Small Number Of Snapshots Research Articles

Research on the vector DOA estimation method with limited number of snapshots

The number of sample snapshots of array signals directly affects the performance of direction of arrival (DOA) estimation methods, and smaller snapshots often cannot represent all the features of array signals. However, in practical applications, owing to short-time abrupt changes, low intensity, large noise interference, and other factors of the target signal, the acoustic vector array sometimes cannot obtain sufficient signal data, making it difficult to achieve accurate DOA estimation. Therefore, this study proposes a transfer-learning-based DOA estimation method for acoustic vector arrays. This method extracts the spatial–temporal features of existing signal data by constructing a pre-trained network model based on a convolutional neural network (CNN) and long short-term memory (LSTM), and transfers the trained model to scenes with limited snapshot data through model fine-tuning, achieving the goal of improving the DOA estimation accuracy under a small number of snapshots. Simulation experiments show that the accuracy and RMSE of the proposed DOA estimation method are superior to those of traditional methods when only 1% of the target data are used. This indicates that the pre-training model based on LSTM and CNN can preserve the effective information of signal data and provides a new solution for the real-time prediction of acoustic vector arrays in scenes with a limited number of snapshots through transfer learning.

Source number estimation based on sequential ratio for the invariant subspace of matrices

In this paper, we propose a method to estimate the number of sources based on the sequential ratio for the invariant subspace of matrices that can provide accurate results in scenarios involving colored noise and a small number of snapshots. We first form a pair of projection matrices on each eigenvector of the sample covariance matrices by using the invariant subspace of matrices. We then use the generalized cosine-squared method to evaluate the differences of M pairs of projection matrices, according to the gap between the projection matrices corresponding to the eigenvectors of the signals and noise. This yields a distinct transition from the signal subspace to the noise subspace. Based on this, we develop a sequential ratio-based method to precisely determine the number of sources by identifying the position at which the ratio of differences significantly decreases. The proposed method can identify the index value at which a significant drop occurs in the number of sources according to the transition from the signal subspace to the noise subspace. The simulation results showed that the proposed method is superior to the current methods, and excels particularly in conditions involving colored noise.

A Novel DOA Estimation Algorithm Based on Robust Mixed Fractional Lower-Order Correntropy in Impulsive Noise

The estimation of direction of arrival (DOA) is paramount in the realm of practical array signal processing systems. Nevertheless, traditional estimation methods often rely heavily on the Gaussian noise assumption, rendering them ineffective in achieving high-precision estimates in environments plagued by strong impulsive noise. To address this challenge, this paper introduces a novel DOA estimation algorithm that leverages mixed fractional lower-order correntropy (MFLOCR) in the context of Alpha-stable distributed impulsive noise. Correntropy is used as a measure of the similarity of the signals, using a Gaussian function to smooth extreme values and provide greater robustness against impulsive noise. By utilizing diverse kernel lengths to jointly regulate the kernel function, the concept of correntropy is expanded and implemented in the fractional lower-order moment (FLOM) algorithm for received signals. Subsequently, the MFLOCR is derived by adjusting the resulting form of correntropy. Finally, an enhanced DOA estimation algorithm is proposed that combines the MFLOCR operator with the MUSIC algorithm, specifically tailored for impulsive noise environments. Furthermore, a proof of boundedness is provided to validate the effectiveness of the proposed approach in such noisy conditions. Simulation experiments confirmed that the proposed method outperforms existing DOA estimation methods in the context of intense impulsive noise, a low generalized signal-to-noise ratio (GSNR), and a smaller number of snapshots.

A New Sparse Bayesian Learning-Based Direction of Arrival Estimation Method with Array Position Errors

In practical applications, the hydrophone array has element position errors, which seriously degrade the performance of the direction of arrival estimation. We propose a direction of arrival (DOA) estimation method based on sparse Bayesian learning using existing array position errors to solve this problem. The array position error and angle grid error parameters are introduced, and the prior distribution of these two errors is determined. The joint probability density distribution function is established by means of a sparse Bayesian learning model. At the same time, the unknown parameters are optimized and iterated using the expectation maximum algorithm and the corresponding parameters are solved to obtain the spatial spectrum. The results of the simulation and the lake experiments show that the proposed method effectively overcomes the problem of array element position errors and has strong robustness. It shows a good performance in terms of its estimation accuracy, meaning that the resolution ability can be greatly improved in the case of a low signal-to-noise ratio or small number of snapshots.

DOA estimation of coherent signals in underdetermined problems using sparse-based Toeplitz covariance reconstruction

Direction-Of-Arrival (DOA) estimation in environments with coherent sources is a challenging problem, when the number of narrowband sources is more than elements and current coherent algorithms cannot accurately overcome such underdetermined problems. In this paper, we propose the Sparse-based Toeplitz Covariance Reconstruction (STCR) algorithm, which obtains a hole-free extended-aperture array with increased Degrees of Freedom (DOF) by exploiting a minimum redundancy array. This method provides superiority in estimating coherent sources by Toeplitz covariance matrix reconstruction. Also, using a Sparse Signal Representation (SSR) framework makes the DOA estimator stronger in source detection and robust to the noise power. Numerical results show the effectiveness of the proposed method even at low SNRs for over- and underdetermined DOA estimators compared to well-known methods. Also, it has high accuracy in DOA estimation of closely-located coherent sources using a small number of snapshots.

On the challenges of estimating the low-wavenumber wall pressure field beneath a turbulent boundary layer using a microphone array

The low-wavenumber components of the turbulent boundary layer (TBL) wall pressure field (WPF) are known to be the primary cause of structural vibration in low-Mach number flows, despite the maximal energy of the TBL being at the convective wavenumber. Existing semi-empirical TBL models show good agreement in predicting the WPF levels in convective region but differ significantly in the low-wavenumber domain. This study aims to highlight the challenges of estimating the low-wavenumber WPF in a TBL using a microphone array. A regularized Fourier-based approach is proposed to numerically study the estimation of the low-wavenumber WPF. Performance of the proposed method is initially evaluated by comparing the estimated WPF against a closed-form input TBL model. Effects of sensor spacing, co-array factor, and sensor distribution on the estimation of the low-wavenumber WPF levels are then investigated. To mimic experimental measurements a virtual acoustic experiment is proposed, involving the synthesis of snapshots of TBL-induced WPF. It is demonstrated that although with relatively small number of snapshots the convective region can be identified, a significant number of snapshots is required to well estimate the TBL low-wavenumber region.

An Efficient Convolutional Neural Network with Supervised Contrastive Learning for Multi-Target DOA Estimation in Low SNR

In this paper, a modified high-efficiency Convolutional Neural Network (CNN) with a novel Supervised Contrastive Learning (SCL) approach is introduced to estimate direction-of-arrival (DOA) of multiple targets in low signal-to-noise ratio (SNR) regimes with uniform linear arrays (ULA). The model is trained using an on-grid setting, and thus the problem is modeled as a multi-label classification task. Simulation results demonstrate the robustness of the proposed approach in scenarios with low SNR and a small number of snapshots. Notably, the method exhibits strong capability in detecting the number of sources while estimating their DOAs. Furthermore, compared to traditional CNN methods, our refined efficient CNN significantly reduces the number of parameters by a factor of sixteen while still achieving comparable results. The effectiveness of the proposed method is analyzed through the visualization of latent space and through the advanced theory of feature learning.

LFM based Wideband DOA Estimation using Deep Neural Network at Low SNR

This work focuses on deep learning-based wideband direction-of-arrival (DoA) estimation for a wideband in particular LFM in case of extreme noise. We propose a convolutional neural network (CNN) that utilizes the correlation matrix to estimate and trained using multi-channel data in low SNR conditions. By using a systematic approach and treating the problem as a way to identify multiple possible DoAs, the CNN is trained to predict DoAs under different SNR conditions. This allows the CNN to accurately estimate the directions from which signals are coming, regardless of the level of noise in the environment. The architecture proposed exhibits robustness to noise, works effectively with a small number of snapshots, and achieves high resolution in angle estimation. Experimental findings demonstrate notable enhancements in performance under low SNR conditions when compared to existing methods, without the need for parameter tuning for correlated and uncorrelated sources. The enhanced robustness of our solution has broad applications in various fields, including wireless array sensors, acoustic microphones, and sonars.

Covariance Matrix Estimation of Texture Correlated Compound-Gaussian Vectors for Adaptive Radar Detection

Covariance matrix estimation of compound-Gaussian vectors with texture-correlation (spatial correlation for the adaptive radar detectors) is examined. The texture parameters are treated as hidden random parameters whose statistical description is given by a Markov chain. States of the chain represent the value of texture coefficient and the transition probabilities establish the correlation in the texture sequence. An Expectation-Maximization (EM) method based covariance matrix estimation solution is given for both noiseless and noisy snapshots. An extension to the practically important case of persymmetric covariance matrices is developed and possible extensions to other structured covariance matrices are described. The numerical results indicate that the benefit of utilizing spatial correlation in the covariance matrix estimation can be significant especially when the total number of snapshots in the secondary data is small. From applications viewpoint, the suggested model is well suited for the adaptive target detection in sea-clutter where some spatial correlation between range cells has been experimentally observed. The performance improvements of the suggested approach for small number of snapshots can be particularly important in this application area.

DOA estimation of coherently and incoherently distributed sources using a characteristic function based ESPRIT algorithm with heavy-tailed signals and noises

Numerous methods exist for estimating the direction of arrival (DOA) of distributed sources in the presence of the Gaussian noises. However, they are inefficient when impulsive signals and noises are present. A novel empirical characteristic function (ECF)-based ESPRIT approach for localizing coherently and incoherently distributed sources is proposed in this study. This method makes use of the interesting properties of characteristic functions like simplicity, information preservation, analytic form, and high precision to build a technique that really is accurate and robust against impulsive signals and noises. The array characteristic function (CF) is modeled using the α-stable distribution to represent the impulsive nature of the signals and sources. This function generates a covariance matrix that can be utilized directly in ESPRIT algorithm. Due to the interesting properties of the ECF, an accurate algorithm is developed that is highly effective in suppressing the effect of impulsive noises, especially when the signal and noise have extremely heavy tails, the signal-to-noise ratio is low, and only a small number of snapshots are available. The results of Monte-Carlo simulation indicate that the suggested method beats existing methods in terms of resolution probability and estimation error. Therefore, this strategy is strongly recommended for localizing coherently and incoherently distributed sources in environments with strong impulses.

Improved block sparse Bayesian learning based DOA estimation for massive MIMO systems

Direction-of-arrival (DOA) estimation is crucial for suppressing inter-cell interference in massive multiple-input multiple-output (MIMO) systems. However, conventional algorithms are unsuitable for low signal-to-noise ratio (SNR) and a small number of snapshots. Consequently, in an attempt to achieve fast reconstruction speed while ensuring high accuracy, this study proposes an improved block sparse Bayesian learning-based DOA estimation algorithm for two-dimension massive MIMO systems. Using the sparse characteristics and inherent structure of the signal, the DOA estimation problem is transformed to a joint task of sparse signal reconstruction and parameter optimization. Subsequently, the estimation accuracy is improved through complete excavation and learning of the signal temporal structure. In addition, to avoid the direct solution of the posterior probability distribution, reduce the number of iterations and increase the reconstruction speed, variational inference is used to approximate the Bayesian model and solve the joint problem through parameter learning. Moreover, the auxiliary angle is introduced to avoid extra angle matching, which further reduces the complexity. Simulations are performed to verify the proposed method and the results prove its superiority when applied to massive MIMO systems compared with some existing DOA estimation algorithms.

Multi-Target Parameter Estimation of the FMCW-MIMO Radar Based on the Pseudo-Noise Resampling Method.

Subspace methods are widely used in FMCW-MIMO radars for target parameter estimations. However, the performances of the existing algorithms degrade rapidly in non-ideal situations. For example, a small number of snapshots may result in the distortion of the covariance matrix estimation and a low signal-to-noise ratio (SNR) can lead to subspace leakage problems, which affects the parameter estimation accuracy. In this paper, a joint DOA-range estimation algorithm is proposed to solve the above issues. Firstly, the improved unitary root-MUSIC algorithm is applied to reduce the influence of non-ideal terms in building the covariance matrix. Subsequently, the least squares method is employed to process the data and obtain paired range estimation. However, in a small number of snapshots and low SNR scenarios, even if the impact of non-ideal terms is reduced, there will still be cases where the estimators sometimes deviate from the true target. The estimators that deviate greatly from targets are regarded as outliers. Therefore, threshold detection is applied to determine whether outliers exist. After that, a pseudo-noise resampling (PR) technology is proposed to form a new data observation matrix, which further alleviates the error of the estimators. The proposed method overcomes performance degradation in a small number of snapshots or low SNRs simultaneously. Theoretical analyses and simulation results demonstrate the effectiveness and superiority.

High-precision DOA estimation for underwater acoustic signals based on sparsity adaptation

The direction of arrival (DOA) estimation technique is to obtain the direction information of the source when it reaches the array by processing and analyzing the received signal. In recent years, the DOA estimation of an array signal has been a research hotspot. For application scenarios with a small number of snapshots and a low signal-to-noise ratio, the compressive sensing theory has been commonly used to estimate the DOA of an array signal to achieve better estimation performance. However, the DOA estimation methods based on compressive sensing theory require information on source sparsity. Moreover, the influence of a complex underwater acoustic environment limits the accuracy of estimation algorithms. To address this limitation, this study proposes a high-precision DOA estimation model for underwater acoustic signals based on sparsity adaptation. The proposed model includes mainly two parts. In the first part, a source sparsity adaptive model based on a causal convolutional neural network is proposed. The model is used to address the constraint that the source sparsity should be known a priori when compressed sensing is used for DOA estimation. In the second part, a differential combination matching pursuit (DCMP) algorithm is adopted. First, a differentiated path filtering strategy is employed to reduce algorithm complexity and avoid the problem of invalid filtering. In addition, the combined optimization strategy is used to improve the prediction accuracy of the algorithm, providing an efficient error correction idea for the compressed sensing application to DOA estimation. The results of simulations conducted under seven different signal-to-noise ratios and using three different array types show that the proposed source sparsity adaptive model can reach an average prediction accuracy of 89.6%. In addition, compared with the other reconstruction algorithm accuracy, on the basis of ensuring low time complexity, the proposed DCMP algorithm can achieve an accuracy improvement of 9.99%–19.94% under seven different signal-to-noise ratio values. Moreover, the mean absolute error of the proposed DCMP algorithm is lower by approximately 0.05°–14° than those of the OMP and MMP algorithms.

Direction of arrival estimation based on slope fitting of wideband array signal in fractional Fourier transform domain

AbstractTraditional direction of arrival (DOA) estimation methods of wideband linear frequency modulated (LFM) signal based on the fractional Fourier transform (FRFT) highly depend on the peak value of LFM signal in the FRFT domain. However, the peak value can be affected by various factors, such as a low signal‐to‐noise ratio (SNR), a small number of snapshots, or the large incident angle of signals, which can lead to a decrease in DOA estimation accuracy. To tackle this problem, based on the energy‐concentrated property of LFM signal in the FRFT domain, the DOA estimation is accomplished by adopting the approach of slope fitting for the wideband array signal in the FRFT domain in this study. The method uses the correspondence between the peak position in the FRFT domain and the delay of the received signal on different uniform linear array elements. The least square method based on threshold outlier detection is used for slope fitting. Compared to conventional methods, the method of this study has high accuracy and relatively low complexity in the case of low SNR or large incident angle of the signal without relying on the peak value. The effectiveness of this method is verified by theoretical analysis and Monte‐Carlo simulations. The proposed method provides a new path for DOA estimation of LFM signal.

Conjugate Augmented Decoupled 3-D Parameters Estimation Method for Near-Field Sources

A near-field source localization method is proposed for 2-D direction-of-arrival (DOA) and range estimation based on a symmetrical cross array. It first employs the conjugate symmetry property of signal autocorrelation for different time delays to construct a conjugate augmented spatial–temporal cross-correlation matrix, then the extended steering vector is decoupled to avoid the usual multidimensional search based on the properties of the Khatri–Rao product, and finally three 1-D MUSIC-type searches are employed to obtain the results. The proposed method can realize automatic pairing of multiple parameters associated with each source and it also works in the underdetermined case. Furthermore, the stochastic Cramer–Rao lower bound with different time delays is derived. Compared with two existing methods, simulation results demonstrate that the proposed method provides satisfactory estimation performance for both the DOA and range parameters at low signal-to-noise ratio and with a small number of snapshots.

Bayesian Detection in Gaussian Clutter for FDA-MIMO Radar

This paper investigates the Bayesian detection problem for a moving target that is embedded in a homogeneous Gaussian clutter with an unknown but stochastic covariance matrix for frequency diverse array multiple-input multiple-output (FDA-MIMO) radar. First, we propose a Bayesian detector based on structured generalized likelihood ratio test (SGLRT), namely BSGLRT, criteria that requires no training data. Then, we present a detector based on the Bayesian unstructured generalized likelihood ratio test (BUGLRT) to reduce the three dimensions (range-angle-Doppler) search into one-dimension Doppler searches for low-complexity implementation in practical applications. Moreover, the robustness of the BSGLRT and BUGLRT detectors is also analyzed. Numerical results reveal that the proposed Bayesian detectors and estimators, i.e. BSGLRT and BUGLRT, outperform their non-Bayesian counterparts in Gaussian clutter with a small number of snapshots and/or low signal-to-clutter rate (SCR) for FDA-MIMO radar.

Efficient Angle Estimation for MIMO Systems via Redundancy Reduction Representation

This paper proposes an efficient direction of departure (DOD) and direction of arrival (DOA) estimation method for multi-input multi-output (MIMO) systems. For uncorrelated scenarios, the redundancy of the covariance matrix is first exploited by establishing its concise representation through redundancy reduction, which transforms the original large-size covariance matrix into a smaller-size matrix without loss of useful angle information. Then, the resulting transformed matrix, which retains a salient structure, permits efficient two-dimensional (2D) angle estimators working on a reduced-size problem for DOD and DOA estimation. Compared with conventional subspace-based methods, the proposed method incorporating an appropriate 2D angle estimator is more computationally efficient and can achieve higher estimation accuracy for small numbers of snapshots and low signal-to-noise ratios, which are verified by simulation results.

Block Newtonised orthogonal matching pursuit for off‐grid DOA estimation in the presence of unknown mutual coupling

Mutual coupling (MC) between array elements can lead to severe accuracy degradation in direction-of-arrival (DOA) estimation. In this study, an off-grid compressed sensing (CS) approach for DOA estimation in the presence of unknown MC is proposed using block Newtonised orthogonal matching pursuit (NOMP). First, the model of DOA estimation with MC is block sparsely represented to fully utilise the whole array aperture. Then, a block NOMP algorithm with multiple measurement vectors (MMV) is developed to achieve the estimates of DOA, in which the Newton refinement procedure is presented by deriving the first- and second-order derivatives of the block steering matrix with respect to the angle grid. Compared with the subspace-based and sparse recovery-based methods with MC, the proposed block NOMP approach has robustness in a small number of snapshots and owns no grid-mismatch effect. Meanwhile, in comparison to several existing off-grid DOA estimation methods with MC, it can achieve higher estimation accuracy and similarly low computational complexity. The superior performance of the proposed approach is shown via numerical simulations.

Deep Networks for Direction-of-Arrival Estimation in Low SNR

In this work, we consider direction-of-arrival (DoA) estimation in the presence of extreme noise using Deep Learning (DL). In particular, we introduce a Convolutional Neural Network (CNN) that is trained from mutli-channel data of the true array manifold matrix and is able to predict angular directions using the sample covariance estimate. We model the problem as a multi-label classification task and train a CNN in the low-SNR regime to predict DoAs across all SNRs. The proposed architecture demonstrates enhanced robustness in the presence of noise, and resilience to a small number of snapshots. Moreover, it is able to resolve angles within the grid resolution. Experimental results demonstrate significant performance gains in the low-SNR regime compared to state-of-the-art methods and without the requirement of any parameter tuning. We relax the assumption that the number of sources is known a priori and present a training method, where the CNN learns to infer the number of sources jointly with the DoAs. Simulation results demonstrate that the proposed CNN can accurately estimate off-grid angles in low SNR, while at the same time the number of sources is successfully inferred for a sufficient number of snapshots. Our robust solution can be applied in several fields, ranging from wireless array sensors to acoustic microphones or sonars.

Application of Sparse Representation to Bartlett Spectra for Improved Direction of Arrival Estimation.

A new technique for high-resolution direction of arrival estimation is presented. The method utilizes the traditional Bartlett spectra and sparse representation to locate emitters in single and multiple emitter scenarios. A method for selecting the sparse representation regularization parameter is also presented. Using Monte Carlo simulations, we show that the proposed approach achieves accurate direction of arrival (DOA) estimations that are unbiased and a variance that approaches the Cramer–Rao lower bound. We show that our method outperforms the popular MUSIC algorithm, and is slightly better than the sparse representation based L1-SVD algorithm when angular separation between emitters is small, signal SNR is low, and a small number of snapshots are used in DOA estimation.