Wideband Direction Of Arrival Estimation Research Articles

Grid-less wideband direction of arrival estimation based on variational Bayesian inference.

Many recent works have addressed the problem of wideband direction of arrival (DOA) estimation using grid-less sparse techniques, and these methods have been shown to outperform the traditional wideband DOA estimation methods. However, these methods often suffer from the problem of requiring manual parameter tuning or high computational complexity, which reduces their practicality. To alleviate this problem, a grid-less wideband DOA estimation method based on variational Bayesian inference is proposed in this paper. The method approximates the posterior probability density function of DOA with the help of variational Bayesian inference, which does not require manual adjustment of parameters and can obtain accurate DOA estimation results with low computational complexity. Numerical simulations and real measurement data processing show that the proposed method has a higher DOA estimation accuracy than other grid-less wideband methods while providing higher computational speed.

High-resolution DOA estimation in the hydrophone array shape with uncertainty based on dynamic compressed sensing

Compressed sensing (CS) technology is a popular method for the direction of arrival (DOA) estimation of underwater acoustic radiation noise due to its high resolution. However, in practical applications such as buried arrays and other arrays, uncertainty in the hydrophone array shape can lead to model mismatch which significantly reduces DOA estimation accuracy. This paper focuses on high-resolution wideband DOA estimation in the radiated noise from underwater targets of interest using dynamic compressed sensing. The study introduces phase error into the signal model to simulate the model mismatch, and improves DOA estimation accuracy by jointly estimating both the DOA and phase error. Simulation results demonstrate that the proposed algorithm is effective in improving the accuracy of DOA estimation.

Direction of Arrival Estimation and Highlighting Characteristics of Testing Wideband Echoes from Multiple Autonomous Underwater Vehicles.

Multiple autonomous underwater vehicles (AUVs) have gradually become the trend in underwater operations. Identifying and detecting these new underwater multi-targets is difficult when studying underwater moving targets. A 28-element transducer is used to test the echo of multiple AUVs with different layouts in a lake. The characteristics of the wideband echo signals are studied. Under the condition that the direction of arrival (DOA) is not known, an autofocus coherent signal subspace (ACCSM) method is proposed. The focusing matrix is constructed based on the received data. The spatial spectrum of the array signal of multiple AUVs at different attitudes is calculated. The algorithm estimates the DOA of the echo signals to overcome the shortcomings of traditional wideband DOA estimation and improve its accuracy. The results show that the highlights are not only related to the number of AUVs, but are also modified by scale and attitude. The contribution of the microstructure of the target in the overall echo cannot be ignored. Different parts of the target affect the number of highlights, thus resulting in varying numbers of highlights at different attitude angle intervals. The results have significant implications for underwater multi-target recognition.

Markov chain-based frequency correlation processing algorithm for wideband DOA estimation

For wideband direction-of-arrival (DOA) estimation, a Markov Chain-based frequency correlation processing algorithm is proposed in the sparse Bayesian learning (SBL) framework, called the MC-FC-SBL algorithm. The algorithm adopts a new frequency-domain structural correlation prior model, which can be adaptively changed to accommodate multi-wideband sources scenarios with different frequency characteristics. Specifically, the MC-FC-SBL algorithm separates the amplitudes and supports of the sparse coefficients through the spike-and-slab model, and judges the frequency correlation by the consistency of the supports at adjacent frequency points. The support prior is represented by a Gaussian mixture model, and the switching between the supports at adjacent frequency points is simulated by a Markov chain. The MC-FC-SBL algorithm performs the DOA estimation in the SBL framework to determine the adaptive prior of each coefficient by evaluating the appropriate frequency-correlation structural pattern. In addition, the MC-FC-SBL algorithm is processed in the real-domain, and the real and imaginary parts of complex signal are regarded as multi-snapshot data to implement joint sparse constraints, which can reduce the computational complexity and improve the algorithm performance. Numerical simulations demonstrate that the MC-FC-SBL algorithm is superior to the existing algorithms for wideband DOA estimation, and the results of field experiments show that this algorithm is still effective when the source is weak.

Underdetermined direction of arrival estimation of wideband signal based on sparse array

To solve the problem of the mismatch of the wideband underdetermined direction of arrival (DOA) estimation under the condition of the On-grid model, this paper extends the narrowband Off-Grid model to wideband and proposes a new DOA estimation algorithm for Off-Grid sources based on group sparsity. The proposed algorithm first obtains the preliminary estimation result under the current predefined discrete grid through the group sparsity wideband DOA estimation algorithm. Then, the Off-Grid optimisation problem is adopted to calculate the Off-Grid deviation vector. It is also assumed that the off-grid deviation vectors of each frequency subband are exactly the same, thereby reducing the number of parameters to be estimated. Therefore, the proposed algorithm can not only maintain similar or even better estimation accuracy but also greatly reduce the computational complexity. Finally, simulation is conducted and the results verify the effectiveness and performance of the proposed method.

Super-Resolution DOA Estimation for Wideband Signals Using Non-Uniform Linear Arrays With No Focusing Matrix

We focus on developing an effective Direction Of Arrival (DOA) estimation method for wideband sources based on the super-resolution concept. In this letter, we represent the data model of a wideband DOA estimation problem in a new form. Then, using this model, we propose an atomic norm minimization problem that leads to an accurate wideband DOA estimation method with no need for any focusing matrices. Moreover, this method requires no initial estimate and can be implemented by non-uniform linear arrays. Numerical simulations show that in comparison to some well-known techniques, the proposed method generates outstanding accuracy and higher robustness to noise. The effectiveness of the method is also verified in presence of close adjacent sources.

An off-grid wideband DOA estimation method with the variational Bayes expectation-maximization framework

Wideband direction-of-arrival (DOA) estimation has important applications in many fields. To improve the performance of wideband DOA estimation, an off-grid approach with the variational Bayes Expectation-Maximization (VBEM) framework is proposed. In this work, a hierarchical Bernoulli-Gaussian model with several latent variables and parameters is formulated to describe the array observation. A latent indicator vector is assigned to describe the existence of the potential sources as well as promote sparsity in the angle domain. The VBEM framework is utilized to solve the latent variables and parameters. By modeling the existence and non-existence of potential sources separately and utilizing the wideband data jointly, our method performs better than the existing methods. The proposed method does not require any prior knowledge of the number of sources nor the initial DOAs, and it can solve both coherent and incoherent wideband sources. Simulation results show that the proposed method is superior to the existing wideband DOA estimation methods with few snapshots in frequency.

Low-complexity neural network based DOA estimation for wideband signals in massive MIMO systems

Massive multiple-input multiple-output (MIMO) has become one of the most promising technologies for wireless communication systems, in which the direction-of-arrival (DOA) plays an important role in interference cancellation and transmission reliability. However, the challenge of conventional wideband DOA estimation algorithms is that their high computational complexity brings great difficulties for their effective application in massive MIMO systems. In this paper, we propose a wideband low-complexity DOA estimation algorithm based on a principal component analysis (PCA) neural network for massive MIMO systems. First, a new criterion for constructing a focusing matrix is proposed to avoid complex angle pre-estimation. To further reduce the complexity of the eigenvalue decomposition (EVD), we propose a signal subspace estimation algorithm based on PCA, which uses only a limited amount of self-organizing learning to estimate the weights of the network and the signal subspace and does not require prior sample training. Moreover, to increase the estimation accuracy, we use the Akaike information criterion (AIC) to divide signal and noise subspaces accurately. The theoretical analysis and simulation results show that the computational complexity of the proposed algorithm is effectively reduced, and the angles of wideband sources can be accurately estimated in massive MIMO systems.

Cramér-Rao Bound Analysis of Underdetermined Wideband DOA Estimation Under the Subband Model via Frequency Decomposition

A class of Cramér-Rao bounds (CRBs) for wideband direction-of-arrival (DOA) estimation under the subband (or frequency bin) model is studied for the underdetermined case, where the number of sources is no less than that of physical sensors. A unified framework is proposed to encompass the closed-form CRB expressions for DOAs in four cases where the sources are known a priori to 1) have flat spectra/cross spectra, 2) be spatially uncorrelated, 3) be spatially uncorrelated and have proportional spectra up to unknown factors, 4) be spatially uncorrelated and have flat spectra. The relationship between the wideband CRBs and the subband ones is investigated, and the order relationship among the derived CRBs are provided. The asymptotic behavior of the CRBs with respect to the number of snapshots and the signal-to-noise ratio (SNR) is discussed. Two asymptotic expressions for sufficiently large SNR are derived in both overdetermined and underdetermined cases. Existence of the derived CRBs is examined through rank conditions of the introduced matrices, which yields upper bounds on the resolution capacities. Different from the narrowband scenario, underdetermined wideband DOA estimation is feasible even if a sparse array is not used given different a priori knowledge about the source spectra. It is possible to resolve more wideband Gaussian sources than the number of DOFs offered by the difference co-array. Finally, further interpretations of the subband model are provided, revealing the underlying connections with the multi-frequency co-array augmentation concept and the non-coherent subarray system.

Robust Wideband DOA Estimation Based on Element-Space Data Reconstruction in a Multi-Source Environment

In the presence of multiple sources, the performance of direction-of-arrival (DOA) estimation based on beam power maximization is susceptible to the energy leaking from the interference beams to the target beam, especially in the case that the signal of interest (SOI) is quite weak. To address this issue, a robust wideband DOA estimation method is proposed in this paper. Unlike those conventional high-resolution methods which mitigate the influence of energy leakage by reducing beamwidths and sidelobe levels, the proposed method achieves this by directly reconstructing the element-space data to approach the received hydrophone data of the single-source scenario containing only the SOI. Element-space data reconstruction (ESDR) for the SOI is achieved by removing the element-space waveforms of all the interference signals from the received hydrophone data. Moreover, an iterative algorithm is developed to adaptively extract the element-space waveform of each interference signal, without requiring the prior information of the array amplitude response coefficients and hydrophone coordinates of a distorted towed array. Simulation results show that the proposed method outperforms its counterparts in terms of estimation accuracy for a multi-source scenario. Meanwhile, the DOA estimation performance of the proposed method in a multi-source environment is close to that obtained by the beam power maximization method in the single-source scenario, even if the signal-to-interference ratio (SIR) is as low as −25 dB. At-sea experimental results prove that, even though the number of signal sources is as many as seven and the SOI is contaminated by real ocean ambient noise, the proposed method still achieves a better DOA estimation performance compared to existing state-of-the-art methods.

Underdetermined wideband DOA estimation for off‐grid targets: a computationally efficient sparse Bayesian learning approach

Underdetermined wideband direction of arrival (DOA) estimation based on the sparse array is studied here and a novel algorithm is developed to improve the estimation performance of off-grid targets in the framework of sparse Bayesian learning. First, the narrowband off-grid model is extended to a wideband case and the sparse Bayesian model containing off-grid biases is deduced. Then, a sequential solution is proposed to obtain the estimation, where the fast sparse Bayesian learning strategy is employed to improve the computational efficiency. The estimation accuracy is improved significantly through off-grid compensation and the computational complexity is reduced remarkably. Simulation results verify the effectiveness of the proposed method.

Wideband DOA Estimation on Co-prime Array via Atomic Norm Minimization

This paper introduces a low complexity wideband direction-of-arrival (DOA) estimation algorithm on the co-prime array. To increase the number of the detectable signal sources and to prevent an unnecessary increase in complexity, the low dimensional co-prime array vector is constructed by arranging elements of the correlation matrix at every frequency bin. The atomic norm minimization (ANM)-based approach resolves the grid-mismatch, which causes an inevitable error in the compressive sensing (CS)-based DOA estimation. However, the complexity surges when the ANM is exploited to the wideband DOA estimation on the co-prime array. The surging complexity of the ANM-based wideband DOA estimation on the co-prime array is handled by solving the time-saving semidefinite programming (SDP) motivated by the ANM for multiple measurement vector (MMV) case. Simulation results show that the proposed algorithm has high accuracy and low complexity compared to compressive sensing (CS)-based wideband DOA estimation algorithms that exploit the co-prime array.

Gridless Underdetermined DOA Estimation of Wideband LFM Signals With Unknown Amplitude Distortion Based on Fractional Fourier Transform

In this article, a wideband Direction-of-Arrival (DOA) estimation method for underdetermined scenarios is proposed, which effectively solves the basis mismatch problem. Based on the fractional Fourier transform (FRFT), the wideband received signal model with a coprime array is first derived by exploiting the aggregation characteristic of wideband linear frequency modulated (LFM) signals in the fractional Fourier (FRF) domain. Then, in order to increase the degree of freedom, an extended uniform linear array is built, and the covariance matrix of the signal is reconstructed by employing the penalized atomic norm minimization with the consecutive spatial dictionary. Meanwhile, without the knowledge of the noise level, the noise variance is estimated from the noisy incomplete data, which is utilized to improve the covariance matrix reconstruction performance. Additionally, for the unconditional model, the Cramér-Rao bound for the wideband DOA estimation based on a coprime array is derived. Different from the existing methods, the proposed method not only can estimate more DOAs of wideband signals than the number of physical sensors in the presence of unknown amplitude distortion but also can obtain more accurate DOA estimation performance without basis mismatch. The effectiveness of the proposed method is verified by our numerical results.

Underdetermined DOA Estimation for Wideband Signals via Focused Atomic Norm Minimization.

In underwater acoustic signal processing, direction of arrival (DOA) estimation can provide important information for target tracking and localization. To address underdetermined wideband signal processing in underwater passive detection system, this paper proposes a novel underdetermined wideband DOA estimation method equipped with the nested array (NA) using focused atomic norm minimization (ANM), where the signal source number detection is accomplished by information theory criteria. In the proposed DOA estimation method, especially, after vectoring the covariance matrix of each frequency bin, each corresponding obtained vector is focused into the predefined frequency bin by focused matrix. Then, the collected averaged vector is considered as virtual array model, whose steering vector exhibits the Vandermonde structure in terms of the obtained virtual array geometries. Further, the new covariance matrix is recovered based on ANM by semi-definite programming (SDP), which utilizes the information of the Toeplitz structure. Finally, the Root-MUSIC algorithm is applied to estimate the DOAs. Simulation results show that the proposed method outperforms other underdetermined DOA estimation methods based on information theory in term of higher estimation accuracy.

Wideband DOA estimation with deficient snapshots using low rank Toeplitz structure

In array signal processing, most existing direction-of-arrival (DOA) estimation methods fail to work given deficient snapshots. To solve this problem, this Letter proposes a novel wideband DOA estimation technique by utilising the sparse representation in terms of the low rank Toeplitz structure presented in uniform array geometries, followed by an enhanced MUSIC method. Specifically, each sub-band segment is first focused into the reference frequency band to collect the coherent covariance matrix even in the lack of sufficient samples. Then, the covariance matrix is denoised through a structure-based sparse reconstruction, which exploits the low rank Toeplitz structure. Finally, the DOAs is efficiently estimated via an enhanced MUSIC method. Simulation result confirms the efficacy of the proposed method that works well in MIMO and radar applications.

Direction-of-Arrival Estimation of Circular and Noncircular Wideband Source Signals via Augmented Envelope Alignment

In practical applications of array system, the incident signals may come from either circular or noncircular sources, or both. The problem of direction-of-arrival (DOA) estimation is herein addressed for both circular and noncircular wideband source signals. Based on the concept of effective rank, the aligned augmented effective noise subspace, spanned by the subordinate eigenvectors of the aligned array output augmented covariance matrix, is constructed for each scanning angle. It is shown that the aligned augmented effective noise subspace corresponding to a true DOA of signal is: 1) approximately orthogonal to a frequency-invariant one-dimensional subspace spanned by the aligned augmented transfer vector of the signal in the presence of multiple strictly noncircular sources; and 2) approximately orthogonal to a frequency-invariant two-dimensional subspace spanned by the aligned augmented transfer matrix of the signal in the presence of multiple circular or partially noncircular sources. This enables the noncircularity exploited wideband DOA estimation based on rank-reduction and norm-nulling. The performance of the proposed method has been evaluated and compared with some existing popular wideband DOA estimators by extensive simulations.

Coherent SVR Learning for Wideband Direction-of-Arrival Estimation

In this letter, we propose a coherent support vector regression (SVR) scheme to address the wideband direction of arrival (DOA) estimation problem. This learning-based method deals with wideband DOA estimation by treating it as a function approximation issue. The proposed approach first decomposes the wideband array outputs into several narrowband components, then approximates the functional relationship between the decomposed narrowband data and the DOA with coherent SVR scheme through training. The trained function is then capable of estimating the DOA when wideband signal with unknown impinging direction arrives. We prove the effectiveness and superiority of the presented method by simulation experiments. Simulation results show that the new technique has a better performance in terms of estimation errors than the conventional broadband DOA estimation method, especially in demanding scenarios with low SNR and limited snapshots. Moreover, the proposed approach also relaxes the unambiguous array element-spacing restrictions, i.e., it has extended the frequency range of wideband signals where direction finding without angle ambiguity is achievable.

Weighted Incoherent Signal Subspace Method for DOA Estimation on Wideband Colored Signals

Wideband direction-of-arrival (DOA) estimation is a key part in array signal processing. The existing algorithms for the wideband DOA estimation are often studied in the situation of uniformly distributed energy. In addition, all the frequency bins are weighted equally in these algorithms. However, these algorithms perform unsatisfactorily when encountering wideband colored signals with nonuniform energy spectrum. To improve the performance of DOA estimation for wideband colored signals, we proposed two weighting methods, which are based on the perturbed subspace theory and random matrix theory, respectively. The two methods weight the space spectrum from all the frequency bins according to the mean square error of DOA estimation in each frequency bin. The numerical results show that the random matrix theory based method performs well, due to the inference premise that the dimensions of matrices increase at the same rate. The perturbed subspace-based method, which is concise in calculating the weights, shows high accuracy only at high-signal-to-noise ratio and with adequate snapshots. The effectiveness of the two algorithms are also demonstrated by comparing them to various existing algorithms and the Cramer–Rao bound.

Wideband DOA estimation based on focusing signal subspace

The traditional wideband direction-of-arrival (DOA) estimation algorithms usually require the preliminary DOA estimations, which determine the accuracy of the final DOA estimations. To remedy the apparent performance degradation, this paper introduces a novel direction-of-arrival (DOA) estimation algorithm for wideband sources called the focusing signal subspace (FSS). This novel algorithm constructs a unitary focusing matrix which combines the eigenvector of signal subspace of the reference frequency and the eigenvector of signal subspace of other discrete frequencies with the constraint of Frobenius norm. The focusing matrix does not require the preliminary DOA estimations. Furthermore, the covariance matrix at each frequency is transformed to the focusing covariance matrix at the reference focusing frequency by using the focusing matrix. Experiments and simulation results show that focusing signal subspace outperforms the traditional rotational signal subspace and the test of orthogonality of projected subspace. FSS features a high resolution and a low root-mean-square error without the preliminary DOA estimations.

A particle filter based compressive sensing method for tracking moving wideband sound sources

Tracking moving wideband sound sources is one of the most challenging issues in the acoustic array signal processing which is based on the direction of arrival (DOA) estimation. Compressive sensing (CS) is a recent theory exploring the signal sparsity representation, which has been proved to be superior for the DOA estimation. However, the spatial aliasing and the offset at endfire are the main obstacles for CS applied in the wideband DOA estimation. We propose a particle filter based compressive sensing method for tracking moving wideband sound sources. First, the initial DOA estimates are obtained by wideband CS algorithms. Then, the real sources are approximated by a set of particles with different weights assigned. The kernel density estimator is used as the likelihood function of particle filter. We present the results for both uniform and random linear array. Simulation results show that the spatial aliasing is disappeared and the offset at endfire is reduced. We show that the proposed method can achieve satisfactory tracking performance regardless of using uniform or random linear array.