (MRA), minimum hole array (MHA), and sparse uniform linear array (SULA). Array motion can fill the holes in the spatial autocorrelation lags associated with a fixed platform and, therefore, increases the number of sources detectable by the same number of array sensors. Quasi-stationarity of the environment is assumed where the source locations and waveforms are considered invariant over array motion of half wavelength. Closed-form expressions of the number of DOFs and consecutive spatial correlation lags for coprime and nested arrays as well as SULA, due to array translation motion, are derived. The number of DOFs and consecutive lags for the specific cases of MRA an 5 avaluated. We show the respective DOA estimation performance based on sparse reconstruction techniques.