Sparse Linear Array Research Articles

Gridless DOA Estimation Method for Arbitrary Array Geometries Based on Complex-Valued Deep Neural Networks

Gridless direction of arrival (DOA) estimation methods have garnered significant attention due to their ability to avoid grid mismatch errors, which can adversely affect the performance of high-resolution DOA estimation algorithms. However, most existing gridless methods are primarily restricted to applications involving uniform linear arrays or sparse linear arrays. In this paper, we derive the relationship between the element-domain covariance matrix and the angular-domain covariance matrix for arbitrary array geometries by expanding the steering vector using a Fourier series. Then, a deep neural network is designed to reconstruct the angular-domain covariance matrix from the sample covariance matrix and the gridless DOA estimation can be obtained by Root-MUSIC. Simulation results on arbitrary array geometries demonstrate that the proposed method outperforms existing methods like MUSIC, SPICE, and SBL in terms of resolution probability and DOA estimation accuracy, especially when the angular separation between targets is small. Additionally, the proposed method does not require any hyperparameter tuning, is robust to varying snapshot numbers, and has a lower computational complexity. Finally, real hydrophone data from the SWellEx-96 ocean experiment validates the effectiveness of the proposed method in practical underwater acoustic environments.

Phase Error Correction in Sparse Linear MIMO Radar Based on the Equivalent Phase Center Principle

Multiple-input multiple-output (MIMO) technology is widely used in the field of radar imaging. Array sparse optimization reduces the hardware cost of MIMO radar, while virtual aperture and the equivalent phase center (EPC) principle simplify the radar signal model and reduce the computation and complexity of imaging algorithms. However, the application of sparse array structure and the EPC principle produces a non-negligible phase error, which affects the imaging quality. This paper simplifies the MIMO radar signal model based on the phase center approximation, analyzes the phase error generated by this method, and proposes an improved phase error correction method to solve the problem that the target cannot be well-focused at non-reference distance during imaging. In addition, this paper designs a sparse linear MIMO array with a periodic structure, which reduces the number of transmitting and receiving units, system complexity, and hardware costs. The proposed phase correction method was combined with the wavenumber domain algorithm to simulate and experiment on the designed antenna array, and good experimental results were obtained to verify the effectiveness of the proposed method.

2-D DOA Estimation Based on Sparse Linear Arrays Exploiting Arbitrary Linear Motion

2-D DOA Estimation Based on Sparse Linear Arrays Exploiting Arbitrary Linear Motion

DOA Estimation Based on Virtual Array Aperture Expansion Using Covariance Fitting Criterion

Providing higher precision Direction of Arrival (DOA) estimation has become a hot topic in the field of array signal processing for parameter estimation in recent years. However, when the physical aperture of the actual array is small, its aperture limitation means that even with super-resolution estimation algorithms, the achievable estimation precision is limited. This paper takes a novel approach by constructing an optimization algorithm using the covariance fitting criterion based on the array output’s covariance matrix to fit and obtain the covariance matrix of a large aperture virtual array, thereby providing high-precision angular resolution through virtual aperture expansion. The covariance fitting expansion analysis and discussion are unfolded for both uniform linear arrays (ULAs) and sparse linear arrays (SLAs) under four different scenarios. Theoretical analysis and simulation experiments demonstrate that these methods can enhance the effective performance of angle estimation, especially in low signal-to-noise ratios (SNRs) and at small angular intervals by fitting virtual extended aperture data.

Antenna Selection and Receive Beamforming for Multi-Functional Sparse Linear Array via Consensus ADMM

Antenna Selection and Receive Beamforming for Multi-Functional Sparse Linear Array via Consensus ADMM

Sparse linear array synthesis using artificial neural network and nonconvex optimization

AbstractThe 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 ‐norm minimization nonconvex optimization method is integrated into the proposed framework to reduce the number of activated elements. The effectiveness and efficiency of the method are demonstrated through numerical and full‐wave simulations for synthesizing various linear sparse arrays, including large‐scale arrays. In comparison to existing algorithms, our proposed method exhibits superior computational efficiency and predicted accuracy with fewer elements.

W-Band FMCW MIMO System for 3-D Imaging Based on Sparse Array

Multiple-input multiple-output (MIMO) technology is widely used in the field of security imaging. However, existing imaging systems have shortcomings such as numerous array units, high hardware costs, and low imaging resolutions. In this paper, a sparse array-based frequency modulated continuous wave (FMCW) millimeter wave imaging system, operating in the W-band, is presented. In order to reduce the number of transceiver units of the system and lower the hardware cost, a linear sparse array with a periodic structure was designed using the MIMO technique. The system operates at 70~80 GHz, and the high operating frequency band and 10 GHz bandwidth provide good imaging resolution. The system consists of a one-dimensional linear array, a motion control system, and hardware for signal generation and image reconstruction. The channel calibration technique was used to eliminate inherent errors. The system combines mechanical and electrical scanning, and uses FMCW signals to extract distance information. The three-dimensional (3-D) fast imaging algorithm in the wave number domain was utilized to quickly process the detection data. The 3-D imaging of the target in the near-field was obtained, with an imaging resolution of 2 mm. The imaging ability of the system was verified through simulations and experiments.

Direction-of-Arrival Estimation for a Random Sparse Linear Array Based on a Graph Neural Network.

This article proposes a direction-of-arrival (DOA) estimation algorithm for a random sparse linear array based on a novel graph neural network (GNN). Unlike convolutional layers and fully connected layers, which do not interact well with information between different antennas, the GNN model can adapt to the goniometry problem of non-uniform random sparse linear arrays without any prior information by applying neighbor nodes' aggregation and update operations. This helps the model in learning signal features under complex environmental conditions. We train the model in an end-to-end way to reduce the complexity of the network. Experiments are conducted on the uniform and sparse linear arrays for various signal-to-noise ratio (SNR) and numbers of snapshots for comparison. We prove that the GNN model has superior angle estimation performance on arrays with large sparsity that cannot be used by traditional algorithms and surpasses existing deep learning models based on convolutional or fully connected structures. The proposed algorithm shows excellent DOA estimation performance under the complex conditions of limited snapshots, low signal-to-noise ratio, and large array sparsity as well. In addition, the algorithm has a low time calculation cost and is suitable for scenarios that require low latency.

Optimal placement of sensors to enhance degrees of freedom in monostatic collocated MIMO radar

Compared to the traditional monostatic MIMO radar which uses uniform linear arrays (ULAs) for transmitting and receiving signals, sparse linear arrays (SLAs) monostatic MIMO radars can achieve greater Degrees Of Freedom (DOF) and a higher resolution. The optimal placement of sensors in both transmit and receive arrays to attain the maximum DOF is, however, a basic problem in the collocated monostatic MIMO radar. Optimum solution of such a problem is restricted to an exhaustive computer search. Some popular arrays such as nested and coprime arrays have been previously proposed as alternative solutions that can achieve a good DOF, but they do not necessarily lead to the maximum one. In this paper at first, we formulate the optimal placement of sensors in the collocated monostatic MIMO radar to improve the sum coarray as well as the difference coarray of the sum coarray. After that, we present a mathematical framework to achieve the optimal solution for both problems. Finally, we demonstrate that the proposed method yields the optimal MR-MIMO array while demanding much less computational complexity as compared with the computer search.

Sparse Non-Uniform Linear Array-Based Propagator Method for Direction of Arrival Estimation

A novel approach that does not require the number of sources as a priori is proposed to estimate the direction of arrival (DOA) based on a sparse non-uniform linear antenna array. To ensure the identifiability of the DOA, a specific configuration scheme of sparse array is designed. Based on this specific sparse array, firstly the fourth-order cumulant (FOC) is adopted to eliminate the impact imposed by Gaussian noise. Secondly, to circumvent eigenvalue decomposition or singular value decomposition, a propagator is constructed by using a Hermitian FOC matrix and a hyperparameter. Finally, a projection onto an irregular Toeplitz set is proposed to further improve estimation accuracy.

Hole‐free sparse array for highly efficient direction of arrival estimation: Enhanced uniform difference co‐array

AbstractSparse arrays with sensors can offer number of degrees of freedom by exploiting the difference co‐array that can be obtained from the second‐order statistics of received signals. In this article, a novel sparse array with seven subarrays (SA‐7S) by carefully assembling the subarrays is proposed, and the resulting SA‐7S can generate a hole‐free uniform difference co‐array. The sensor locations of the SA‐7S array are uniquely determined by a closed‐form expression and the number of achievable degrees of freedom is analytically presented as well. Theoretical analysis shows that the SA‐7S can provide a higher number of degrees of freedom than most sparse linear arrays. Simulations are performed to validate the advantage of the proposed array in terms of uDOFs, mutual coupling and direction of arrival estimation performance.

Synthesis of Linear Sparse Array Using DNN-Based Machine-Learning Method

In this paper, a deep neural network (DNN)-based machine learning (ML) approach is presented to synthesize linear sparse arrays (LSAs). Due to the powerful fitting capability of neural networks, a DNN framework is established to map the relation between the desired array pattern and LSA geometry. In this manner, the array synthesis is accomplished by training a proper DNN that can generate the desired LSA geometry. To obtain better training, the density tapering (DT) technique is introduced to the training process as the prior domain knowledge to specify the varying boundaries of each element in the LSA. Consequently, an efficient DT-assisted DNN (D-DNN) synthesis method is developed. The proposed D-DNN method has the ability to simultaneously optimize the element positions and excitations, and directly constrain the inter-element spacings. Furthermore, by introducing the active element pattern (AEP) technique, the presented method can synthesize both ideal arrays and arrays with mutual coupling. Numerical results of a wide variety of synthesis scenarios are presented to demonstrate the validity, efficiency, and flexibility of the proposed method.

Optimal sparse linear array design with reduced mutual coupling effect

Sparse linear arrays (SLAs) provide a high number of degrees of freedom (DOF) and reduce the mutual coupling effect between sensors of the array. Many design methods for SLAs have been proposed in the last two decades but most of the existing SLA design methods fail to achieve minimum number of sensors for a desired DOF. In this paper, a design method is proposed which utilizes the branch and bound (B&B) optimization algorithm to give a SLA with the desired DOF and minimum number of physical sensors. The proposed SLA design method is obtained by generalizing the minimum sensor array (MSA) design method which is recently proposed in the literature. This generalized method provides the same DOF as the MSA method but with a smaller number of physical sensors. In addition, a version of this design method is proposed which provides more robustness against mutual coupling effect between the sensors of the array. Simulation results demonstrate the superiority of the performance of the SLAs obtained with the proposed method over the arrays obtained with the MSA method and also over the other existing SLAs.

Pattern-Reconfigurable Sparse Linear Array Synthesis Under Minimum Element Spacing Control by Alternating Sequential Quadratic Programming

A new method called alternating sequential quadratic programming (ASQP) is proposed to synthesize pattern-reconfigurable sparse linear arrays with minimum element spacing control. The method can find the common element positions and multiple sets of excitations for generating multiple reconfigurable patterns which accurately meet their given upper and lower pattern bounds. In addition, by introducing auxiliary weighting coefficients and collective excitation coefficient vectors and choosing them as optimization variables alternately, the proposed method can appropriately incorporate the minimum element spacing constraint into the pattern synthesis. Synthesized results show that the proposed method can give satisfactory reconfigurable pattern performance but save much more elements compared with some existing methods.

Teaching quality evaluation-based differential evolution and its application on synthesis of linear sparse arrays

Teaching quality evaluation-based differential evolution and its application on synthesis of linear sparse arrays

Hybridization of Bayesian Compressive Sensing and Array Dilation Technique for Synthesis of Linear Isophoric Sparse Antenna Arrays

This paper presents a deterministic hybrid algorithm combining the merits of Bayesian Compressive Sensing (BCS) and Array Dilation Technique (ADT) for the synthesis of aperiodic and isophoric (equally-fed) Linear Sparse Array Antennas (LSAA). The hybrid technique overcomes the shortcomings of BCS, i.e., non-uniform amplitude taper which results into a lower taper efficiency, utilizing hybridization with ADT resulting into an isophoric LSAA, thereby improving the taper efficiency. The proposed algorithm can be used to synthesize arbitrary antenna array patterns as per the reference pattern while complementing the constraints on the aperture length and the desired thinning levels. The hybrid algorithm provides a computationally efficient and deterministic technique for synthesizing LSAAs with low SLL and demonstrates a wide angular scanning with minimal loss in directivity and SLL over the scan volume. The results demonstrated are comparable or better than the prior literature on LSAAs.

Multistatic MIMO Sparse Imaging Based on FFT and Low-Rank Matrix Recovery Techniques

This article proposes a simple sparse imaging scheme using a linear sparse aperiodic array and a new fast Fourier transform matched filtering (FFTMF) algorithm for a THz multistatic multiple-input and multiple-output (MIMO) imaging system. The simple linear sparse aperiodic array and multipass interferometric synthetic aperture focusing technique are used to achieve fast sampling, low system cost, and high imaging performance. Unlike a traditional generalized synthetic aperture focusing technique (GSAFT) for multistatic MIMO imaging, which is time-consuming and exhibits increased reconstruction time with increased data volume, the proposed FFTMF image reconstruction algorithm is capable of providing comparable image quality but significantly reducing the reconstruction time. For example, we show that for an image of 300 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times320$ </tex-math></inline-formula> mm with a pixel size of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.75\times0.83$ </tex-math></inline-formula> mm, the reconstruction time is reduced from about 1.50 min to 0.25 s in the 220-GHz five-pass synthetic imaging experiments. The proposed imaging algorithm uses internal zero padding, a multipass interferometric synthetic aperture focusing technique, and a wideband imaging technique to improve the imaging performance under a low-cost, sparse sampling scheme. It shows a strong antinoise ability and a high tolerance to target focusing distance. In addition, integrated with an algorithm of principal component pursuit by alternating directions method (PCPADM), sparse imaging is available to further save system cost and sampling data without a loss of image quality while the novel use of an error matrix provides an additional detection capability for imaging systems.

Ternary redundant sparse linear array design with high robustness

Sparse linear array is prone to element failure affected by environmental and other factors in practical application, resulting in the decline of degrees of freedom and the attenuation or even failure of direction of arrival (DOA) estimation performance. To address this problem, a ternary redundant sparse array composed of three uniform linear arrays with different spacings at specific distances is designed, and the analytical expression of its degrees of freedom is derived. The configuration rules of the array are concise, and the difference coarrays of the array are hole-free. Mathematically proves that all virtual array elements can be covered with a weight of not less than 3 except the 4 farthest. The array has lower sensors importance and less generalized k-fragility. The array design takes into account the maximum degrees of freedom, redundancy and sparsity. In case of sensors failure, compared with the other sparse linear arrays, the array has more stable difference coarrays and higher uniform degrees of freedom. Compared with multiple-fold redundancy arrays, the array has lower mutual coupling. Simulation results show that the ternary redundant array has superior robustness and higher DOA estimation accuracy under sensors failure.

A Robust and Statistically Efficient Maximum-Likelihood Method for DOA Estimation Using Sparse Linear Arrays

A recent trend of research on direction-of-arrival (DOA) estimation is to localize more uncorrelated sources than sensors by using a proper sparse linear array (SLA), at the cost of robustness to source correlations even in the regime of less sources than sensors. This paper is devoted to proposing one algorithm that can simultaneously tackle two challenging scenarios: 1) more uncorrelated sources than sensors and 2) highly correlated or coherent sources. In order to statistically efficiently localize a maximal number of uncorrelated sources, we use the stochastic maximum likelihood (SML) criterion and propose an effective algorithm based on elegant problem reformulations and the alternating direction method of multipliers (ADMM). Moreover, we prove that the SML is robust to source correlations under mild conditions though it is derived under the assumption of uncorrelated sources. The proposed algorithm is usable for arbitrary SLAs (e.g., minimum redundancy arrays, nested arrays and coprime arrays) and is named as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> aximum-likelihood <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</i> stimation via <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i> equential <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</i> DMM (MESA). Extensive numerical results are provided that collaborate our analysis and demonstrate the statistical efficiency and robustness of MESA against state-of-the-art algorithms. Our results also imply that it is possible to localize more sources than sensors in presence of high source correlations.

A gridless method for direction finding with sparse arrays in nonuniform noise

The performance of direction finding methods would deteriorate due to unknown nonuniform noise. To cope with this problem, we propose a novel gridless direction finding method based on atomic norm minimization exploiting sparse linear array in nonuniform noise. Specifically, after eliminating the concentrated nonuniform noise related term in coarray signal, the concept of array interpolation is used to recover both the noiseless counterpart of the removed term as well as the holes in coarray. Thus, the effect of nonuniform noise is removed. Besides, we impose a new constraint based on the estimation error distribution of the noise independent terms in the coarray signal. The regularization parameter can thus be selected directly from the Chi-square distribution probability table. In the proposed method, the tedious selection of regularization parameter and the effect of grid mismatch are avoided. Moreover, we derive the corresponding semidefinite programming (SDP) form. With its optimal solution, eigen-decomposition with high complexity is avoided for subsequent DOA estimation. Different from the traditional SDP form, it has an additional transformation matrix composed of the estimation error. Simulations show that the proposed method owns the highest estimation accuracy than previous algorithms in the nonuniform noise.