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In correlation-based processing, sparse arrays offer the capacity to resolve a greater number of uncorrelated sources than physical sensors due to the considerable breadth of their difference coarrays, originating from variations in the locations of elements. Consequently, there is significant interest in devising sparse arrays with sizable difference coarrays and expanding the analysis to encompass additional array characteristics like symmetry, resilience, and cost-effective engineering. We present a scalable and systematic methodology for designing large sparse arrays. Considering several attributes and factors, we can address Fractal arrays that were used for low-side lobe antenna array designing and have very low degrees of freedom; hence, sparsity is introduced to design a hole-free difference coarray which not only increases the number of degrees of freedom in fractal arrays but also aids in better beamforming applications and enhanced DoA results due to regularization in coarrays. We develop an innovative sparse fractal array to enhance the accuracy of DoA estimation for predicting a maximum number of uncorrelated sources with a minimum possible actual sensors. First, the 1D sparse fractal array is constructed and then it is extended to a 2D sparse fractal array for both azimuth and elevation angle estimation. Comprehensive robustness analysis is conducted on the proposed sparse fractal array, encompassing one-dimensional (1D) and two-dimensional (2D) configurations, in response to sensor failures. RMSE analysis shows that the proposed 1D and 2D arrays possess the minimum error when used for direction estimation. [ABSTRACT FROM AUTHOR]

In this study, a moving single-station direct position determination (DPD) algorithm based on virtual interpolated arrays is proposed. Existing moving single-station algorithms face challenges such as the incomplete utilization of sparse array apertures and insufficient consideration of mixed circular and non-circular signals. To address these issues, we propose an enhanced gridless DPD algorithm, suitable for multiple mixed circular and non-circular sources. Through constructing a non-zero unconjugated covariance matrix from the non-circular components of the mixed signals, the data dimensionality is expanded, and the gridless method is used to fill the voids in the coarray, significantly improving localization performance. Additionally, a unitary transformation method is applied to reduce computational complexity. This method transforms complex operations into real operations by applying unitary transformations to steering vectors and subspaces. Simulation results demonstrate that the proposed algorithm offers significant advantages in terms of array degrees of freedom and localization accuracy. [ABSTRACT FROM AUTHOR]

In this paper, the direction of arrival (DOA) estimation problem for the unfolded coprime linear array (UCLA) is researched. Existing common stacking subarray-based methods for the coprime array are invalid in the case of its subarrays, which have the same steering vectors of source angles. To solve the phase ambiguity problem, we reconstruct an improved unfolded coprime linear array (IUCLA) by rearranging the reference element of the prototype UCLA. Specifically, we design the multiple coprime inter pairs by introducing the third coprime integer, which can be pairwise with the other two integers. Then, the phase ambiguity problem can be solved via the multiple coprime property. Furthermore, we employ a spectral peak searching method that can exploit the whole aperture and full DOFs of the IUCLA to detect targets and achieve angle estimation. Meanwhile, the proposed method avoids extra processing in eliminating ambiguous angles, and reduces the computational complexity. Finally, the Cramer–Rao bound (CRB) and numerical simulations are provided to demonstrate the effectiveness and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Based on the principle of spatial power combination of sparse array time reversed signals, the relationship of distances between constructive interference points to cross angle of beams and viewing angles has been analyzed. Then the formulas of distances between adjacent constructive points at 360-degree views are derived. Considering that the distance between constructive interference points around target is frequently needed to be less than target's antenna size, The variation law of the view range with beam crossover angle has been simulated and analyzed with MATLAB when the above conditions are met at the same frequency and without errors. On this basis, array deployment recommendations are summed up. In addition, the effects of the received time window length and the difference of the distance between each array element and the target point on the synthesized power have been analyzed. Finally, the spatial power combination simulation experiments of the sparse array time-reversed signal have been carried out. The experimental results show that the methods and conclusions of this paper can provide theoretical basis and reference for the research and application of sparse array power combination technology in long-range wireless energy delivery, high-power microwave weapons, electronic warfare, etc. [ABSTRACT FROM AUTHOR]

Using sparse matrix for total focusing method (TFM) imaging can improve computational efficiency in non-destructive testing (NDT). In sparse matrix design, binary particle swarm optimisation (BPSO) and genetic algorithm (GA) often fall into local optimal solution, and the computational efficiency decreases significantly with the expansion of array scale. In this paper, a discrete war strategy optimisation (DWSO) is proposed to realise sparse array ultrasonic imaging. This method uses equidistant scatter mapping to real-number encode the array position and limit the search range. Then, the fitness function is constructed with low side lobe peak and narrow main lobe width to obtain the optimal array element distribution. Experiments on standard test block demonstrate the DWSO algorithm has a narrower main lobe width and lower side lobe peaks than BPSO and GA. The imaging time of the sparse array constructed by this algorithm is reduced by more than 65% compared with the full array. As array scale grows, the running time variation of the proposed method is reduced by 73.2% and 77.3% compared with GA and BPSO, which has good adaptability and provides theoretical support for real-time defect detection. [ABSTRACT FROM AUTHOR]

Enhancing imaging performance is one of long-term goals pursued by ultrasonic phased array in the field of nondestructive testing. However, the computational complexity will grow when the imaging methods are improved. In this work, delay-multiply-and-sum (DMAS) is combined with sparse array technique to achieve better imaging performance and maintain the almost same computational cost as sparse total focus method (TFM) needs. Comparison analysis is conducted on the beam pattern and imaging metrics, and the result indicates that sparse DMAS works better over sparse TFM at the same level of imaging time. [ABSTRACT FROM AUTHOR]

The paper considers the design of sparse arrays in the interference active environment to minimise the system complexity and achieve reduced hardware cost. For this, we propose a sparse array design methodology to attain maximum signal-to-interference plus noise ratio (MaxSINR) in the presence of interfering signals. We formulate the optimisation problem as a real-valued quadratically constrained quadratic program (QCQP) with the non-convex $\textstyle\ell_p$ ℓ p norm to promote sparsity, which is iteratively controlled in the proposed approach. We employ the semidefinite relaxation (SDR) technique and the principle of the majorization-minimisation (MM) algorithm to solve the non-convex QCQP problem. The efficacy of the proposed algorithm is demonstrated through the simulation results. The sparse array obtained through the proposed method performs well when compared with the reweighted $\textstyle\ell_1$ ℓ 1 algorithm. [ABSTRACT FROM AUTHOR]

To address the problem of the destruction of virtual array continuity and the degradation of degree of freedom due to missing data in two-dimensional sparse array under the conditions of sensor failures, a two-dimensional DOA estimation algorithm is proposed. Firstly, the virtual array is constructed based on the two-dimensional difference coarray, and then the covariance matrix data is recovered in the form of matrix completion by using decoupled atomic norm minimization to realize the virtual array interpolation. Finally, the SS-MUSIC algorithm is used for the two-dimensional DOA estimation of multiple sources. The proposed method compensates for the effects caused by the failure of physical sensors. It recovers the complete aperture characteristics of the original virtual array and maintains the degree of freedom of the virtual array, which ensures a higher-precision two-dimensional DOA estimation performance. Simulation results demonstrate that under the same number of physical elements and sensor failure, the proposed algorithm can effectively estimate more sources compared with the existing methods, and exhibits higher robustness under the conditions of a small number of snapshots and low signal-to-noise ratio. This approach maximally retains and utilizes the degree of freedom advantage of sparse arrays in the two-dimensional DOA estimation.

The concept of sparse array synthesis has attracted considerable attention due to its potential to reduce hardware costs in array design and enhance the efficiency of array aperture utilization. In contrast to conventional artificial neural networks (ANNs), a more efficient encoder–decoding ANN framework is proposed in this letter for designing sparse linear arrays. The decoder is pretrained with a randomly generated training set, enabling its ability to rapidly predictiction of far‐field patterns. This process considers the actual coupling effect among the antenna elements. The output of the encoder is used as the input of the decoder to synthesize the sparse arrays by providing the desired pattern to the encoder. During the training process, a novel lp ${l}_{p}$‐norm (0

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Copyright of Aero Weaponry is the property of Aero Weaponry Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we propose a tensor-based subspace algorithm for the two-dimensional direction of arrival (2D-DOA) estimation using a sparse array equipped with electromagnetic vector sensors (EMVS). Our approach capitalizes on the multidimensional characteristics of the collected data by arranging its covariance into a fourth-order tensor. Through the application of higher-order singular value decomposition, we improve signal subspace estimation compared to existing methods. To further enhance our algorithm, we integrate spatial rotation invariance techniques and vector cross-product methods. This combination enables automatic angle estimation without the need for pairing and without compromising aperture loss. Our proposed algorithm exhibits superior estimation performance, particularly in challenging scenarios characterized by low signal-to-noise ratios and limited snapshot availability. To validate the effectiveness and enhancements of our approach, we conduct numerical simulation experiments. [ABSTRACT FROM AUTHOR]

An optical phased array (OPA) with 2-D circular sparse array aperture has been proposed and demonstrated in the silicon integrated photonic platform. The sparse distribution of the antenna array can realize no grating lobes in 2-D full field of view (FOV). To achieve fast and accurate phase calibration for OPA, an improved rotating element electric field vector algorithm based on golden section search method (GSS-REV) has also been proposed and verified. The 32-element antenna sparse distribution of the proposed OPA is designed and fabricated. A far-field beam steering measurement across 20° × 20° range features the side lobe suppression ratio (SLSR) of larger than 4.81 dB and a full width at half-maximum (FWHM) of approximately 0.63° × 0.59°. The resolvable points are derived to be ∼1076. The OPA chip has also been demonstrated on range measurement with frequency-modulated continuous-wave (FMCW) system.

In this study, a moving single-station direct position determination (DPD) algorithm based on virtual interpolated arrays is proposed. Existing moving single-station algorithms face challenges such as the incomplete utilization of sparse array apertures and insufficient consideration of mixed circular and non-circular signals. To address these issues, we propose an enhanced gridless DPD algorithm, suitable for multiple mixed circular and non-circular sources. Through constructing a non-zero unconjugated covariance matrix from the non-circular components of the mixed signals, the data dimensionality is expanded, and the gridless method is used to fill the voids in the coarray, significantly improving localization performance. Additionally, a unitary transformation method is applied to reduce computational complexity. This method transforms complex operations into real operations by applying unitary transformations to steering vectors and subspaces. Simulation results demonstrate that the proposed algorithm offers significant advantages in terms of array degrees of freedom and localization accuracy.

In this paper, the direction of arrival (DOA) estimation problem for the unfolded coprime linear array (UCLA) is researched. Existing common stacking subarray-based methods for the coprime array are invalid in the case of its subarrays, which have the same steering vectors of source angles. To solve the phase ambiguity problem, we reconstruct an improved unfolded coprime linear array (IUCLA) by rearranging the reference element of the prototype UCLA. Specifically, we design the multiple coprime inter pairs by introducing the third coprime integer, which can be pairwise with the other two integers. Then, the phase ambiguity problem can be solved via the multiple coprime property. Furthermore, we employ a spectral peak searching method that can exploit the whole aperture and full DOFs of the IUCLA to detect targets and achieve angle estimation. Meanwhile, the proposed method avoids extra processing in eliminating ambiguous angles, and reduces the computational complexity. Finally, the Cramer–Rao bound (CRB) and numerical simulations are provided to demonstrate the effectiveness and superiority of the proposed method.

3D synthetic aperture (SA) imaging of volumes can be obtained using sparse 2D ultrasound arrays. However, even with just 256 elements, the volumetric imaging rate can be relatively slow due to having to transmit on each element in succession. Hadamard Aperiodic Interval (HAPI) codes can be used to image the full SA dataset in one extended transmit to speed up the synthetic aperture imaging, but their long nature produces large deadzones if the same elements are used as both transmitters and receivers. In this simulation study, we use a 2D Costas sparse array with separate transmitters and receivers to remedy the deadzone problem, and use it with the HAPI-coded imaging scheme to obtain fully transmit-receive focused, wide field-of-view 3D volumes with high-resolution and high SNR at ultrafast volumetric imaging rates of more than 500 volumes per second, almost nine times faster than non-coded SA imaging with the same imaging parameters. We show similar PSF performance compared to non-coded SA, and a 26 dB improvement in SNR with order-256 HAPI codes. We also present cyst simulations showing similar contrast for the HAPI-coded SA method compared to non-coded SA in the context of no noise, and improved contrast in the context of noise., Competing Interests: Declaration of competing interest The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Roger Zemp reports financial support was provided by Alberta Innovates. Roger Zemp reports financial support was provided by Natural Sciences and Engineering Research Council of Canada. Roger Zemp reports financial support was provided by AB Innovat. Roger Zemp reports financial support was provided by Canadian Institutes of Health Research. Roger Zemp reports financial support was provided by National Institutes of Health. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 The Authors. Published by Elsevier B.V. All rights reserved.)

Sparse array antennas are significant in communication and radar systems due to the advantages of high resolution, low complexity, and immunity to interference. In this letter, a novel array synthesis method based on an improved genetic algorithm (IGA) is proposed to optimize the antenna position in the sparse array. Different from the traditional generic methods with high computational complexity, a method combined with Gaussian process regression (GPR) prediction is proposed to optimize the antenna position with low computational complexity. The proposed method can minimize the peak sidelobe level (PSLL) during the beam scanning procedures. Moreover, the minimum antenna spacing constraint is also considered to ensure a physically achievable solution. Simulation results show that the proposed method can achieve a lower PSLL with fewer iterations and provide a global optimization solution for large array synthesis compared with existing methods. Furthermore, a prototype of the sparse array principle optimized by IGA is designed. Measurement results indicate that the optimized sparse array has good synthesis performance in high frequency. • A novel array synthesis method based on an improved genetic algorithm is proposed. • The proposed method can minimize the PSLL during the beam scanning procedures. • A prototype of the sparse array principle optimized by IGA is designed. [ABSTRACT FROM AUTHOR]

Null Subtraction Imaging (NSI) is a novel beamforming technique that can produce B-mode images resulting in high spatial resolution and low computational cost compared to other beamforming techniques. Previous work has demonstrated that in addition to a beam pattern with a narrow main lobe and low side lobes, NSI can also reduce or mitigate grating lobes, which can appear when the array pitch is larger than one half the wavelength of the transmitted pulse. These grating lobes can result in imaging artifacts that produce clutter and lower contrast. By lowering grating lobe levels, a larger pitch array could be used, which could allow arrays with a larger field of view while maintaining a standard element count. This could have important benefits for specific applications such as ultrasonic abdominal imaging. Experiments were conducted to examine the feasibility of using NSI with large pitch, wide field-of-view arrays. Grating lobe reduction was measured against array pitch, DC offset, and f-number. Experiments were conducted on wire targets and contrast targets in a phantom and results were further verified in vivo by imaging the liver of a rabbit. The results demonstrated that NSI was able to reduce grating lobe brightness by up to 45 dB compared to delay-and-sum (DAS) beamforming when using planewave transmissions, reduce the generalized contrast-to-noise ratio (gCNR) of grating lobe regions from 0.60 to 0.08, and maintain a similar speckle quality to DAS. The gCNR of anechoic regions also improves, increasing from 0.09 to 0.15 on an array with a pitch of 5 wavelengths. Due to significant grating lobe level reduction, NSI shows potential to improve image quality over DAS on a large pitch, wide field-of-view array. • Large-pitch arrays can increase field-of-view, but produce grating lobes. • Null Subtraction Imaging eliminates most grating lobes at high pitch sizes. • Null Subtraction Imaging also improves gCNR of anechoic regions. [ABSTRACT FROM AUTHOR]

Dual-function radar and communications (DFRC) systems based on multiple-input multiple-output (MIMO) arrays have received considerable attention in recent years due to their excellent ability to alleviate spectrum congestion. The MIMO DFRC systems enable high-resolution detection of multiple targets while communicating with multiple users simultaneously. However, MIMO arrays require numerous radio frequency (RF) units and suffer a strong mutual coupling among antennas, resulting in significant system overhead and performance degradation, respectively. In light of this, this paper investigates the joint optimization of transmit precoding and antenna selection for MIMO DFRC systems, aiming to improve the angular ambiguity function with a guaranteed communication quality of service (QoS) using a small number of antennas. To address the resultant non-convex optimization problem, both the indirect and direct precoding methods are proposed. In the former, the waveform covariance and antenna selection vector are first jointly optimized via a promoted sparsity along the covariance diagonal, followed by the precoding matrix indirectly derived from the optimal covariance. In the latter, the precoding matrix is directly optimized via an imposed group sparsity under the communication QoS and power constraints. Simulation results demonstrate that the proposed sparse MIMO DFRC system with fewer active antennas can achieve comparable dual-functional performance to that of the full array system. • The joint design of precoding and antenna selection for MIMO DFRC is proposed. • The indirect precoding method is proposed to address the joint optimization problem. • The direct precoding method is proposed to directly optimize the precoding matrix. • The proposed sparse system achieves comparable performance to that of a full system. [ABSTRACT FROM AUTHOR]

Signal processing via subspace-based methods require subspace estimates taken from either the eigenvectors of the sample covariance matrix or the principal singular vectors of the received data matrix. The subspaces spanned by the singular vectors or eigenvectors are perturbed away from ground truth due to the additive noise in the received data. The perturbation reduces the accuracy of algorithms that make use of these estimates. A statistically optimal estimate of the unperturbed subspace in terms of the perturbed signal and orthogonal subspaces has been derived and is accurate up to the first-order terms in the additive noise matrix (Vaccaro, 2019). Here, the second-order optimal approximation for the unperturbed subspace is derived and applied to a uniform linear array (ULA) processing model for both full and sparse geometries. The approximation provides little improvement for a full ULA highlighting the importance of first-order terms for a fully sampled geometry. However, for a sparse array, the source estimation performance is much more clearly improved for a low signal-to-noise ratio (SNR) environment with few temporal samples. • Decomposition of received array data matrix provides zeroth-order perturbed subspace basis. • Second-order perturbation analysis increases optimality of noise-free subspace estimation. • Second-order subspace optimality depends on performance of numerical method used. • Estimation error halved employing second-order over first-order statistics for some shift-invariant arrays. [ABSTRACT FROM AUTHOR]

It is well established that sparse sensor array can estimate more sources than number of sensors exploiting difference coarray. However, the array aperture size is restricted in space limited scenarios and all sensor elements are distributed in limited space. This could raise potential problems due to the mutual coupling effect. To address this issue, a migrated coprime based sparse array configuration is designed considering the following schemes. Enhancing the length of consecutive part in difference coarray while introducing no extra sensor. The mutual coupling level is reduced as low as possible, and the array aperture is also limited to acceptable level to allow possible applications in space limited scenarios. Simulation results elaborate the superiority of proposed strategy from the above aspects. • Migrated coprime sensor array does not require additional sensors and no extra hardware cost is introduced. • The proposed array system can be utilized for space limited scenarios due to the reasonable small aperture size. • Though sensors are distributed at space limited scenarios, mutual coupling effect can be alleviated to small level. [ABSTRACT FROM AUTHOR]

• An end-to-end guided wave joint learning imaging method is proposed for sparse and limited-view transducer arrays. • This method sloves the issues of full array data reconstruction, which required a large amount of time or data labels. • Compared to the previous guided wave imaging method, the proposed method significantly improved the imaging quality. Sparse and limited-view ultrasonic guided wave imaging has become a research hotspot in the field. Studies have shown that traditional under-sampling ultrasonic imaging methods either require a significant amount of time to recover the full data or produce poor quality imaging results. To address these issues, this paper proposes an end-to-end ultrasonic guided wave joint learning imaging method for sparse and limited-view transducer arrays, which integrates sparse feature reconstruction and deep learning imaging methods. Numerical and experimental studies demonstrate that this approach significantly improves the quality of imaging results. The quality of imaging results for sparse and limited-view transducer arrays is evaluated and quantified using average correlation coefficients on the testing set. The feasibility and effectiveness of the proposed method have been verified. [ABSTRACT FROM AUTHOR]

Sparse arrays possess attractive features compared to uniform linear arrays (ULAs) with increased degrees of freedom (DOFs), reduced mutual coupling, and enlarged array aperture, which improves the estimation performance of arrays. Recently, coprime arrays have attracted increasing attention due to reduced mutual coupling, whereas the holes in the difference coarray degrade the uniform coarray. In this paper, we propose a new array configuration called the fragmented coprime array with optimal inter-subarray spacing (FCAOIS). FCAOIS configuration maximizes the intra-subarray spacing of a fragmented coprime array (FCA) and incorporates two interlayer subarrays into the FCA, where the holes in the difference coarray of FCA are the results of the two missing interlayer subarrays. An extended array geometry from FCAOIS is also presented to lengthen the uniform difference coarray. It is noteworthy that the proposed coprime arrays outperform nested arrays in mitigating mutual coupling and especially in the scale of uniform difference coarray. Simulation results validate the superiorities of the proposed FCAOISs over other sparse arrays. • A fragmented coprime array concept is introduced to enlarge array aperture. • Provide the location of holes in the difference coarray of FCAs. • Two missing interlayer subarrays fills the holes in the difference coarray of FCAs. • Improve CA geometry in DOF and mutual coupling by FCAOIS and EFCAOIS arrays. • Optimal configurations of FCAOIS and EFCAOIS are derived. [ABSTRACT FROM AUTHOR]