Sparse Direction Of Arrival Research Articles

Robust and sparse M-estimation of DOA

A robust and sparse Direction of Arrival (DOA) estimator is derived for array data that follows a Complex Elliptically Symmetric (CES) distribution with zero-mean and finite second-order moments. The derivation allows to choose the loss function and four loss functions are discussed in detail: the Gauss loss which is the Maximum-Likelihood (ML) loss for the circularly symmetric complex Gaussian distribution, the ML-loss for the complex multivariate t-distribution (MVT) with ν degrees of freedom, as well as Huber and Tyler loss functions. For Gauss loss, the method reduces to Sparse Bayesian Learning (SBL). The root mean square DOA error of the derived estimators is discussed for Gaussian, MVT, and ϵ-contaminated data. The robust SBL estimators perform well for all cases and nearly identical with classical SBL for Gaussian array data.

An effective DOA estimation method for low SIR in small-size hydrophone array

The estimation ability of traditional direction of arrival (DOA) estimation methods is relatively fragile in small-size hydrophone arrays with limited space. Especially in low signal to interference ratio (SIR), the strong interference signals may submerge some weak signals of interest (SOI) and make DOA estimation difficult in response to this issue. This paper introduces an improved sparse DOA estimation method for practical multi-objective DOA estimation in complex scenarios. The main work is to introduce a noise weight constraint in the sparse iterative covariance process. It leads the algorithm to output sparse peaks and smooth spatial energy spectra and achieve faster fitting while reducing the probability of false peaks. The algorithm can complete DOA estimation of the multi-target reliably without prior information of sources. Then, we propose a fast region grid refinement method based on allocation reconstruction to increase angle resolution. The method increases the accuracy of multi-objective DOA estimation while reducing computational costs. Finally, simulation and experiment have verified the method's effectiveness.

Non-Circular Signal DOA Estimation with Nested Array via Off-Grid Sparse Bayesian Learning.

For the traditional uniform linear array (ULA) direction of arrival (DOA) estimation method with a limited array aperture, a non-circular signal off-grid sparse Bayesian DOA estimation method based on nested arrays is proposed. Firstly, the extended matrix of the received data is constructed by taking advantage of the fact that the statistical properties of non-circular signals are not rotationally invariant. Secondly, we use the difference and sum co-arrays for the nested array technique, thus increasing the array aperture and improving the estimation accuracy. Finally, we take the noise as part of the interest signal and iteratively update the grid points using the sparse Bayesian learning (SBL) method to eliminate the modeling errors caused by off-grid gaps. The simulation results show that the proposed algorithm can improve the accuracy of DOA estimation compared with the existing algorithms.

Structured Nyquist Correlation Reconstruction for DOA Estimation With Sparse Arrays

Sparse arrays are known to achieve an increased number of degrees-of-freedom (DOFs) for direction-of-arrival (DOA) estimation, where an augmented virtual uniform array calculated from the correlations of sub-Nyquist spatial samples is processed to retrieve the angles unambiguously. Nevertheless, the geometry of the derived virtual array is dominated by the specific physical array configurations, as well as the deviation caused by the practical unforeseen circumstances such as detection malfunction and missing data, resulting in a quite sensitive model for virtual array signal processing. In this paper, we propose a novel sparse array DOA estimation algorithm via structured correlation reconstruction, where the Nyquist spatial filling is implemented on the physical array with a compressed transformation related to its equivalent filled array to guarantee the general applicability. While the unknown correlations located in the whole rows and columns of the augmented covariance matrix lead to the fact that strong incoherence property is no longer satisfied for matrix completion, the structural information is introduced as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a prior</i> to formulate the structured correlation reconstruction problem for matrix reconstruction. As such, the reconstructed covariance matrix can be effectively processed with full utilization of the achievable DOFs from the virtual array, but with a more flexible constraint on the array configuration. The described estimation problem is theoretically analyzed by deriving the corresponding Cram´er-Rao bound (CRB). Moreover, we compare the derived CRB with the performance of the virtual array interpolation-based algorithm. Extensive simulations are conducted to demonstrate the effectiveness of the proposed DOA estimation algorithm in terms of achievable DOFs, resolution, and estimation accuracy.

Gridless sparse covariance-based beamforming via alternating projections including co-prime arrays.

This paper presents gridless sparse processing for direction-of-arrival (DOA) estimation. The method solves a gridless version of sparse covariance-based estimation using alternating projections. Gridless sparse DOA estimation is represented by the reconstruction of Toeplitz-structured low-rank matrices, which our method recovers by alternatively projecting a solution matrix. Compared to the existing gridless sparse methods, our method improves speed and accuracy and considers non-uniformly configured linear arrays. High-resolution and reliable DOA estimation are achieved even with single-snapshot data, coherent sources, and non-uniform arrays. Simulation results demonstrate performance improvements compared to the existing DOA estimators, including gridless sparse methods. The method is illustrated using experimental data from a real ocean experiment.

On the Complementarity of Sparse L0 and CEL0 Regularized Loss Landscapes for DOA Estimation.

L0 sparse methods are not widespread in Direction-Of-Arrival (DOA) estimation yet, despite their potential superiority over classical methods in difficult scenarios. This comes from the difficulties encountered for global optimization on hill-climbing error surfaces. In this paper, we explore the loss landscapes of L0 and Continuous Exact L0 (CEL0) regularized problems in order to design a new optimization scheme. As expected, we observe that the recently introduced CEL0 penalty leads to an error surface with less local minima than the L0 one. This property explains the good behavior of the CEL0-regularized sparse DOA estimation problem for well-separated sources. Unfortunately, CEL0-regularized landscape enlarges L0-basins in the middle of close sources, and CEL0 methods are thus unable to resolve two close sources. Consequently, we propose to alternate between both error surfaces to increase the probability of reaching the global solution. Experiments show that the proposed approach offers better performance than existing ones, and particularly an enhanced resolution limit.

Sparse Bayes Tensor and DOA Tracking Inspired Channel Estimation for V2X Millimeter Wave Massive MIMO System

Efficient vehicle-to-everything (V2X) communications improve traffic safety, enable autonomous driving, and help to reduce environmental impacts. To achieve these objectives, accurate channel estimation in highly mobile scenarios becomes necessary. However, in the V2X millimeter-wave massive MIMO system, the high mobility of vehicles leads to the rapid time-varying of the wireless channel and results in the existing static channel estimation algorithms no longer applicable. In this paper, we propose a sparse Bayes tensor and DOA tracking inspired channel estimation for V2X millimeter wave massive MIMO system. Specifically, by exploiting the sparse scattering characteristics of the channel, we transform the channel estimation into a sparse recovery problem. In order to reduce the influence of quantization errors, both the receiving and transmitting angle grids should have super-resolution. We obtain the measurement matrix to increase the resolution of the redundant dictionary. Furthermore, we take the low-rank characteristics of the received signals into consideration rather than singly using the traditional sparse prior. Motivated by the sparse Bayes tensor, a direction of arrival (DOA) tracking method is developed to acquire the DOA at the next moment, which equals the sum of the DOA at the previous moment and the offset. The obtained DOA is expected to provide a significant angle information update for tracking fast time-varying vehicular channels. The proposed approach is evaluated over the different speeds of the vehicle scenarios and compared to the other methods. Simulation results validated the theoretical analysis and demonstrate that the proposed solution outperforms a number of state-of-the-art researches.

Off‐grid sparse DOA estimation based iterative reweighted linear interpolation in spatial coloured noise

An off-grid sparse direction-of-arrival (DOA) estimation algorithm, namely, iterative reweighted linear interpolation (IRLI), is proposed to avoid the declination of the DOA estimation precision present in unknown spatial coloured noise. The authors start by developing an off-grid sparse model based on linear interpolation with reweighted coefficient, which is a trade-off between tangent and secant offset, to guarantee an optimal approximation for off-grid signals. Next, the authors formulate the DOA estimation problem as solving the off-grid sparse model and, finally, the off-grid sparse model is addressed under the general framework of sparse Bayesian learning (SBL). Additional noise in IRLI is spatially coloured for calculating its statistical properties, which is different from SBL relying on the spatial white noise assumption. Numerical results with the limited snapshots and the low signal-to-noise ratio validate the algorithm by comparing with other algorithms.

A Deep Learning Framework for Robust DOA Estimation Using Spherical Harmonic Decomposition

Spherical harmonic decomposition facilitates decomposing the sound pressure at different microphones into independent functions of frequency, azimuth and elevation of the source and microphone locations. This decomposition facilitates the extraction of two sets of features containing different information about elevation and azimuth of the source for the direction of arrival (DOA) estimation. These features can be given as input to a learning approach for the estimation of azimuth and elevation separately. This approach aims at breaking down the problem of DOA estimation into azimuth and elevation estimation separately. An advantage of this is the reduction in computational complexity when compared with the joint DOA estimation. This facilitates a straightforward extension of this approach to denser DOA search grids. The contribution of this paper is threefold. First, we propose spherical harmonic magnitude and phase features and discuss the information present in these features regarding the azimuth and elevation of the source. Second, we propose the convolutional neural network architectures for DOA estimation. Third, we analyse the training, run-time computational complexities and propose to extend the DOA estimation approach to dense DOA search grid rather than restricting to a sparse DOA search grid. The performance of conventional DOA estimation approaches degrades in case of a noisy and reverberant environment. Several advancements to the existing DOA estimation approaches have been recently proposed. However, to the best of the authors’ knowledge, learning approaches to DOA estimation with dense DOA search grids with few frames in the context of spherical arrays have not been proposed. Performance evaluation is carried out using simulated as well as real datasets. The proposed approach is also evaluated on LOCATA dataset in the context of a moving source. The results are motivating enough to consider the application of the proposed method in practical scenarios.

Angle estimation in MIMO radar using a new sparse representation approach

ABSTRACTExisting direction of arrival (DOA) estimation methods in multiple-input multiple-out (MIMO) radar systems will encounter the performance degradation in the cases of few snapshots, low signal-to-noise ratio (SNR), closely spaced targets, or strongly correlated sources. To improve it, this paper develops a new sparse representation-based DOA estimation method. The main contributions are as follows: i) we construct a new real-valued double weighted -norm minimisation model; ii) we derive an improved reduced-dimension technique to enhance estimation accuracy; and iii) we design optimal and sparse weights carefully to improve the corresponding estimation accuracy. Finally, the effectiveness and theoretical analysis of the presented approach are verified by extensive numerical simulations, which proves that the new algorithm performs well at low SNR and with a small number of snapshots as well as at the coherent source case.

Sparse off-grid DOA estimation method with unknown mutual coupling effect

In the array systems, the mutual coupling effect between antennas degrades the estimation performance of direction of arrival (DOA) significantly. In this paper, the DOA estimation problem in a uniform linear array (ULA) is investigated, and a novel system model is formulated by exploiting the mutual coupling effect and the signal sparsity in the spatial domain. In the traditionally compressed sensing (CS)-based system model, the spatial domain is discretized into grids, and the off-grid gap limits the further improvement of the estimation performance. Therefore, the novel system model is proposed by considering both the off-grid problem and the unknown mutual coupling effect. Moreover, a novel algorithm, named sparse off-grid DOA estimation with unknown mutual coupling effect (SODMC), is proposed and updates the unknown parameters including the DOA, the mutual coupling vector, and the off-grid vector iteratively. Simulation results show that compared with state-of-the-art methods, the proposed SODMC algorithm improves the DOA estimation performance significantly in the scenario with unknown mutual coupling effect.

Sparse DOA Estimation Based on Multi-Level Prime Array With Compression

A signal emitter can be located using diverse types of direction finding (DF) techniques. One of the most widely used techniques is the direction of arrival (DOA) estimation using antenna arrays. An array configuration that can increase the degrees of freedom (DOF) or the number of estimated sources is desired. Multi-level prime array (MLPA) uses multiple uniform linear subarrays where the number of elements in the subarrays is a pairwise coprime integer. Compared with nested and coprime arrays, the MLPA requires a smaller aperture size which is important in mobile applications. The different MLPA configurations can be constructed for a given number of antennas and the one that maximizes the DOF is exploited. These configurations have a difference coarray with a large number of consecutive lags and few holes. The number of consecutive lags can be increased by properly compressing the inter-element spacing of one subarray under a fixed number of antennas and without changing the aperture size. This paper proposes a new compressed MLPA configuration and demonstrates its performance in sparse DOA estimation. The resultant array, MLPA with compressed subarray (MLPAC), can have a hole-free difference coarray as in nested array case. The MLPAC can estimate a larger number of sources using both MUSIC and sparse reconstruction algorithms. Mutual coupling between sensors has also been evaluated. The simulation results confirm the achievable DOF and the advantage of the proposed configuration in the DOA estimation.

An $$\ell _p$$ ℓ p -norm Based Method for Off-grid DOA Estimation

The sparse signal recovery-based direction of arrival (DOA) estimation has received a great deal of attention over the past decade. From the sparse representation point of view, $$\ell _0$$ -norm is the best choice to evaluate the sparsity of a vector. However, solving an $$\ell _0$$ -norm minimization problem is non-deterministic polynomial hard (NP-hard). Thus, The common idea for many sparse DOA estimation methods is to use the $$\ell _1$$ -norm as the sparsity metric. However, its sparse solution may not coincide with the solution resulting from the $$\ell _0$$ -norm thus deteriorating the DOA estimation performance. In this paper, we propose a new sparse method based on $$\ell _p$$ ( $$0<p<1$$ ) regularization for DOA estimation to achieve a sparser solution than $$\ell _1$$ regularization. In particular, we use the Taylor expansion to convert the $$\ell _p$$ -norm minimization problem to a weighted $$\ell _1$$ -norm problem. Then, a two-step iterative method is employed to achieve the DOA estimate. The $$\ell _p$$ ( $$0<p<1$$ ) regularization is able to improve the angle resolution, leading to an improved performance in low SNR and correlated signal scenarios. Numerical results show that our proposed method has better estimation performance than many other methods do.

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 . 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 , where M is the number of sensors in the array. Numerical simulations illustrate the superior performance of the proposed method.

Sparse representation-based DOA estimation of coherent wideband LFM signals in FRFT domain

In this paper, the method of direction-of-arrival (DOA) estimation for wideband signals based on sparse representation of FRFT domain is proposed by using the excellent convergence of FRFT to LFM signals. This method focuses the wideband signal to the reference frequency using FRFT, establishes the DOA estimation model and the array manifold matrix in the FRFT domain, and reconstructs the spatial spectral function based on the sparse representation of the spatial angles, so as to realize the wideband LFM signal DOA estimations. The method not only is suitable for non-coherent signals but also can process coherent signals directly without any decoherent operations; in addition, the number of signals is not necessarily known a priori. Simulation results show that the proposed method can achieve better estimation performance and higher angular resolution, especially under low signal-to-noise ratio (SNR) condition.

Covariance matrix based fast smoothed sparse DOA estimation with partly calibrated array

To solve the problem of direction-of-arrival (DOA) estimation for partly calibrated array, a new gain-phase error matrix estimation scheme and a smoothed sparse signal reconstruction method tailored for the complex-valued covariance matrix are proposed. In the proposed method, DOA estimation is achieved by employing the structure of the covariance matrix for the error matrix estimation and the complex-valued gradient matrix based fast non-convexity data reconstruction. The proposed method has much faster computational speed than other sparse DOA estimation methods with partly calibrated array. In addition, simulation results show that it performs well and is independent of the errors.

A sparse direction-of-arrival estimation algorithm for MIMO radar in the presence of gain-phase errors

In this paper, the problem of direction-of-arrival (DOA) estimation for monostatic multiple-input multiple-output (MIMO) radar with gain-phase errors is addressed, by using a sparse DOA estimation algorithm with fourth-order cumulants (FOC) based error matrix estimation. Useful cumulants are designed and extracted to estimate the gain and the phase errors in the transmit array and the receive array, thus a reliable error matrix is obtained. Then the proposed algorithm reduces the gain-phase error matrix to a low dimensional one. Finally, with the updated gain-phase error matrix, the FOC-based reweighted sparse representation framework is introduced to achieve accurate DOA estimation. Thanks to the fourth-order cumulants based gain-phase error matrix estimation, and the reweighted sparse representation framework, the proposed algorithm performs well for both white and colored Gaussian noises, and provides higher angular resolution and better angle estimation performance than reduced-dimension MUSIC (RD-MUSIC), adaptive sparse representation (adaptive-SR) and ESPRIT-based algorithms. Simulation results verify the effectiveness and advantages of the proposed method.

Joint Smoothed l₀-Norm DOA Estimation Algorithm for Multiple Measurement Vectors in MIMO Radar.

Direction-of-arrival (DOA) estimation is usually confronted with a multiple measurement vector (MMV) case. In this paper, a novel fast sparse DOA estimation algorithm, named the joint smoothed -norm algorithm, is proposed for multiple measurement vectors in multiple-input multiple-output (MIMO) radar. To eliminate the white or colored Gaussian noises, the new method first obtains a low-complexity high-order cumulants based data matrix. Then, the proposed algorithm designs a joint smoothed function tailored for the MMV case, based on which joint smoothed -norm sparse representation framework is constructed. Finally, for the MMV-based joint smoothed function, the corresponding gradient-based sparse signal reconstruction is designed, thus the DOA estimation can be achieved. The proposed method is a fast sparse representation algorithm, which can solve the MMV problem and perform well for both white and colored Gaussian noises. The proposed joint algorithm is about two orders of magnitude faster than the -norm minimization based methods, such as -SVD (singular value decomposition), RV (real-valued) -SVD and RV -SRACV (sparse representation array covariance vectors), and achieves better DOA estimation performance.

The Real-Valued Sparse Direction of Arrival (DOA) Estimation Based on the Khatri-Rao Product.

There is a problem that complex operation which leads to a heavy calculation burden is required when the direction of arrival (DOA) of a sparse signal is estimated by using the array covariance matrix. The solution of the multiple measurement vectors (MMV) model is difficult. In this paper, a real-valued sparse DOA estimation algorithm based on the Khatri-Rao (KR) product called the L1-RVSKR is proposed. The proposed algorithm is based on the sparse representation of the array covariance matrix. The array covariance matrix is transformed to a real-valued matrix via a unitary transformation so that a real-valued sparse model is achieved. The real-valued sparse model is vectorized for transforming to a single measurement vector (SMV) model, and a new virtual overcomplete dictionary is constructed according to the KR product’s property. Finally, the sparse DOA estimation is solved by utilizing the idea of a sparse representation of array covariance vectors (SRACV). The simulation results demonstrate the superior performance and the low computational complexity of the proposed algorithm.

A Modified Rife Algorithm for Off-Grid DOA Estimation Based on Sparse Representations.

In this paper we address the problem of off-grid direction of arrival (DOA) estimation based on sparse representations in the situation of multiple measurement vectors (MMV). A novel sparse DOA estimation method which changes MMV problem to SMV is proposed. This method uses sparse representations based on weighted eigenvectors (SRBWEV) to deal with the MMV problem. MMV problem can be changed to single measurement vector (SMV) problem by using the linear combination of eigenvectors of array covariance matrix in signal subspace as a new SMV for sparse solution calculation. So the complexity of this proposed algorithm is smaller than other DOA estimation algorithms of MMV. Meanwhile, it can overcome the limitation of the conventional sparsity-based DOA estimation approaches that the unknown directions belong to a predefined discrete angular grid, so it can further improve the DOA estimation accuracy. The modified Rife algorithm for DOA estimation (MRife-DOA) is simulated based on SRBWEV algorithm. In this proposed algorithm, the largest and sub-largest inner products between the measurement vector or its residual and the atoms in the dictionary are utilized to further modify DOA estimation according to the principle of Rife algorithm and the basic idea of coarse-to-fine estimation. Finally, simulation experiments show that the proposed algorithm is effective and can reduce the DOA estimation error caused by grid effect with lower complexity.