Displacement Estimation via 3D-Printed RFID Sensors for Structural Health Monitoring: Leveraging Machine Learning and Photoluminescence to Overcome Data Gaps

Monitoring object displacement is critical for structural health monitoring (SHM). Radio frequency identification (RFID) sensors can be used for this purpose. Using more sensors enhances displacement estimation accuracy, especially when it is realized through the use of machine learning (ML) algorithms for predicting the direction of arrival of the associated signals. Our research shows that ML algorithms, in conjunction with adequate RFID passive sensor data, can precisely evaluate azimuth angles. However, increasing the number of sensors can lead to gaps in the data, which typical numerical methods such as interpolation and imputation may not fully resolve. To overcome this challenge, we propose enhancing the sensitivity of 3D-printed passive RFID sensor arrays using a novel photoluminescence-based RF signal enhancement technique. This can boost received RF signal levels by 2 dB to 8 dB, depending on the propagation mode (near-field or far-field). Hence, it effectively mitigates the issue of missing data without necessitating changes in transmit power levels or the number of sensors. This approach, which enables remote shaping of radiation patterns via light, can herald new prospects in the development of smart antennas for various applications apart from SHM, such as biomedicine and aerospace.

A Novel Sparse Array Configuration for Direction of Arrival Estimation with Increased Uniform Degrees of Freedom and Reduced Mutual Coupling

Sparse arrays are widely employed in array signal processing due to their obvious advantages in array element distribution and uniform degrees of freedom (uDOFs). In this paper, a generalized augmented multi-subarray nested array (GAMSNA-I) and its variant, GAMSNA-II are proposed, with the objective of increasing uDOFs and reducing mutual coupling. Based on two subarrays of the prototype nested array (NA), GAMSNA-I is constructed by reconfiguring the dense uniform linear array (ULA) and forward-shifting the sparse ULA. GAMSNA-II is obtained by sparsifying the dense part of GAMSNA-I, ensuring constant uDOFs while further reducing mutual coupling. Subsequently, the closed-form expression for the uDOFs of GAMSNA-I with an arbitrary number of sensors is derived, and the proof is provided that the uDOFs of GAMSNA-II remain unchanged relative to that of GAMSNA-I. Compared to some existing array configurations, both GAMSNA-I and GAMSNA-II exhibit improved uDOFs, with GAMSNA-II achieving lower mutual coupling. Simulation results show the superior performance of the proposed GAMSNA-I and GAMSNA-II.

An Improved Toeplitz Approximation Method for Coherent DOA Estimation in Impulsive Noise Environments

Direction of arrival (DOA) estimation is an important research topic in array signal processing and widely applied in practical engineering. However, when signal sources are highly correlated or coherent, conventional subspace-based DOA estimation algorithms will perform poorly due to the rank deficiency in the received data covariance matrix. Moreover, conventional DOA estimation algorithms are usually developed under Gaussian-distributed background noise, which will deteriorate significantly in impulsive noise environments. In this paper, a novel method is presented to estimate the DOA of coherent signals in impulsive noise environments. A novel correntropy-based generalized covariance (CEGC) operator is defined and proof of boundedness is given to ensure the effectiveness of the proposed method in impulsive noise environments. Furthermore, an improved Toeplitz approximation method combined CEGC operator is proposed to estimate the DOA of coherent sources. Compared to other existing algorithms, the proposed method can avoid array aperture loss and perform more effectively, even in cases of intense impulsive noise and low snapshot numbers. Finally, comprehensive Monte-Carlo simulations are performed to verify the superiority of the proposed method under various impulsive noise conditions.

Hole-Free Nested Array with Three Sub-ULAs for Direction of Arrival Estimation

Sparse arrays are of deep concern due to their ability to identify more sources than the number of sensors, among which the hole-free difference co-array (DCA) with large degrees of freedom (DOFs) is a topic worth discussing. In this paper, we propose a novel hole-free nested array with three sub-uniform line arrays (NA-TS). The one-dimensional (1D) and two-dimensional (2D) representations demonstrate the detailed configuration of NA-TS, which indicates that both nested array (NA) and improved nested array (INA) are special cases of NA-TS. We subsequently derive the closed-form expressions for the optimal configuration and the available number of DOFs, concluding that the DOFs of NA-TS is a function of the number of sensors and the number of the third sub-ULA. The NA-TS possesses more DOFs than several previously proposed hole-free nested arrays. Finally, the superior direction of arrival (DOA) estimation performance based on the NA-TS is supported by numerical examples.

A Coherent Wideband Acoustic Source Localization Using a Uniform Circular Array

In modern applications such as robotics, autonomous vehicles, and speaker localization, the computational power for sound source localization applications can be limited when other functionalities get more complex. In such application fields, there is a need to maintain high localization accuracy for several sound sources while reducing computational complexity. The array manifold interpolation (AMI) method applied with the Multiple Signal Classification (MUSIC) algorithm enables sound source localization of multiple sources with high accuracy. However, the computational complexity has so far been relatively high. This paper presents a modified AMI for uniform circular array (UCA) that offers reduced computational complexity compared to the original AMI. The complexity reduction is based on the proposed UCA-specific focusing matrix which eliminates the calculation of the Bessel function. The simulation comparison is done with the existing methods of iMUSIC, the Weighted Squared Test of Orthogonality of Projected Subspaces (WS-TOPS), and the original AMI. The experiment result under different scenarios shows that the proposed algorithm outperforms the original AMI method in terms of estimation accuracy and up to a 30% reduction in computation time. An advantage offered by this proposed method is the ability to implement wideband array processing on low-end microprocessors.

Deconvolved Fractional Fourier Domain Beamforming for Linear Frequency Modulation Signals

To estimate the direction of arrival (DOA) of a linear frequency modulation (LFM) signal in a low signal-to-noise ratio (SNR) hydroacoustic environment by a small aperture array, a novel deconvolved beamforming method based on fractional Fourier domain delay-and-sum beamforming (FrFB) was proposed. Fractional Fourier transform (FrFT) was used to convert the received signal into the fractional Fourier domain, and delay-and-sum beamforming was subsequently performed. Noise resistance was acquired by focusing the energy of the LFM signal distributed in the time-frequency domain. Then, according to the convolution structure of the FrFB complex output, the influence of the fractional Fourier domain complex beam pattern was removed by deconvolution, and the target spatial distribution was restored. Therefore, an improved spatial resolution of DOA estimation was obtained without increasing the array aperture. The simulation and experimental results show that, with a small aperture array at low SNR, the proposed method possesses higher spatial resolution than FrFB and frequency-domain deconvolved conventional beamforming.

A Novel Approach for Direction of Arrival Estimation in Co-Located MIMO Radars by Exploiting Extended Array Manifold Vectors

Multiple-input multiple-output (MIMO) radars enable better estimation accuracy with improved resolution in contrast to traditional radar systems; thus, this field has attracted attention in recent years from researchers, funding agencies, and practitioners. The objective of this work is to estimate the direction of arrival of targets for co-located MIMO radars by proposing a novel approach called flower pollination. This approach is simple in concept, easy to implement and has the capability of solving complex optimization problems. The received data from the far field located targets are initially passed through the matched filter to enhance the signal-to-noise ratio, and then the fitness function is optimized by incorporating the concept of virtual or extended array manifold vectors of the system. The proposed approach outperforms other algorithms mentioned in the literature by utilizing statistical tools for fitness, root mean square error, cumulative distribution function, histograms, and box plots.

Implementation of the Digital QS-SVM-Based Beamformer on an FPGA Platform

To address practical challenges in establishing and maintaining robust wireless connectivity such as multi-path effects, low latency, size reduction, and high data rate, we have deployed the digital beamformer, as a spatial filter, by using the hybrid antenna array at an operating frequency of 10 GHz. The proposed digital beamformer utilizes a combination of the two well-established beamforming techniques of minimum variance distortionless response (MVDR) and linearly constrained minimum variance (LCMV). In this case, the MVDR beamforming method updates weight vectors on the FPGA board, while the LCMV beamforming technique performs nullsteering in directions of interference signals in the real environment. The most well-established machine learning technique of support vector machine (SVM) for the Direction of Arrival (DoA) estimation is limited to problems with linearly-separable datasets. To overcome the aforementioned constraint, the quadratic surface support vector machine (QS-SVM) classifier with a small regularizer has been used in the proposed beamformer for the DoA estimation in addition to the two beamforming techniques of LCMV and MVDR. In this work, we have assumed that five hybrid array antennas and three sources are available, at which one of the sources transmits the signal of interest. The QS-SVM-based beamformer has been deployed on the FPGA board for spatially filtering two signals from undesired directions and passing only one of the signals from the desired direction. The simulation results have verified the strong performance of the QS-SVM-based beamformer in suppressing interference signals, which are accompanied by placing deep nulls with powers less than -10 dB in directions of interference signals, and transferring the desired signal. Furthermore, we have verified that the performance of the QS-SVM-based beamformer yields other advantages including average latency time in the order of milliseconds, performance efficiency of more than 90%, and throughput of nearly 100%.

Direction of Arrival Estimation of Generalized Nested Array via Difference-Sum Co-Array

To address the weakness that the difference co-array (DCA) only enhances the degrees of freedom (DOFs) to a limited extent, a new configuration called the generalized nested array via difference-sum co-array (GNA-DSCA) is proposed for direction of arrival (DOA) estimation. We consider both the temporal and spatial information of the array output to construct the DSCA model, based on which the DCA and sum co-array (SCA) of the GNA are systematically analyzed. The closed-form expression of the DOFs for the GNA-DSCA is derived under the determined dilation factors. The optimal results show that the GNA-DSCA has a more flexible configuration and more DOFs than the GNA-DCA. Moreover, the larger dilation factors yield significantly wider virtual aperture, which indicates that it is more attractive than the reported DSCA-based sparse arrays. Finally, a hole-filling strategy based on atomic norm minimization (ANM) is utilized to overcome the degradation of the estimation performance due to the non-uniform virtual array, thus achieving accurate DOA estimation. The simulation results verify the superiority of the proposed configuration in terms of virtual array properties and estimation performance.

Coherent Signal DOA Estimation for MIMO Radar under Composite Background of Strong Interference and Non-Uniform Noise

To address the problems of low accuracy and low robustness of the conventional algorithm in estimating the direction of arrival (DOA) of coherent signals against a composite background of strong interference and non-uniform noise, in this paper, a coherent signal DOA estimation algorithm based on fixed projection blocking is proposed in conjunction with a multi-input multi-output (MIMO) radar. The covariance matrix of the received signal is first decomposed by eigenvalues, and a fixed projection matrix orthogonal to the interference guidance vector is constructed as the interference blocking matrix. Then, the received array signal is pre-processed to re-form the covariance matrix, and this matrix is rendered decoherent through a Toeplitz reconstruction. Finally, the reconstructed covariance matrix is estimated by DOA using the propagation operator algorithm to reduce the complexity. The simulation verifies that the proposed algorithm has a better robustness and higher accuracy than conventional algorithms for the DOA estimation of coherent signals in composite backgrounds.

A Computationally Efficient and Virtualization-Free Two-Dimensional DOA Estimation Method for Nested Planar Array: RD-Root-MUSIC Algorithm

To address the problem of expensive computation in traditional two-dimensional (2D) direction of arrival (DOA) estimation, in this paper, we propose a 2D DOA estimation method based on a reduced dimension and root-finding MUSIC algorithm for nested planar arrays (NPAs). Specifically, the algorithm proposed in this paper transforms the problem based on 2D spectral peak search into two one-dimensional estimation problems by reducing the dimension, and then transforms the one-dimensional estimation problem into a problem of polynomial root finding. Finally the parameters are paired to realize the 2D DOA estimation. The proposed algorithm not only performs two root finding operations directly according to the 2D spectral function transformation, avoiding the performance degradation caused by intermediate operations, but can also fully exploit the enlarged array aperture offered by NPAs with reduced computational complexity and no need for virtualization. The superiorities of the proposed algorithm in terms of estimation accuracy and complexity are verified by simulations.

A High-Precision Algorithm for DOA Estimation Using a Long-Baseline Array Based on the Hearing Mechanism of the Ormia Ochracea

Inspired by the Ormia Ochracea hearing mechanism, a new direction of arrival estimation using multiple antenna arrays has been considered in spatially colored noise fields. This parasitoid insect can locate s cricket’s position accurately using the small distance between its ears, far beyond the standard array with the same aperture. This phenomenon can be understood as a mechanical coupled structure existing between the Ormia ears. The amplitude and phase differences between the received signals are amplified by the mechanical coupling, which is functionally equivalent to a longer baseline. In this paper, we regard this coupled structure as a multi-input multi-output filter, where coupling exists between each pair of array elements. Then, an iterative direction-finding algorithm based on fourth-order cumulants with fully coupled array is presented. In this manner, the orientation of the mainlobe can direct at the incident angle. Hence, the direction-finding accuracy can be improved in all possible incident angles. We derive the Cramér-Rao lower bound for our proposed algorithm and validate its performance based on simulations. Our proposed DOA estimation algorithm is superior to the existing biologically inspired direction-finding and fourth-order cumulants-based estimation algorithms.

3D Multiple Sound Source Localization by Proposed T-Shaped Circular Distributed Microphone Arrays in Combination with GEVD and Adaptive GCC-PHAT/ML Algorithms

Multiple simultaneous sound source localization (SSL) is one of the most important applications in the speech signal processing. The one-step algorithms with the advantage of low computational complexity (and low accuracy), and the two-step methods with high accuracy (and high computational complexity) are proposed for multiple SSL. In this article, a combination of one-step-based method based on the generalized eigenvalue decomposition (GEVD), and a two-step-based method based on the adaptive generalized cross-correlation (GCC) by using the phase transform/maximum likelihood (PHAT/ML) filters along with a novel T-shaped circular distributed microphone array (TCDMA) is proposed for 3D multiple simultaneous SSL. In addition, the low computational complexity advantage of the GCC algorithm is considered in combination with the high accuracy of the GEVD method by using the distributed microphone array to eliminate spatial aliasing and thus obtain more appropriate information. The proposed T-shaped circular distributed microphone array-based adaptive GEVD and GCC-PHAT/ML algorithms (TCDMA-AGGPM) is compared with hierarchical grid refinement (HiGRID), temporal extension of multiple response model of sparse Bayesian learning with spherical harmonic (SH) extension (SH-TMSBL), sound field morphological component analysis (SF-MCA), and time-frequency mixture weight Bayesian nonparametric acoustical holography beamforming (TF-MW-BNP-AHB) methods based on the mean absolute estimation error (MAEE) criteria in noisy and reverberant environments on simulated and real data. The superiority of the proposed method is presented by showing the high accuracy and low computational complexity for 3D multiple simultaneous SSL.

Implementation of Resonant Electric Based Metamaterials for Electromagnetic Wave Manipulation at Microwave Frequencies

In this paper, we present the application of a resonant electric based metamaterial element and its two-dimensional metasurface implementation for a variety of emerging wireless applications. Metasurface apertures developed in this work are synthesized using sub-wavelength sampled resonant electric-based unit-cell structures and can achieve electromagnetic wave manipulation at microwave frequencies. The presented surfaces are implemented in a variety of forms, from absorption surfaces for energy harvesting and wireless power transfer to wave-chaotic surfaces for compressive sensing based single-pixel direction of arrival estimation and reflecting surfaces. It is shown that the resonant electric-synthesized metasurface concept offers a significant potential for these applications with high fidelity absorption, transmission and reflection characteristics within the microwave frequency spectrum.

A Direction-of-Arrival Estimation Algorithm Based on Compressed Sensing and Density-Based Spatial Clustering and Its Application in Signal Processing of MEMS Vector Hydrophone

Direction of arrival (DOA) estimation has always been a hot topic for researchers. The complex and changeable environment makes it very challenging to estimate the DOA in a small snapshot and strong noise environment. The direction-of-arrival estimation method based on compressed sensing (CS) is a new method proposed in recent years. It has received widespread attention because it can realize the direction-of-arrival estimation under small snapshots. However, this method will cause serious distortion in a strong noise environment. To solve this problem, this paper proposes a DOA estimation algorithm based on the principle of CS and density-based spatial clustering (DBSCAN). First of all, in order to make the estimation accuracy higher, this paper selects a signal reconstruction strategy based on the basis pursuit de-noising (BPDN). In response to the challenge of the selection of regularization parameters in this strategy, the power spectrum entropy is proposed to characterize the noise intensity of the signal, so as to provide reasonable suggestions for the selection of regularization parameters; Then, this paper finds out that the DOA estimation based on the principle of CS will get a denser estimation near the real angle under the condition of small snapshots through analysis, so it is proposed to use a DBSCAN method to process the above data to obtain the final DOA estimate; Finally, calculate the cluster center value of each cluster, the number of clusters is the number of signal sources, and the cluster center value is the final DOA estimate. The proposed method is applied to the simulation experiment and the micro electro mechanical system (MEMS) vector hydrophone lake test experiment, and they are proved that the proposed method can obtain good results of DOA estimation under the conditions of small snapshots and low signal-to-noise ratio (SNR).

Underwater Localization via Wideband Direction-of-Arrival Estimation Using Acoustic Arrays of Arbitrary Shape

Underwater sensing and remote telemetry tasks necessitate the accurate geo-location of sensor data series, which often requires underwater acoustic arrays. These are ensembles of hydrophones that can be jointly operated in order to, e.g., direct acoustic energy towards a given direction, or to estimate the direction of arrival of a desired signal. When the available equipment does not provide the required level of accuracy, it may be convenient to merge multiple transceivers into a larger acoustic array, in order to achieve better processing performance. In this paper, we name such a structure an “array of opportunity” to signify the often inevitable sub-optimality of the resulting array design, e.g., a distance between nearest array elements larger than half the shortest acoustic wavelength that the array would receive. The most immediate consequence is that arrays of opportunity may be affected by spatial ambiguity, and may require additional processing to avoid large errors in wideband direction of arrival (DoA) estimation, especially as opposed to narrowband processing. We consider the design of practical algorithms to achieve accurate detections, DoA estimates, and position estimates using wideband arrays of opportunity. For this purpose, we rely jointly on DoA and rough multilateration estimates to eliminate spatial ambiguities arising from the array layout. By means of emulations that realistically reproduce underwater noise and acoustic clutter, we show that our algorithm yields accurate DoA and location estimates, and in some cases it allows arrays of opportunity to outperform properly designed arrays. For example, at a signal-to-noise ratio of –20 dB, a 15-element array of opportunity achieves lower average and median localization error (27 m and 12 m, respectively) than a 30-element array with proper λ/2 element spacing (33 m and 15 m, respectively). We confirm the good accuracy of our approach via emulation results, and through a proof-of-concept lake experiment, where our algorithm applied to a 10-element array of opportunity achieves a 90th-percentile DoA estimation error of 4∘ and a 90th-percentile total location error of 5 m when applied to a real 10-element array of opportunity.

Direction of Arrival Estimation Using Two Hydrophones: Frequency Diversity Technique for Passive Sonar

The traditional passive azimuth estimation algorithm using two hydrophones, such as cross-correlation time-delay estimation and cross-spectral phase estimation, requires a high signal-to-noise ratio (SNR) to ensure the clarity of the estimated target trajectory. This paper proposes an algorithm to apply the frequency diversity technique to passive azimuth estimation. The algorithm also uses two hydrophones but can obtain clear trajectories at a lower SNR. Firstly, the initial phase of the signal at different frequencies is removed by calculating the cross-spectral density matrix. Then, phase information between frequencies is used for beamforming. In this way, the frequency dimension information is used to improve the signal processing gain. This paper theoretically analyzes the resolution and processing gain of the algorithm. The simulation results show that the proposed algorithm can estimate the target azimuth robustly under the conditions of a single target (SNR = −16 dB) and multiple targets (SNR = −10 dB), while the cross-correlation algorithm cannot. Finally, the algorithm is tested by the swell96 data and the South Sea experimental data. When dealing with rich frequency signals, the performance of the algorithm using two hydrophones is even better than that of the conventional broadband beamforming of the 64-element array. This further validates the effectiveness and advantages of the algorithm.

Computationally Efficient Sources Location Method for Nested Array via Massive Virtual Difference Co-Array

In this paper, we derive the discrete Fourier transform (DFT) method for direction of arrival (DOA) estimation by generating the massive virtual difference co-array with the nested array. By contrast with the spatial smoothing (SS) subspace-based methods for nested array, which halve the array aperture, the proposed method can take full advantage of the total array aperture. Since the conventional DFT method is a non-parametric method and is limited by Rayleigh threshold, we perform the phase rotation operation to obtain the fine DOA estimates. Owing to the full utilization of the array aperture and phase rotation operation, the proposed method can achieve better performance than SS subspace-based methods for far-field sources especially with massive virtual difference co-arrays which possess a large number of virtual sensors. Besides, as the fast Fourier transform (FFT) is attractive in practical implementation, the proposed method lowers the computational cost, as compared with the subspace-based methods. Numerical simulation results validate the superiority of the proposed method in both estimation performance and complexity.

A Novel PARAFAC Model for Processing the Nested Vector-Sensor Array

In this paper, a novel parallel factor (PARAFAC) model for processing the nested vector-sensor array is proposed. It is first shown that a nested vector-sensor array can be divided into multiple nested scalar-sensor subarrays. By means of the autocorrelation matrices of the measurements of these subarrays and the cross-correlation matrices among them, it is then demonstrated that these subarrays can be transformed into virtual scalar-sensor uniform linear arrays (ULAs). When the measurement matrices of these scalar-sensor ULAs are combined to form a third-order tensor, a novel PARAFAC model is obtained, which corresponds to a longer vector-sensor ULA and includes all of the measurements of the difference co-array constructed from the original nested vector-sensor array. Analyses show that the proposed PARAFAC model can fully use all of the measurements of the difference co-array, instead of its partial measurements as the reported models do in literature. It implies that all of the measurements of the difference co-array can be fully exploited to do the 2-D direction of arrival (DOA) and polarization parameter estimation effectively by a PARAFAC decomposition method so that both the better estimation performance and slightly improved identifiability are achieved. Simulation results confirm the efficiency of the proposed model.

Multiple Sound Sources Localization with Frame-by-Frame Component Removal of Statistically Dominant Source

Multiple sound sources localization is a hot topic in audio signal processing and is widely utilized in many application areas. This paper proposed a multiple sound sources localization method based on a statistically dominant source component removal (SDSCR) algorithm by soundfield microphone. The existence of the statistically weak source (SWS) among soundfield microphone signals is validated by statistical analysis. The SDSCR algorithm with joint an intra-frame and inter-frame statistically dominant source (SDS) discriminations is designed to remove the component of SDS while reserve the SWS component. The degradation of localization accuracy caused by the existence of the SWS is resolved using the SDSCR algorithm. The objective evaluation of the proposed method is conducted in simulated and real environments. The results show that the proposed method achieves a better performance compared with the conventional SSZ-based method both in sources localization and counting.

Two-Dimensional Angle Estimation of Two-Parallel Nested Arrays Based on Sparse Bayesian Estimation

To increase the number of estimable signal sources, two-parallel nested arrays are proposed, which consist of two subarrays with M sensors, and can estimate the two-dimensional (2-D) direction of arrival (DOA) of M2 signal sources. To solve the problem of direction finding with two-parallel nested arrays, a 2-D DOA estimation algorithm based on sparse Bayesian estimation is proposed. Through a vectorization matrix, smoothing reconstruction matrix and singular value decomposition (SVD), the algorithm reduces the size of the sparse dictionary and data noise. A sparse Bayesian learning algorithm is used to estimate one dimension angle. By a joint covariance matrix, another dimension angle is estimated, and the estimated angles from two dimensions can be automatically paired. The simulation results show that the number of DOA signals that can be estimated by the proposed two-parallel nested arrays is much larger than the number of sensors. The proposed two-dimensional DOA estimation algorithm has excellent estimation performance.

Sparse Method for Direction of Arrival Estimation Using Denoised Fourth-Order Cumulants Vector

Fourth-order cumulants (FOCs) vector-based direction of arrival (DOA) estimation methods of non-Gaussian sources may suffer from poor performance for limited snapshots or difficulty in setting parameters. In this paper, a novel FOCs vector-based sparse DOA estimation method is proposed. Firstly, by utilizing the concept of a fourth-order difference co-array (FODCA), an advanced FOCs vector denoising or dimension reduction procedure is presented for arbitrary array geometries. Then, a novel single measurement vector (SMV) model is established by the denoised FOCs vector, and efficiently solved by an off-grid sparse Bayesian inference (OGSBI) method. The estimation errors of FOCs are integrated in the SMV model, and are approximately estimated in a simple way. A necessary condition regarding the number of identifiable sources of our method is presented that, in order to uniquely identify all sources, the number of sources K must fulfill K≤(M4−2M3+7M2−6M)/8. The proposed method suits any geometry, does not need prior knowledge of the number of sources, is insensitive to associated parameters, and has maximum identifiability O(M4), where M is the number of sensors in the array. Numerical simulations illustrate the superior performance of the proposed method.

DOA Estimation for Underwater Wideband Weak Targets Based on Coherent Signal Subspace and Compressed Sensing

Direction of arrival (DOA) estimation is the basis for underwater target localization and tracking using towed line array sonar devices. A method of DOA estimation for underwater wideband weak targets based on coherent signal subspace (CSS) processing and compressed sensing (CS) theory is proposed. Under the CSS processing framework, wideband frequency focusing is accompanied by a two-sided correlation transformation, allowing the DOA of underwater wideband targets to be estimated based on the spatial sparsity of the targets and the compressed sensing reconstruction algorithm. Through analysis and processing of simulation data and marine trial data, it is shown that this method can accomplish the DOA estimation of underwater wideband weak targets. Results also show that this method can considerably improve the spatial spectrum of weak target signals, enhancing the ability to detect them. It can solve the problems of low directional resolution and unreliable weak-target detection in traditional beamforming technology. Compared with the conventional minimum variance distortionless response beamformers (MVDR), this method has many advantages, such as higher directional resolution, wider detection range, fewer required snapshots and more accurate detection for weak targets.

Underdetermined Wideband DOA Estimation for Off-Grid Sources with Coprime Array Using Sparse Bayesian Learning

Sparse Bayesian learning (SBL) is applied to the coprime array for underdetermined wideband direction of arrival (DOA) estimation. Using the augmented covariance matrix, the coprime array can achieve a higher number of degrees of freedom (DOFs) to resolve more sources than the number of physical sensors. The sparse-based DOA estimation can deteriorate the detection and estimation performance because the sources may be off the search grid no matter how fine the grid is. This dictionary mismatch problem can be well resolved by the SBL using fixed point updates. The SBL can automatically choose sparsity and approximately resolve the non-convex optimizaton problem. Numerical simulations are conducted to validate the effectiveness of the underdetermined wideband DOA estimation via SBL based on coprime array. It is clear that SBL can obtain good performance in detection and estimation compared to least absolute shrinkage and selection operator (LASSO), simultaneous orthogonal matching pursuit least squares (SOMP-LS) , simultaneous orthogonal matching pursuit total least squares (SOMP-TLS) and off-grid sparse Bayesian inference (OGSBI).

Direction of Arrival Estimation for MIMO Radar via Unitary Nuclear Norm Minimization

In this paper, we consider the direction of arrival (DOA) estimation issue of noncircular (NC) source in multiple-input multiple-output (MIMO) radar and propose a novel unitary nuclear norm minimization (UNNM) algorithm. In the proposed method, the noncircular properties of signals are used to double the virtual array aperture, and the real-valued data are obtained by utilizing unitary transformation. Then a real-valued block sparse model is established based on a novel over-complete dictionary, and a UNNM algorithm is formulated for recovering the block-sparse matrix. In addition, the real-valued NC-MUSIC spectrum is used to design a weight matrix for reweighting the nuclear norm minimization to achieve the enhanced sparsity of solutions. Finally, the DOA is estimated by searching the non-zero blocks of the recovered matrix. Because of using the noncircular properties of signals to extend the virtual array aperture and an additional real structure to suppress the noise, the proposed method provides better performance compared with the conventional sparse recovery based algorithms. Furthermore, the proposed method can handle the case of underdetermined DOA estimation. Simulation results show the effectiveness and advantages of the proposed method.

DOA Estimation Based on Real-Valued Cross Correlation Matrix of Coprime Arrays

A fast direction of arrival (DOA) estimation method using a real-valued cross-correlation matrix (CCM) of coprime subarrays is proposed. Firstly, real-valued CCM with extended aperture is constructed to obtain the signal subspaces corresponding to the two subarrays. By analysing the relationship between the two subspaces, DOA estimations from the two subarrays are simultaneously obtained with automatic pairing. Finally, unique DOA is determined based on the common results from the two subarrays. Compared to partial spectral search (PSS) method and estimation of signal parameter via rotational invariance (ESPRIT) based method for coprime arrays, the proposed algorithm has lower complexity but achieves better DOA estimation performance and handles more sources. Simulation results verify the effectiveness of the approach.

Underdetermined DOA Estimation Using MVDR-Weighted LASSO

The direction of arrival (DOA) estimation problem is formulated in a compressive sensing (CS) framework, and an extended array aperture is presented to increase the number of degrees of freedom of the array. The ordinary least square adaptable least absolute shrinkage and selection operator (OLS A-LASSO) is applied for the first time for DOA estimation. Furthermore, a new LASSO algorithm, the minimum variance distortionless response (MVDR) A-LASSO, which solves the DOA problem in the CS framework, is presented. The proposed algorithm does not depend on the singular value decomposition nor on the orthogonality of the signal and the noise subspaces. Hence, the DOA estimation can be done without a priori knowledge of the number of sources. The proposed algorithm can estimate up to ( ( M 2 - 2 ) / 2 + M - 1 ) / 2 sources using M sensors without any constraints or assumptions about the nature of the signal sources. Furthermore, the proposed algorithm exhibits performance that is superior compared to that of the classical DOA estimation methods, especially for low signal to noise ratios (SNR), spatially-closed sources and coherent scenarios.