Direction Of Arrival Estimation Of Signals Research Articles

DOA estimation of noncircular signals with direction-dependent mutual coupling

In this paper, a reweighted sparse recovery algorithm based on the optimal weighted subspace fitting (WSF) for non-circular signals in direction-dependent mutual coupling (MC) is proposed. Firstly, a new augmented model is constructed by leveraging the characteristics of non-circular signals. Next, a new direction matrix without mutual coupling coefficients is obtained by a novel transformation method. Then, two sparse recovery models are constructed by utilizing the WSF technique, and the sparsity of the solution is increased by constructing a weighted matrix. Finally, the direction of arrival (DOA) is achieved by a sparse recovery approach. For both coherent and incoherent signals, the developed approach can achieve precise DOA estimation in the case of direction-dependent MC. The robustness and advantage of the developed approach are testified by various experiments.

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.

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.

Design of relocating sparse nested arrays for DOA estimation of non-circular signals

Recently, the ability of sparse arrays to achieve higher degrees of freedom (DOFs) and to be less sensitive to the mutual coupling (MC) effect has aroused increasing attention. Aiming at this, we investigate the sparse array design problem for direction of arrival (DOA) estimation of non-circular (NC) signals. Then, we propose two novel relocating sparse nested array (RSNA) structures, named RSNA-I and RSNA-II, respectively, and derive simple explicit expressions for their array locations and DOFs. Specifically, the RSNA-I is composed of two subarrays plus a separate sensor. By utilizing the separate sensor to enable the virtual sum and difference co-array (SDCA) with a longer consecutive segment and to alleviate the MC effect. In addition, to further make the array structure more robust to the MC effect, RSNA-II relocates the dense subarray of RSNA-I. Theoretical analysis and numerical simulation results demonstrate that the proposed RSNA-I and RSNA-II achieve a better balance between DOFs and the MC effect, which in turn effectively solves DOA estimation of NC signals and yields better DOA estimation performance.

An Enhanced Spatial Smoothing Technique of Coherent DOA Estimation with Moving Coprime Array.

This paper investigates the direction of arrival (DOA) estimation of coherent signals with a moving coprime array (MCA). Spatial smoothing techniques are often used to deal with the covariance matrix of coherent signals, but they cannot be used in sparse arrays. Therefore, super-resolution algorithms such as multiple signal classification (MUSIC) cannot be applied in the DOA estimation of coherent signals in sparse arrays. In this study, we propose an enhanced spatial smoothing method specifically designed for MCA. Firstly, we combine the signals received by the MCA at different times, which can be regarded as a sparse array with a larger number of array sensors. Secondly, we describe how to compute the covariance matrix, derive the signal subspace by eigenvalue decomposition, and prove that the signal subspace is also equivalent to a received signal. Thirdly, we apply enhanced spatial smoothing to the signal subspace and construct a rank recovered covariance matrix. Finally, the DOA of coherent signals are well estimated by the MUSIC algorithm. The simulation results validate the improved performance of the proposed algorithm compared with traditional methods, particularly in scenarios with low signal-to-noise ratios.

Polarization Direction of Arrival Estimation Using Dual Algorithms Based on Time-Frequency Cross Terms

In radar array signal processing, weak nonstationary polarization signal direction of arrival (DOA) estimation is a challenging and significant issue when both strong and weak nonstationary signals coexist. Time-frequency (T-F) analysis is an effective method to deal with nonstationary signals. In the last decade, spatial time-frequency distributions (STFDs) have been proposed for multiple dual-polarization antenna arrays and efficaciously used for nonstationary signal DOA estimation. In this article, we introduced a novelty means for estimating weak nonstationary polarization signal DOA by utilizing spatial polarimetric time-frequency distributions (SPTFDs) of cross terms when there are strong nonstationary polarization interference signals and additive Gaussian white noise. The cross terms’ SPTFDs are considered via a replaceability matrix for data covariance in multiple signal classification (MUSIC) and the estimation of signal parameters using the rotational invariance technique (ESPRIT). Combining the STFDs of cross terms with polarization information about weak nonstationary signals improves signal DOA estimation accuracy. The combined MUSIC and ESPRIT are used in the algorithm to further ensure the success probability and accuracy of DOA estimation. Through simulation analyses, the proposed algorithm is more suitable for the required application scenarios than other algorithms and is superior to other algorithms.

DOA Estimation of Underwater Acoustic Array Signal Based on Wavelet Transform With Double Branch Convolutional Neural Network

In underwater acoustic communications, a hydrophone array is often used to receive the underwater acoustic signals to improve the gain of the received signal. The direction of arrival (DOA) estimation is a basic task in underwater acoustic array signal processing. In underwater signal transmission, due to the channel complexity, a large signal transmission loss, and heavy noise interference, the received signal is seriously distorted, and the DOA estimation is poor. In order to improve the accuracy of DOA estimation for underwater acoustic array signals, in this work, we propose continuous wavelet transform with convolutional neural network (CWT-CNN) method. We use a linear factor to improve the calculation process of continuous wavelet transform. The characteristics of time-frequency fusion of signals are calculated by constructing time-frequency array model with modified wavelet factors. The fused features are then used to train the proposed double branch CNN. As compared with other DOA algorithms based on neural networks, the proposed algorithm shows a 5%–20% higher accuracy and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$0.479^{\circ }-1.172^{\circ }$</tex-math></inline-formula> lower RMSE at 7 different values of SNR. In addition, the proposed algorithm is less computationally complex.

L0 Regularization parameter for sparse DOA estimation of coherent signals with modeling errors

Sparse methods have been recently introduced in Direction-Of-Arrival (DOA) estimation as an alternative to subspace-based methods and Maximum Likelihood (ML) techniques. This paper proposes a low complexity sparse L0-regularized method for DOA estimation of coherent signals in multipath environment, a scenario in which subspace-based methods fail. The first eigenvector of the covariance matrix is used as an observation and its statistics in the presence of modeling errors are derived. Thanks to those statistics, we present a theoretical statistical analysis of an interval in which the regularization parameter, usually empirically tuned, should stand. For a regularization parameter in this interval, the global solution of the L0-regularized problem coincides with the solution of the deterministic ML. An off-line selection of the regularization parameter is therefore proposed. Simulations confirm the relevance of this interval and of the proposed method.

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.

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.

Biquaternion-based DOA estimation of noncircular signals with time-modulated antenna arrays

A novel direction of arrival (DOA) estimation method of noncircular signals based on biquaternion with time-modulated antenna arrays is proposed in this paper. Time-modulated antenna arrays (TMAA) is introduced into the DOA estimation of noncircular signals for the first time, which makes the receiver only need a single RF processing channel, which effectively saves hardware resources. The noncircular features of the signal are fully exploited for virtual array expansion with the biquaternion framework. Aiming at the problem of nonuniform noise in the array output after time modulation, the nonuniform noise correction is realized by using the theoretical analysis of the time sequence scheme. The simulation illustrates that the proposed method has superior performance than conventional DOA estimation method with TMAA, in terms of resolution and numbers of localizable sources.

A novel DOA estimation method for an antenna array under strong interference

Strong interference will affect direction of arrival (DOA) estimation of weak desired signal and even cause DOA estimation failure. This paper investigates the weak signal DOA estimation for an antenna array under strong interference signals, and proposed a novel DOA estimation method for strong interference source suppression and weighted l1-norm sparse representation. A parallel adaptive beamforming algorithm based on power inversion is used to suppress strong interference and form new array data. To reduce spurious peaks in the spectrum under strong interference, a weighted matrix is determined by the optimized subspace algorithm for the subspace projection. Then, the DOA estimation, which is calculated by weighted l1-norm sparse representation, is formed by the weighted matrix and new array data. In this paper, the superiority of the proposed algorithm is illustrated by an example of unmanned aerial vehicle (UAV) video signal DOA estimation under strong interference signals. The simulated results of an orthogonal frequency division multiplexing signal indicate that the proposed algorithm shows merits of fewer snapshots, a sharper main lobe, a lower average noise spectrum value, higher DOA estimation accuracy and success rate. For validation, an outdoor experiment was conducted which demonstrated that the proposed algorithm is superior to other algorithms and can be used for DOA estimation of UAV video signals under strong WiFi interference. Both the simulations and experiments verify that the proposed algorithm can effectively suppress strong interference and achieve better DOA estimation performance for weak signals.

The DOA Estimation for a Mixture of Uncorrelated and Coherent Sources via Decomposing the Coprime Array

The spatial smoothing-based and matrix reconstruction-based decorrelation algorithms are widely used to realize the accurate direction-of-arrival (DOA) estimation with the coexistence of both uncorrelated and coherent sources. However, these methods apply only to the traditional uniform linear array (ULA), of which the manifold matrix is a Vandermonde structure. In this paper, to achieve the DOA estimation of mixed signals on coprime array, the coprime array is decomposed into two independent sub-ULAs, and the received data is processed, respectively. An improved spatial differencing technique is exploited to estimate the uncorrelated and coherent sources separately, and the lost degree of freedom (DOF) caused by array decomposition is recovered. The final high-precision DOA estimation is obtained by conducting an ambiguity resolution method to the estimation results of the decomposed subarrays. Furthermore, double-phase partial spectral search scheme is introduced to diminish the computational complexity. The feasibility and superiority of the proposed algorithm are validated through detailed experimental simulations.

The Limited Aperture Sparse Array for DOA Estimation of Coherent Signals: A Mutual-Coupling-Optimized Array and Coherent DOA Estimation Algorithm

The paper investigates DOA estimation of coherent Signals with the limited aperture sparse array. Mutual coupling between the sensors of the array cannot be ignored in practical radar with a limited aperture of array sensors, which will result in a degradation in the performance of Direction of Arrival (DOA) estimation. This paper proposes a Mutual-coupling-optimized array (MCOA) with a limited aperture in this scenario to reduce the mutual coupling effect. Firstly, we prove the sparse uniform linear array (SULA) has the smallest mutual coupling leakage when the array aperture and the number of sensors is determined. Secondly, we modify the spacing of the array sensors in SULA to make sure that the spacing between all array sensors and the reference sensor are coprime aiming to estimate DOA without spatial aliasing. Thirdly, we give an expression for the array element spacing arrangement with reduced mutual coupling leakage. Finally, the coherent signals are well resolved by the Sparse Bayesian Learning (SBL) algorithm. Numerous simulations are conducted to validate the advantages of the proposed array compared to several sparse arrays for estimating coherent signals in the presence of mutual coupling.

Two-Stage Nested Array Direction of Arrival Estimation for Mixed Signals.

In this paper, a novel two-stage subspace-based direction of arrival (DOA) estimation algorithm with the nested array is proposed for mixed signals containing circular and non-circular ones. By exploiting the difference between the two types of steering vectors, the DOAs of circular signals are estimated in the first stage. After eliminating the estimated information of circular signals by the covariance matrix reconstruction and oblique projection methods, the dimensions of the noise subspace are increased in estimating the DOAs of non-circular signals in the second stage. Through the two-stage estimation, the DOAs of the circular and non-circular signals are estimated separately and different types of signals with similar or the same DOAs can be distinguished. Furthermore, to avoid the two-dimensional (2-D) search with huge computational burden, a one-dimensional (1-D) search method exploiting the rank deficiency is proposed in the DOA estimation for non-circular signals. The simulation results show that the proposed algorithm can effectively improve the estimation accuracy and resolution probability, especially when circular and non-circular signals have similar DOAs.

The DOA Estimation Method for Low-Altitude Targets under the Background of Impulse Noise.

Due to the discontinuity of ocean waves and mountains, there are often multipath propagation effects and obvious pulse characteristics in low-altitude detection. If the conventional direction of arrival (DOA) estimation method is directly used for direction finding, it will lead to a large error. In view of serious misalignment in the DOA estimation of multipath signals under the background of impulse noise, a DOA estimation method based on spatial difference and a modified projection subspace algorithm is proposed in this paper. Firstly, the covariance matrix of the received data vector is used for spatial difference to eliminate the multipath effects of low-altitude targets. Secondly, the modified projection matrix is constructed using the signal source estimated with the least squares criterion and then used for modifying the covariance matrix, thus eliminating the cross-covariance matrices that affect the estimation accuracy. Finally, the modified covariance matrix is used for the DOA estimation of targets. Simulations show that the proposed algorithm achieves a higher accuracy in the DOA estimation of low-altitude targets than conventional algorithms under two common impulse noise models, without requiring prior knowledge of impulse noise.

Fast and Accurate Approach for DOA Estimation of Coherent Signals

An algorithm for estimation of direction of arrival (DOA) based on QR decomposition is proposed for coherent signals in this paper. When coherent is present, the rank of the signal covariance matrix is generally less than the signal number, making the estimation of the signal or noise subspace inaccurate. Therefore, we need to eliminate the spatial covariance matrix rank loss. According to the idea of matrix reconstruction, we try to construct three different data matrices, one is the signal covariance matrix, the other is the eigenvector reconstruction matrix of the signal covariance matrix, and the other is reconstructed matrix with the addition of spatial smoothing technology. Based on the resulting data matrix, whereafter, QR decomposition with the iteratively weighted least squares (IWLS) as solver is proposed to reduce the computational complexity of DOA estimation. Compared with other existing algorithms, the simulation results show that our method has high accuracy and great increase in the computational efficiency.

DOA Estimation for Non-Gaussian Signals: Three-Level Nested Array and a Successive SS-MUSIC Algorithm

Direction of arrival (DOA) estimation for non-Gaussian signals using three-level nested array (THL-NA) is investigated in this paper. Motivation from larger consecutive degree of freedom (DOF) and array aperture, the THL-NA is proposed, which can take full advantages of the consecutive coarrays of TL-NA and has the closed-form expression of DOF. Specifically, firstly, the array aperture is expanded by the second order sum coarray (2-SC) of the proposed array, secondly, the nested relationship between subarrays is employed to obtain the difference coarray of 2-SC (2-DCSC), finally, a consecutive virtual array with large array aperture is obtained. Besides, a successive SS-MUSIC algorithm is proposed, which employs the spatial smoothing estimating signal parameter via rotational invariance techniques (SS-ESPRIT) algorithm and partial spectrum searching multiple signal classification (PSS-MUSIC) to obtain initial estimations and fine estimations, respectively, resulting in a better balance between computational complexity and estimation accuracy.

Far-Field DOA Estimation of Uncorrelated RADAR Signals through Coprime Arrays in Low SNR Regime by Implementing Cuckoo Search Algorithm

For the purpose of attaining a high degree of freedom (DOF) for the direction of arrival (DOA) estimations in radar technology, coprime sensor arrays (CSAs) are evaluated in this paper. In addition, the global and local minima of extremely non-linear functions are investigated, aiming to improve DOF. The optimization features of the cuckoo search (CS) algorithm are utilized for DOA estimation of far-field sources in a low signal-to-noise ratio (SNR) environment. The analytical approach of the proposed CSAs, CS and global and local minima in terms of cumulative distribution function (CDF), fitness function and SNR for DOA accuracy are presented. The parameters like root mean square error (RMSE) for frequency distribution, RMSE variability analysis, estimation accuracy, RMSE for CDF, robustness against snapshots and noise and RMSE for Monte Carlo simulation runs are explored for proposed model performance estimation. In conclusion, the proposed DOA estimation in radar technology through CS and CSA achievements are contrasted with existing tools such as particle swarm optimization (PSO).

DOA Estimation Method of Weak Signal under the Compound Background of Strong Interference and Colored Noise

The traditional algorithm performing direction of arrival (DOA) estimation under the background of strong interference and colored noise has the problems of low estimation accuracy and small measurement targets. Based on the construction of a fourth-order cumulant (FOC) matrix to suppress colored noise, this paper adopts the extended noise subspace (ENS) algorithm and the fixed projection blocking (FPB) algorithm to estimate the DOA of weak targets. Firstly, a FOC matrix of the received signal vector is established to curb the noise component, and the eigenvalue decomposition is performed. Then, two approaches of weak signal DOA estimation are proposed. One approach is to merge the space where the strong interference steering vector lies into the noise subspace to construct an extended noise subspace, and then, the multisignal classification (MUSIC) algorithm is used to obtain the DOA estimation of the weak signal on the basis of the extended noise subspace. Another approach is to build the orthogonal projection matrix of the interference subspace as the interference blocking matrix, and the receiving array signal is preprocessed, and on the basis of it, the eigen decomposition is performed again to obtain the DOA information of the weak signal. Both algorithms make breakthroughs in the aperture limitation of the traditional algorithm, effectively expand the aperture, and promote the accuracy of estimation. The simulation tests the effectiveness of the proposed method.