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This study developed a novel S-band radar system for planar location applications. High-resolution range imaging and target angle estimation were achieved by using a stepped frequency continuous wave (SFCW) signal and single input multiple output (SIMO) architecture with a linear sparse array layout, respectively. An improved time-frequency method was utilized to link the independent range profile and angle spectrum results to obtain the plane positions of the targets. The radar hardware was composed of the antenna array with one transmit element and five receive elements, an RF transceiver, and a signal processing component. Under the proposed waveform parameters and signal processing scheme, a 16-ms process cycle, 0.3-m ranging error, and 0.4° angle estimation error for target positioning were achieved in field tests. These results demonstrate the effectiveness and advantages of the proposed radar system.

Colocated multiple-input multiple-output (MIMO) radar can transmit a group of distinct waveforms via its colocated transmit antennas and the waveform diversity leads to several advantages in contrast to conventional phased-array radar. The performance depends highly on the degrees available, and element spacing can be deemed as another source of degrees of freedom. In this paper, we study the joint waveform and element spacing optimization problem. A joint waveform and array optimization criterion is proposed to match the transmit beampattern, the suppression range, and the angular sidelobes, under the constraints of minimal element spacing and total array aperture. Meanwhile, the effect of receive beamforming on suppressing mutual correlation between returns from different spatial directions is also incorporated into the optimization criterion. The optimization problem is solved by the sequential quadratic programming algorithm. Numerical results indicate that with more degrees of freedom from array spacings, colocated MIMO radar achieves a better transmit beampattern matching performance and a lower sidelobe level, compared with a fixed half-wavelength spaced array, but the benefits from additional degrees of freedom from array spacing optimization have a limit.

As a notable sparse array, Low redundant linear array (LRLA) plays an important role in lots of areas, especially in the areas of passive synthetic aperture imaging and direction of arrival (DOA) estimation. The existing LRLAs have a problem that they generally contain some dense segments of unit-spaced elements, which restricts the element aperture and hence the radiometric sensitivity, and simultaneously causes serious mutual coupling effect that deteriorates the array performance. To solve this problem, a new kind of sparse array named as super low redundant linear array (S-LRLA) is proposed in this paper. The key characteristic of S-LRLA is that, it has no unit-spaced sensor pairs but has the largest continuous difference co-array spanning from 2 to N-2 with a redundancy of less than 2. Lots of S-LRLAs are obtained by using differential evolution (DE) method. On this basis, two types of S-LRLAs including 7 close-formed patterns and 2 semi-closed-formed patterns are discovered. The property and designing factors of S-LRLA are analyzed. Furthermore, the adapted S-LRLA (AS-LRLA) with full difference co-array is also discussed. Comparisons with other prominent arrays are finally presented to demonstrate the superiority of AS-LRLA.

The microwave interferometric radiometer (MIR) uses aperture synthesis technology to equate multiple small-aperture antennas into a large-aperture antenna to improve spatial resolution. At present, MIR antennas that operate at frequencies above the C-band mostly use horn antennas, waveguide slot antennas, etc., which have the disadvantages of a high profile and large mass. In this paper, a new type of miniaturized, low-profile, and lightweight K-band fan-beam microstrip grid antenna is designed for the airborne campaign of the K-band one-dimensional MIR of a Microwave Imager Combined Active and Passive (MICAP) onboard a Chinese Ocean Salinity Mission (COSM). With a limited size constraint (12.33 mm) on the antenna width, a fan-beam shape antenna pattern was achieved with a 5.34° 3-dB beamwidth in the narrow beam direction and up to a 55° 3-dB beamwidth in the fan-beam direction. A periodic structural unit is proposed in this paper to reduce the design complexity of Taylor weighting, achieving desirable performances on gain (19.1 dB) and sidelobe level (

In the past decade, sparse arrays have aroused considerable attention for the ability to provide larger array aperture, more degrees of freedom (DOFs) and better estimation performance compared with the uniform linear array (ULA). In this paper, the problem of sparse array design is investigated for direction of arrival (DOA) estimation of non-circular (NC) signals, where both the difference co-array (DCA) and sum co-array (SCA) of physical array configuration can be utilized. Specifically, we first introduce a sliding array strategy which moves the array along the axis as a whole in order to reduce the co-array redundancy and enhance the consecutive DOFs of the sum-difference co-array (SDCA). Subsequently, we focus on the SCA of the conventional nested array (NA) and propose an approach which increases the DOFs of the SCA by relocating proper sensors. Furthermore, based on the above strategy and approach, we derive an extended sliding nested array (ESNA) with few redundant virtual sensors and an enhanced SCA, which can offer increased consecutive DOFs, enlarged virtual array aperture (VAA) and can thus bring high angle estimation accuracy of NC signals. Finally, analytic solutions and simulation results are given to validate the superiority of the proposed ESNA in terms of DOFs and estimation performance.

A cognitive antenna selection strategy for multi-in multi-out (MIMO) imaging radar is proposed in this article. The basic idea of our strategy relies on the dynamic selection of the antenna location according to the feedback information to enhance the image quality and reduce the computational burden simultaneously. The aim of our strategy is to indirectly minimize the mean squared error associated with the amplitudes and positions of the strong scattering centers of the target through the frame potential. Specifically, it is assumed that the imaging process is initially performed via a conventional uniform linear array/random sparse array of collocated MIMO radar; hence, based on the collected data, an initial image of the target is derived (perception). Then, the accuracy of low-resolution images is enhanced progressively according to the cognitive paradigm via a specific antenna location selection at the next transmission (action). Benefit from the enhanced accuracy, the support area of targets can be estimated to reduce the dimension of the undersampling matrix and, finally, the computational burden in the subsequent high-resolution image reconstruction process is reduced. The simulation results highlight the capabilities of our cognitive approach to provide more interesting benefits in imaging than the random selection strategy and demonstrate the enhanced imaging performance of cognitive sparse MIMO array under the condition of limited antennas and noise.

For tacking and localizing sources in the mobile wireless sensor network, underdetermined direction of arrival (DOA) estimation with high-accuracy is a crucial issue. In this paper, a novel sparse array configuration is developed for accurate DOA estimation from the perspective of sum-difference coarray (SDCA). As compared with most of the existing sparse array configurations, the proposed array can effectively reduce the overlap between difference coarray (DCA) and sum coarray (SCA) and can achieve more consecutive degrees of freedom (DOF), more sources can be resolved accordingly. Additionally, the proposed array has hole-free DCA and SDCA. Then, the concept of coarray redundancy ratio (CRR) is introduced for evaluating the coarray overlap quantitatively and the closed-form CRR expressions of the proposed array are derived in detail. Based on the good properties of the proposed array, vectorized conjugate augmented MUSIC (VCAM) is adopted for underdetermined DOA estimation. The theoretical propositions and numerical simulations demonstrate the superior performance of the proposed array in terms of CRR, consecutive DOF, and DOA estimation accuracy.

To achieve a better tradeoff between the direction-of-arrival (DOA) estimation resolution and complexity compared to the existing sparse array based estimators, this letter proposes a pseudo noise subspace based DOA estimator for an unfolded coprime linear array (UCLA). On one hand, by unfolding the two subarrays of a general coprime linear array (CLA), the UCLA acquires a larger aperture, giving rise to a higher angular resolution. On the other hand, a mapping relationship is explored to convert the original noise subspace into the pseudo noise subspace (in the Nyquist spatial sampling sense), from which the DOAs can be accurately estimated by root-MUSIC method instead of exhaustive peak searching, thereby reducing the complexity. Numerical results also confirm this superiority over other sparse array based estimators.

Recent years have seen a steady convergence of Radar and Communications band Radio Frequency (RF) transceiver systems. Not only have Communications systems colonised large swathes of previously allocated Radar bands but there is also a convergence of technologies driven by the relatively low cost of software‐defined transceivers and solid‐sate RF sources. Thus, where conventional radar transmissions are characterised by short narrowband pulses with high peak power, new classes of ‘pulse‐compression’ radar are being developed to exploit this new technology. The resulting Low Probability of Intercept waveforms are designed to spread energy in both time and frequency, yielding a very low instantaneous power spectral density. Methods to detect, analyse and distinguish such sources require longer acquisition periods to collect more energy from the sources. Here, a novel solution is provided for detection and separation based on direction‐finding utilising polynomial matrix methods in conjunction with sparse array geometries. This approach provides enhanced detection, separation and direction finding while using relatively few antenna elements.

This paper shows how to compile sparse array programming languages. A sparse array programming language is an array programming language that supports element-wise application, reduction, and broadcasting of arbitrary functions over dense and sparse arrays with any fill value. Such a language has great expressive power and can express sparse and dense linear and tensor algebra, functions over images, exclusion and inclusion filters, and even graph algorithms. Our compiler strategy generalizes prior work in the literature on sparse tensor algebra compilation to support any function applied to sparse arrays, instead of only addition and multiplication. To achieve this, we generalize the notion of sparse iteration spaces beyond intersections and unions. These iteration spaces are automatically derived by considering how algebraic properties annotated onto functions interact with the fill values of the arrays. We then show how to compile these iteration spaces to efficient code. When compared with two widely-used Python sparse array packages, our evaluation shows that we generate built-in sparse array library features with a performance of 1.4× to 53.7× when measured against PyData/Sparse for user-defined functions and between 0.98× and 5.53× when measured against SciPy/Sparse for sparse array slicing. Our technique outperforms PyData/Sparse by 6.58× to 70.3×, and (where applicable) performs between 0.96× and 28.9× that of a dense NumPy implementation, on end-to-end sparse array applications. We also implement graph linear algebra kernels in our system with a performance of between 0.56× and 3.50× compared to that of the hand-optimized SuiteSparse:GraphBLAS library.

Beamforming is widely used in structural health monitoring (SHM) systems for impact or damage localization. Beamforming directionality is achieved by the constructive interference of sensor wavefronts, which results in a significant amplification of the measured signal in a particular direction. For beamforming applications, the cost per sensor is typically significant, because of the sensor itself, and the associated electronics. Therefore, in order to minimize the cost of SHM in practice, it is highly desirable to reduce the number of sensors. Beamforming with an array of sensors requires an advanced signal processing technique to detect the direction-of-arrival (DOA). In addition, by deploying more sensors, better detection accuracy can be achieved. In this paper, the non-equidistant linear sensor array is proposed, to obtain lower costs while guaranteeing reasonable detection accuracy. In addition, the proposed sensor deployment scheme is able to reduce the effects of “spatial aliasing,” which phenomenon is typically encountered in the equidistant linear sensor array layout. To validate the performance of the proposed non-equidistant linear array technique in SHM applications, several finite element models (FEM) simulation and experimental investigations are carried out. Different sensor array layouts are also compared to optimize the performance of the non-equidistant linear array.

Based on the traditional adaptive integral method(AIM), a fast method called array AIM is proposed to accelerate the scattering calculation of the finite periodic array and the sparse array. On one hand, this method could eliminate the idle grids through the utilization of 5-level block-Toeplitz matrix. Furthermore, the procedure of near correction is eliminated by applying the zeros shielding technique. On the other hand, the block Jacobi preconditioning technique is used to improve the iterative convergence, and the technique of wave path difference compensation is applied to accelerate the post-processing. The numerical results show that the proposed method not only possesses good accuracy, but also has much less cost both in time and memory, in comparison with the traditional AIM. Moreover, this method could be applied to solve the scattering problems for the finite periodic array, as well as the sparse array.

Multiple‐input‐multiple‐output (MIMO) radar imaging systems require a high angular resolution to realize a high detectability level of the target directly related to the aperture size of the virtual array. Since in MIMO radars, the virtual array topology depends on the transmit and receive array topologies, two methods are proposed for the synthesis of sparse virtual arrays by designing the sparse transmit and receive arrays using a two‐step synthesis procedure (TSP) for antenna array sparsity via convex optimization. Both methods are formulated in detail, and it is shown that adjustments in formulations with respect to physical constraints in design specifications are feasible. In the first method, both the sparse transmit and the sparse receive array are synthesized using the TSP independently of each other. In the second method, the sparse receive array is synthesizedbased on the transmit array topology or vice versa using the method of least squares.With the help of numerical examples, it is shown that a sparse virtual array has betterperformance in terms of beamwidth and side lobe level compared with the traditionaldense virtual array with the same number of transmit and receive array elements. It is alsoshown that the proposed design methods lead to broadband performance.

The Soil Moisture and Ocean Salinity (SMOS) mission led by the European Space Agency (ESA) is aimed to globally monitor the Earth surface moisture and ocean salinity. As the single payload of SMOS satellite, the Microwave Interferometric Radiometer with Aperture Synthesis (MIRAS) operates in the protected L-band. Nonetheless, the artificial sources emitting close to or/and fully in this band are contaminating the collected remote sensing data and deteriorating the performance of the SMOS mission. Identifying and localizing such sources is crucial to improve the quality of SMOS scientific products. In this article, we propose a method based on matrix completion (MC) for localization of radio frequency interference (RFI) sources. This method mainly exploits the low-rank property of the augmented covariance matrix (ACM) of the sparse array and addresses the ACM incompleteness (i.e., sampling data loss) due to inherent array geometry (e.g., the SMOS Y-shaped array) or potential hardware malfunction (e.g., the correlator failure). Validation results show that, compared with existing RFI localization approaches such as the discrete Fourier transformation (DFT) inversion and covariance-based direction-of-arrival (DOA) estimation, the proposed MC method possesses competitive localization accuracy, superior spatial resolution, and reduced artifacts.

Sparse arrays of only $N$ physical sensors can attain $O(N^{2})$ degrees of freedom (DOF), which profits from the $O(N^{2})$ length of the central uniform linear array (ULA) segment in their difference coarrays. However, this $O(N^{2})$ ULA segment of such configurations (e.g., minimum-/low-redundancy arrays (MRAs/LRAs), nested arrays, and coprime arrays as well as their variations) is inevitably susceptible to sensor failures, which is a crucial issue concerning array robustness (or system reliability) in practical applications. In this article, we present a novel sparse array geometry, named multiple-fold redundancy array (MFRA), by exploiting element redundancies in the difference coarray. The MFRA is not only more robust to sensor failures than the conventional minimum-/low-redundancy, nested, and coprime arrays but also can enjoy up to $O(N^{2})$ DOF as these conventional arrays do. To efficiently construct MFRAs with desirable characteristics (including multiple-fold redundancy, satisfactory DOF, and hole-free difference coarray), a systematic design method is developed. Based on this method, some analytical structure patterns are derived for closed-form geometric construction. Several important properties of MFRAs are proved theoretically, and numerical examples are presented to demonstrate their characteristics and superior performances.

A high-gain transmit–reflect-array (TRA) antenna with asymmetric bidirectional beams using sparse-array method is presented in this communication. The proposed element consists of three-layer hexagonal-ring-patch (HRP) structure, able to achieve both amplitude (0 or 1) and phase modulation. Based on this kind of element structure, a 125 mm $\times \,\, 125$ mm square-shaped TRA is designed and fabricated. A 45.3% of the radiation units operate in transmission mode while others in reflection mode. Spatially fed by a conical horn antenna, two well-defined beams are obtained on both sides of the TRA, pointing to the direction of $\theta = 0^{\circ }$ and 170° ( $\varphi =0^{\circ }$ ), respectively. The measured results show a maximum gain of 21.4 dBi with a 1 dB gain bandwidth of 6.7% for the transmitted beam, and a maximum gain of 24.4 dBi with a 1 dB gain bandwidth of 9.3% for the reflected beam. To the authors’ best knowledge, it is the first time that the sparse-array method is employed in spatially fed antenna design. The proposed method can conveniently manipulate the pointing directions and beampattern characteristics of the bidirectional beams, providing a promising candidate for bidirectional wireless communication applications.

Sparse arrays based on the concept of a sum-difference coarray (SDCA) have increased degrees of freedom and enlarged effective array aperture compared to those only considering a difference coarray. Nevertheless, there still exist a number of overlapping virtual sensors between the difference coarray and the sum coarray, yielding high coarray redundancy. In this paper, we propose a k-level extended sparse array configuration consisting of one sparse subarray with k-level expansion and one uniform linear subarray. By systematically analyzing the inherent structure of the k-level extended sparse array, the closed-form expressions for sensor locations, uniform DOF and coarray redundancy ratio (CARR) are derived. Moreover, with the utilization of a k-level extended strategy, the proposed array remains a hole-free property and achieves low coarray redundancy. According to the proposed sparse array, the spatial and temporal information of the incident sources are jointly exploited for underdetermined direction-of-arrival estimation. The theoretical propositions are proven and numerical simulations are performed to demonstrate the superior performance of the proposed array.

3-D contrast enhanced ultrasound enables better visualization of inherently 3-D vascular geometries compared to an intersecting plane. Additionally, it would allow the application of motion correction techniques for all directions. Both contrast detection and motion correction work better on high-frame rate data. However high-frame rate 3-D ultrasound imaging with dense matrix arrays is challenging to realize. Sparse arrays alleviate some of the limitations in cable count and data rate that fully populated arrays encounter, but their increased level of secondary lobes negatively impacts image contrast. Meanwhile the use of unfocused transmit beams needed to achieve high-frame rates negatively impacts resolution. Here we propose to use adaptive beamforming by deep learning (ABLE) to improve the image quality of contrast enhanced ultrasound images acquired with a sparse spiral array. We train the neural network on simulated data and evaluate simulated images and in vivo images of an ex ovo chicken embryo. ABLE improved resolution compared to delay-and-sum (DAS) and spatial coherence (SC) beamforming on the simulated and in vivo data. The qualitative improvements persist after histogram matching, indicating that the image quality improvement of the ABLE images was not purely due to dynamic range stretching.

The design of conical frustum phased array antennas for air traffic control (ATC) radar systems is addressed. The array architecture, which is controlled by a fully digital beam-forming (DBF) network, is composed by a set of equal vertical modules. Each module consists of a linear sparse array that generates on receive multiple instantaneous beams pointing along different directions in elevation. To reach the best trade-off between the antenna complexity (i.e., minimum number of array elements and/or radio frequency components) and radiation performance (i.e., matching a set of reference patterns), the synthesis problem is formulated in the Compressive Sampling (CS) framework. Then, the positions of the array elements and the complex excitations for generating each single beam are jointly determined through a customized version of the Bayesian CS (BCS) tool. Representative numerical results, concerned with ideal as well as real antenna models, are reported both to validate the proposed design strategy and to assess the effectiveness of the synthesized modular sparse array architecture also in comparison with conventional arrays with uniformly-spaced elements.

This paper introduces a constrained normalized adaptive sparse array beamforming algorithm based on approximate L0-norm and logarithmic cost (L0-CNLMLS). The proposed algorithm can control the sparsity of the array by introducing an approximate function of L0-norm. In addition, the introduction of logarithmic cost improves the stability of the algorithm as well as the convergence rate of the algorithm. The sparsity of the array can be controlled when adjusting related parameter in the proposed algorithm. Simulation results show the better performance of L0-CNLMLS compared with some conventional algorithms.

Synthesis of sparse arrays is a promising area of research for a wide range of applications including radar and millimeter-wave wireless communication. The design goal of array thinning problems is to reduce the number of elements of an array without significantly affecting its performance. This work presents a technique for synthesizing a sparse phased-array antenna from a 16×16 uniform rectangular array (URA). The proposed approach reduces the number of elements by 50% without any significant increase in the peak sidelobe level (PSLL) for all possible scan angles in the azimuthal and elevation plans within a finite range of scan angles. The synthesis includes an artificial neural network (ANN) model for estimation of the excitation weights of the URA for a given scan-angle. The weights of the sparse array are computed by the Hadamard product of the weight matrix of the URA with a binary matrix that is obtained using particle swarm optimization (PSO) to minimize the PSLL.

In acoustic sensing systems, acoustic vector sensor (also known as vector hydrophone for underwater applications) arrays are widely used. Most of the acoustic vector sensor array signal processing methods presume the minimum spacing between two adjacent sensors or sensor components to be within a half-wavelength in order to avoid azimuth–elevation angle estimation aliasing. This would limit the effective array aperture, thereby reducing the potential estimation accuracy. Furthermore, they are unapplicable to the underdetermined scenarios, where the number of sources exceeds that of sensor components. Exploiting the recently proposed nested array concept, we present a new type of nested array, termed as Sparse Nested spatially spread Square Acoustic Vector sensor Array (SNSAVA) to realize underdetermined 2-D direction finding with increased estimation accuracy. In SNSAVA, interspacing of two sensors and two components of a sensor can be spread to be much higher than a half-wavelength so that the effective array aperture will be significantly extended. An unambiguous angle estimation method is further derived to make this fully sparse array configuration practically feasible. Performance studies focused on underdetermined high-accuracy azimuth–elevation angle estimation are provided via numerical examples. The estimation performance for the SNSAVA is also compared with that of the nested acoustic vector sensor arrays, proposed in [33], and with the Cramer–Rao bound.

Ultrasonic phased array all-focus imaging algorithm has the advantages of high accuracy and full range dynamic focusing, but the existing imaging time-consuming problem limits its practical industrial application. In order to meet the requirements of real-time imaging and clear and distinguishable image defects in all-focus array ultrasound scanning. In this paper, a sparse optimization model of TFM phased array is established. Based on the Fermat principle, the delay time of each element under two layers of media is calculated, and a two-layer media phased array all-focus imaging algorithm is established, using minimal redundancy. The sparse design of the MRLA is carried out, and the all-focus imaging and sparse all-focus imaging experiments of the two-layer medium are carried out, and the influence of the sparse emission array on the defect quantitative accuracy and the calculation efficiency of the all-focus algorithm is discussed. The final optimized sparse array is compared with the sound field beam pattern of the full array, the smallest redundant array, and the genetic algorithm optimized array, and an all-focus scanning environment is established based on the array. Scanning images can not only obtain the maximum amount of information under minimum redundancy, but also have good sidelobe characteristics. At the same time, the array is sparse, which greatly improves the efficiency of all-focus scanning, and provides a certain reference value for the research of all-focus imaging technology.

A sparse array synthesis method based on improved wind-driven optimization algorithm (IWDO) and fast Fourier transform (FFT) for the purpose of sidelobe suppression was introduced. First, the unifo...

In this paper, we address the problem of direction finding using coprime array, which is one of the most preferred sparse array configurations. Motivated by the fact that non-uniform element spacing hinders full utilization of the underlying information in the receive signals, we propose a direction-of-arrival (DoA) estimation algorithm based on low-rank reconstruction of the Toeplitz covariance matrix. The atomic-norm representation of the measurements from the interpolated virtual array is considered, and the equivalent dual-variable rank minimization problem is formulated and solved using a cyclic optimization approach. The recovered covariance matrix enables the application of conventional subspace-based spectral estimation algorithms, such as MUSIC, to achieve enhanced DoA estimation performance. The estimation performance of the proposed approach, in terms of the degrees-of-freedom and spatial resolution, is examined. We also show the superiority of the proposed method over the competitive approaches in the root-mean-square error sense., Comment: 6 pages, 5 figures, under review with the IEEE Communications Letters

In this work, we consider the problem of joint sparse array antenna design and phase-only beampattern shaping with reconfigurability. Our design objective is to reduce the cost of the antenna system for the unmanned aerial vehicle (UAV) radar with a large-aperture array. We formulate this co-design problem as a sparse optimization problem with angular response and binary-like modulus constraints. To solve the resultant NP-hard nonconvex problem, we propose a consensus alternating direction method of multipliers (ADMM) based algorithm. This method transforms the original problem into a higher-dimensional one by introducing two categories of auxiliary variables. By doing so, the problem can be effectively tackled via alternately solving several subproblems, meanwhile the tricky binary modulus constraints can be well handled by utilizing the geometric property of the subproblem. We further prove that the proposed algorithm converges to the KKT points of the original problem. In addition, we extend our methodology to the discrete phase case to handle the practical finite-bit phase quantization. The devised algorithm is capable of generating phase-only weight vector meanwhile automatically selecting appropriate antenna elements according to the specific beam shape. Numerical examples are given to demonstrate the effectiveness of the proposed approach.

In the present study, the generalized compressed nested array (GCNA) is proposed to improve the fourth-order cumulant-based direction of arrival (DOA) estimation performance when the small-scale array is deployed. The main objective of this study is to demonstrate that the new-formed array can form the sum co-array, which is close to the nested array, by a few sensors. Meanwhile, it is found that the difference co-array of its sum co-array or the fourth-order difference co-array (FODC) of GCNA is hole-free so that it can achieve a long consecutive virtual array. Obtained results show that for less than 12 sensors, GCNA can achieve the longest consecutive virtual array when the comparison is made with conventional FODC-based sparse arrays. It is inferred that for a small-scale sensor array, the GCNA can acquire more degrees of freedom (DOFs) for DOA estimation than other sparse arrays. In order to evaluate the performance of the proposed sparse array, numerous simulations are carried out to compare the number of resolved sources and estimation accuracy of different sparse arrays. Accordingly, it is concluded that the proposed GCNA outperforms conventional representative sparse arrays.

Purpose Because of the small size and high integration of capacitive micromachined ultrasonic transducer (CMUT) component, it can be made into large-scale array, but this lead to high hardware complexity, so the purpose of this paper is to use less elements to achieve better imaging results. In this research, an optimized sparse array is studied, which can suppress the side lobe and reduce the imaging artifacts compared with the equispaced sparse array with the same number of elements. Design/methodology/approach Genetic algorithm is used to sparse the CMUT linear array, and Kaiser window apodization is added to reduce imaging artifacts, the beam pattern and peak-to-side lobe ratio are calculated, point targets imaging comparisons are performed. Furthermore, a 256-elements CMUT linear array is used to carry out the imaging experiment of embedded mass and forearm blood vessel, and the imaging results are compared quantitatively. Findings Through the imaging comparison of embedded mass and forearm blood vessel, the feasibility of optimized sparse array of CMUT is verified, and the purpose of reducing the hardware complexity is achieved. Originality/value This research provides a basis for the large-scale CMUT array to reduce the hardware complexity and the amount of calculation. At present, the CMUT array has been used in medical ultrasound imaging and has huge market potential.

In this study we propose a novel sparse antenna array and suitable beamforming algorithm in order to decrease the number of antennas in large-scale antenna systems (LSASs) and achieving the performance of a dense antenna array. To design a sparse array we use the familiar array geometry that is called co-prime sensor array (CSA), which has been recently introduced as an effective sparse configuration in direction of arrival (DOA) estimation and beamforming applications. The prototype CSA can achieve narrow beam widths using far fewer sensors than a fully populated uniform linear array (Full ULA), but at a cost of the appearance of grating lobes. Grating lobe manifests itself as leakage in the spectral domain, distorting other weak spectral responses. To mitigate this issue, we use a new processing method based on digital beamforming at sub-array level. Moreover, we developed a novel sparse array geometry, so-called Extended Optimum CSA (EOCSA), for DOA estimation of received signal. The EOCSA would be very useful in many practical applications where the number of sensors is limited. The performance of the proposed beamfoming method in EOCSA with $$N=O(N_1+N_2)$$ sensors is compared to a Full ULA with $$M=O(N_1N_2)$$ physical sensors. The results illustrate the EOSCA ability to reaches the same power pattern of a Full ULA using relatively few sensors. Analytical and simulated results demonstrate that the power pattern obtained by the proposed beamforming processor in the EOCSA, in terms of side lobe level (SSL), peak side lobe level (PSL) and integrated side lobe level (ISL), is better than the previous arrays and processors.

Conventional transmit subarray partitioning schemes of phased-MIMO radar will cause several problems, the reduction of array aperture, the increase of feeding network complexity and optimization algorithms time cost. Focus on the problems above, this paper proposes a deep learning-based interleaved sparse transmit subarray partitioning method. Firstly, the training data is generated by phased-MIMO array manifold matrix. Secondly, a dimensionality reduction method for radar data is introduced to reduce the dimensionality of the sample data while minimizing information loss. Then, a lightweight convolutional neural network is constructed for training and the optimal array structures is selected by classification. Finally, linear and plane arrays experiment results show that our proposed method can achieve 97.95% classification accuracy, better than other conventional dimensionality reduction methods and neural networks; compared with the traditional SCP partitioning method, our proposed method has similar beampattern sidelobe level and DOA estimation accuracy, but the time cost is greatly reduced.

A novel method based on alternating linear programming optimization is presented to synthesize sparse linear arrays with sum and difference patterns. This method can find the optimized element positions and excitations shared for both sum and difference patterns with accurate control of multiregion sidelobe distribution and difference pattern null slope. In addition, the constraints on the minimum element spacing and dynamic range ratio of the obtained excitations can be also appropriately incorporated into this alternating optimization process. Two synthesis examples with different pattern shape requirements are conducted to validate the effectiveness and advantages of the proposed method.

We propose a high-resolution imaging radar system to enable high-fidelity four-dimensional (4D) sensing for autonomous driving, i.e., range, Doppler, azimuth, and elevation, through a joint sparsity design in frequency spectrum and array configurations. To accommodate a high number of automotive radars operating at the same frequency band while avoiding mutual interference, random sparse step-frequency waveform (RSSFW) is proposed to synthesize a large effective bandwidth to achieve high range resolution profiles. To mitigate high range sidelobes in RSSFW radars, optimal weights are designed to minimize the peak sidelobe level such that targets with a relatively small radar cross section are detectable without introducing high probability of false alarm. We extend the RSSFW concept to multi-input multi-output (MIMO) radar by applying phase codes along slow time to synthesize a two-dimensional (2D) sparse array with hundreds of virtual array elements to enable high-resolution direction finding in both azimuth and elevation. The 2D sparse array acts as a sub-Nyquist sampler of the corresponding uniform rectangular array (URA) with half-wavelength interelement spacing, and the corresponding URA response is recovered by completing a low-rank block Hankel matrix. Consequently, the high sidelobes in the azimuth and elevation spectra are greatly suppressed so that weak targets can be reliably detected. The proposed imaging radar provides point clouds with a resolution comparable to LiDAR but with a much lower cost. Numerical simulations are conducted to demonstrate the performance of the proposed 4D imaging radar system with joint sparsity in frequency spectrum and antenna arrays.

A method based on reweighted ${l}_{\mathbf {1}}$ norm regularization for synthesizing a near-field (NF) sparse array with accurate control of 3 dB beamwidth(BW), focal distance, and peaksidelobelevel (PSL) is proposed in this communication. We first formulate the problem of synthesizing NF sparse array as a reweighted ${l}_{\mathbf {1}}$ norm optimization problem. The constraints for NF focusing array are proposed to accurately control the 3 dB BW, focal distance, and PSL at the same time. An effective definition of the solution space for the NF synthesis problem is proposed to have the NF pattern well constrained and ensure the practicability and convergence of the proposed method. Finally, simulation examples are presented and compared with full-wave simulation results to validate the effectiveness and advantages of the proposed method.

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Author(s): Cheng, Feng; Xia, Jianghai; Zhang, Kai; Zhou, Changjiang; Ajo-Franklin, Jonathan B | Abstract: SUMMARY Surface wave retrieval from ambient noise records using seismic interferometry techniques has been widely used for multiscale shear wave velocity (Vs) imaging. One key step during Vs imaging is the generation of dispersion spectra and the extraction of a reliable dispersion curve from the retrieved surface waves. However, the sparse array geometry usually affects the ability for high-frequency (g1 Hz) seismic signals’ acquisition. Dispersion measurements are degraded by array response due to sparse sampling and often present smeared dispersion spectra with sidelobe artefacts. Previous studies usually focus on interferograms’ domain (e.g. cross-correlation function) and attempt to enhance coherent signals before dispersion measurement. We propose an alternative technique to explicitly deblur dispersion spectra through use of a phase-weighted slant-stacking algorithm. Numerical examples demonstrate the strength of the proposed technique to attenuate array responses as well as incoherent noise. Three different field examples prove the flexibility and superiority of the proposed technique: the first data set consists of ambient noise records acquired using a nodal seismometer array; the second data set utilizes distributed acoustic sensing (DAS) and a marine fibre-optic cable to acquire a similar ambient noise data set; the last data set is a vibrator-based active-source surface wave data. The enhanced dispersion measurements provide cleaner and higher-resolution spectra without distortions which will assist both human interpreters as well as ML algorithms in efficiently picking curves for subsequent Vs inversion.

Sparse sensor array selection arises in many engineering applications, where it is imperative to obtain maximum spatial resolution from a limited number of array elements. Recent research shows that computational complexity of array selection is reduced by replacing the conventional optimization and greedy search methods with a deep learning network. However, in practice, sufficient and well-calibrated labeled training data are unavailable and, more so, for arbitrary array configurations. To address this, we adopt a deep transfer learning (TL) approach, wherein we train a deep convolutional neural network (CNN) with data of a source sensor array for which calibrated data are readily available and reuse this pre-trained CNN for a different, data-insufficient target array geometry to perform sparse array selection. Numerical experiments with uniform rectangular and circular arrays demonstrate enhanced performance of TL-CNN on the target model than the CNN trained with insufficient data from the same model. In particular, our TL framework provides approximately 20% higher sensor selection accuracy and 10% improvement in the direction-of-arrival estimation error., Accepted paper in IEEE Transactions on Cognitive Communications and Networking

In this article, we propose a novel type of a wideband 2-D array of cold-electron bolometers (CEBs) sensitive to both polarizations of the incoming optical signal. This array was developed for osservatorio per il lontano infrarosso e le microonde su pallone orientabile (OLIMPO) balloon telescope with a requirement on bandwidth more than 10%. Sensitivity to both polarization components was achieved by a special meander-type arrangement of orthogonal L/2 dipoles. We present theoretical estimations for the optimal arrangement of 2-D arrays of CEBs, which allows achieving maximum efficiency in a wide band with the lowest noise equivalent power (NEP). A pixel layout with an optimal density of CEBs, sensitive to dual polarizations, and having more than 10% FWHM bandwidth at around 350 GHz was proposed and numerically analyzed. The layout consists of a periodic sparse array of orthogonal dipoles sensitive to both polarization components of the incoming signal. The numerical analysis confirmed that the sparse array is the most promising for a combination of high absorbing efficiency and low noise of the system and satisfying the 10% bandwidth requirements for the OLIMPO instrument. Different combinations of series and parallel connections of bolometers were considered for better noise properties to achieve the photon noise-limited level.

Unlike conventional phased array (PA), frequency diversity array (FDA) can perform the beampattern synthesis not only in an angle dimension but also in a range dimension by introducing an additional frequency offset (FO) across the array aperture, thus greatly enhancing the beamforming flexibility of an array antenna. Nevertheless, an FDA with uniform inter-element spacing that consists of a huge number of elements is required when a high resolution is needed, which results in a high cost. To substantially reduce the cost while almost maintaining the antenna resolution, it is important to conduct a sparse synthesis of FDA. Under these circumstances, this paper investigated the transmit–receive beamforming of a sparse-fda in range and angle dimensions. In particular, the joint transmit–receive signal formula was first derived and analyzed to resolve the inherent time-varying characteristics of FDA based on a cost-effective signal processing diagram. In the sequel, the GA-based low sidelobe level (SLL) transmit–receive beamforming of the sparse-fda was proposed to generate a focused main lobe in a range-angle space, where the array element positions were incorporated into the optimization problem. Numerical results showed that 50% of the elements can be saved for the two linear FDAs with sinusoidally and logarithmically varying frequency offsets, respectively termed as sin-FO linear-FDA and log-FO linear-FDA, with only a less than 1 dB increment in SLL. The resultant SLLs are below −9.6 dB, and −12.9 dB for these two linear FDAs, respectively.

This paper proposes a joint estimation method for source number and DOA based on an improved convolutional neural network for unknown source number and undetermined DOA estimation. By analyzing the signal model, the paper designs a convolutional neural network model based on the existence of a mapping relationship between the covariance matrix and both the source number and DOA estimation. The model, which discards the pooling layer to avoid data loss and introduces the dropout method to improve generalization, takes the signal covariance matrix as input and the two branches of source number estimation and DOA estimation as outputs, and achieves the unfixed number of DOA estimation by filling in invalid values. Simulation experiments and analysis of the results show that the algorithm can effectively achieve the joint estimation of source number and DOA. Under the conditions of high SNR and a large snapshot number, both the proposed algorithm and the traditional algorithm have high estimation accuracy, while under the conditions of low SNR and a small snapshot, the algorithm is better than the traditional algorithm, and under the underdetermined conditions, where the traditional algorithm often fails, the algorithm can still achieve the joint estimation.

Larger array aperture is provided by sparse arrays than uniform ones, which can improve the angle estimation resolution and reduce the cost of system evidently. However, manifold ambiguity is introduced due to the array sparsity. In this paper, a Power Estimation Multiple-Signal Classification (PE-MUSIC) algorithm is proposed to solve the manifold ambiguity of arbitrary sparse arrays for uncorrelated sources in Multiple-Input Multiple-Output (MIMO) radar. First, the paired direction of departure (DOD) and direction of arrival (DOA) are obtained for all targets by MUSIC algorithm, including the true and spurious ones; then, the well-known Davidon–Fletcher–Powell (DFP) algorithm is applied to estimate all targets’ power values, among which the value of a spurious target trends to zero. Therefore, the ambiguity of sparse array in MIMO radar can be cleared. Simulation results verify the effectiveness and feasibility of the method.

A hybrid efficient optimizing method of wide scanning sparse planar array involving mutual coupling is investigated in this letter. The former work of matrix enhancement and matrix pencil (MEMP)-based synthesis method is extended to the design of pattern reconfigurable sparse arrays in wide-angle scanning. The genetic algorithm was utilized to further optimize the reconstructed sparse array including the actual antenna element, which differs from the only array factor synthesis of MEMP. To improve the optimization efficiency and design accuracy, the space mapping technique was exploited to accomplish the optimizing design, which also involves the interactions among elements during the optimizing process. A wide-scanning sparse array can be realized by the new relationship of parameter mapping courses between low-cost coarse model optimizations and high-accuracy fine model validations based on the characteristic mode and multilevel fast multipole algorithm. Numerical examples show the efficiency of the proposed method.

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.

Recently, dilated nested arrays have been proposed on a moving platform to increase the uniform degrees of freedom (uDOF) by a factor of three by exploiting array motion. However, no literature addresses the issue whether the same dilation method still performs well for other array geometries such as coprime arrays, augmented nested arrays and minimum redundancy arrays. Compared with nested arrays, these arrays either achieve higher uDOF or exhibit more robustness to mutual coupling among sensors. In this paper, we propose a novel sparse array geometry named dilated arrays (DAs) on a moving platform by applying the dilation method to other array geometries. First, by exploiting the relationship between the element positions in the difference coarrays of the original linear array and the synthetic array after motion, we prove that, for a DA on a moving platform, the maximum uDOF can be tripled compared to that of its original array regardless of the array geometry. Therefore, the number of sources that can be resolved for direction-of-arrival (DOA) estimation is increased threefold. Second, we prove that a DA reduces mutual coupling compared with its original array. As a result, the DA is more robust to mutual coupling than its original array. Third, we extend one-dimensional DAs to the two-dimensional (2-D) case, yielding a new 2-D sparse array geometry named two-parallel DAs. We show that by exploiting array motion, two-parallel DAs can increase the number of detectable sources threefold. Numerical simulations demonstrate the superior performance of the proposed array geometries.

The coprime array owns a sparse array structure, which can effectively alleviate mutual coupling, while the holes existing in the difference co-array(DCA) greatly reduce the number of uniform degrees of freedom(uDOFs). In this letter, we propose a new coprime array structure called hole-free coprime array (HFCA) by carefully assembling the subarrays, and the resulting HFCA can generate a hole-free DCA. Furthermore, we derive the optimal HFCA that can produce the largest hole-free DCA with a given number of sensors, which contributes to an increase of uDOFs compared with existing coprime array structures. In addition, the simulations are provided to demonstrate the superiority of HFCA in terms of uDOFs, direction of arrival estimation performance, and spatial resolution.

In this paper, we develop a general framework of multi-frequency sparse array to estimate the direction-of-arrival (DOA) of a significantly higher number of targets than the number of physical sensors. The multi-frequency sparse arrays are designed to offer zero lag redundancy in the rendered difference coarray so that the available degrees of freedom are fully utilized to enable high-resolution DOA estimation. A modified sensor interpolation technique is developed to accurately estimate the signal correlation matrix so that the effect of holes in the difference coarray is mitigated. The proposed technique accounts for both self-lags between signals corresponding to the same frequencies and the cross-lags between signals corresponding to different frequencies. As such, it enhances the DOA estimation performance compared to existing methods that either perform array interpolation utilizing only the self-lags or carry out group sparse reconstruction without exploiting array interpolation. Simulation results verify the offerings of the multi-frequency sparse arrays.

We present novel generalized non-redundant sparse array design strategies that achieve the highest possible number of degrees-of-freedom (DOFs) for direction-of-arrival (DOA) estimation. These array designs offer difference co-arrays that do not contain any lag redundancies except the unavoidable redundancies at lag zero. We first develop a co-array-based zero-redundancy design rule which serves as a baseline for constructing these non-redundant arrays, and a large-aperture naive structured non-redundant sparse array is presented. We then develop a systematized design framework based on disjunctive programming to obtain non-redundant sparse array structures with a minimum array aperture, resulting in minimum hole arrays. The disjunctive programming framework is then extended to an equivalent mixed-integer linear programming problem. As a result, given the same number of physical sensors, the design framework provides a difference co-array with the maximum number of correlation lags and resolves more sources than existing sparse array structures. The non-redundant sparse array design is further generalized in two new directions, respectively achieving an arbitrary array aperture and reducing mutual coupling effects. Among the several new sparse array designs obtained from such generalizations, the hybrid non-redundant sparse array design simultaneously achieves the highest number of DOFs, meets a desired array aperture requirement, and reduces mutual coupling effects. Structured matrix completion methods are employed to interpolate the missing lags in the resulting difference co-arrays, thereby enabling high-resolution gridless DOA estimation with improved performance. Simulation results demonstrate the superiority of the generalized non-redundant sparse array design strategies over existing sparse array structures

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.

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.

In this paper, an aperture expanding direction finding algorithm using L-shaped non-uniform sparse array is proposed. Firstly, the virtual array is expanded by vectorizing, de-redundant and sorting of received data covariance matrix. Secondly, the full rank matrix is got by smoothing the virtual array data, and the signal subspace is obtained by matrix block processing. Finally, the elevation angle and azimuth angle are acquired by using the rotation invariant relation. The algorithm does not need to decompose the covariance matrix of the data, nor does it need to search the two-dimensional spectral peaks. It can greatly reduce the computational complexity when there are many array elements and large number of snapshots. The simulation results show that the sparse array arrangement can enlarge the array aperture, improve the parameter resolution and the accuracy of DOA estimation, and verify the effectiveness of the proposed algorithm.