Efficient Direction Of Arrival Research Articles

Efficient gridless 2D DOA estimation based on generalized matrix‐form atomic norm minimization

AbstractTwo‐dimensional (2D) direction‐of‐arrival (DOA) estimation is crucial in array signal processing. Compressed sensing (CS) provides a superior alternative to spatial spectrum estimation algorithms by enabling 2D DOA estimation of correlated sources from single snapshot data. However, the grid mismatch effect inherent in grid‐based CS algorithms impacts estimation accuracy. Despite recent advancements, the state‐of‐the‐art gridless CS algorithm, decoupled atomic norm minimization, is limited to specific 2D array geometries, such as uniform rectangular arrays. This letter presents an efficient gridless 2D DOA estimation algorithm for generalized rectangular arrays, including both uniform and sparse arrays. The proposed algorithm achieves high accuracy through a novel approach called generalized matrix‐form atomic norm minimization and provides a fast solution using the alternating direction method of multipliers. Validation through computer simulations and practical experiments underscores its efficacy.

An efficient off-grid direction-of-arrival estimation method based on inverse-free sparse Bayesian learning

The direction-of-arrival (DOA) estimation problem can be formulated in a Bayesian framework and solved well through sparse Bayesian learning (SBL). However, SBL-based methods often suffer from high computational complexity due to the matrix inversion of a large matrix in the Bayesian inference procedure. To address this issue, we propose an efficient DOA estimation method based on inverse-free sparse Bayesian learning (IFSBL). A real-valued vectorized array covariance model and a hierarchical Bayesian model are established. Then, a relaxed lower bound on the likelihood, namely relaxed evidence lower bound (relaxed-ELBO), is obtained as the optimization objective of the Bayesian inference. By utilizing the variational expectation–maximization method for the Bayesian inference, the estimation of the statistics of interest can be achieved, which is free of matrix inversion as the matrix to be inverted is diagonal. Moreover, when we take the off-grid DOAs into account, an efficient grid refinement is developed to iteratively modify the DOA estimates derived from the estimated spatial spectrum. The off-grid error obtained by the root of a simple polynomial is used to compensate for the corresponding DOA estimate. Simulations show good accuracy and improved computational efficiency of the proposed method compared with other state-of-art methods. Further experimental results verify the advantage in the runtime for the proposed method.

Super-resolution Direction of Arrival Estimation Using a Minimum Mean-Square Error Framework

This paper develops a novel sparse direction-of-arrival (DOA) estimation technique that avoids the common requirement of hyperparameters, which are typically difficult to set suitably in practice. Using the presented minimum mean-square error (MMSE) estimation framework, we propose a computationally efficient super-resolution DOA estimator that is implemented using an alternate updating of the spatial power distribution of the signals and of the dictionary matrix using a ridge regression algorithm. The regularization parameter determining the sparsity of the solution is formed from the previous spatial power distribution estimates using a SPICE-based criteria. The method employs an adaptive gridding strategy to avoid the grid mismatch problem. The computational complexity is further reduced by the use of an integrated wideband dictionary, determing the active dictionary in an iterative manner. The method offers high resolution estimates of closely spaced sources even for very low sample support (single snapshot) without assuming prior knowledge of the number of sources. Our evaluations illustrate the preferable performance of the proposed estimator as compared to various state-of-the art estimators, also indicating that the method’s performance approaches the Cramér-Rao lower bound (CRB) for the examined problem as the signal-to-noise ratio (SNR) increases.

An Efficient 2D DOA Estimation Algorithm Based on OMP for Rectangular Array

Recently, orthogonal matching pursuit (OMP) has been widely used in direction of arrival (DOA) studies, which not only greatly improves the resolution of DOA, but can also be applied to single-snapshot and coherent source cases. When applying the OMP algorithm to the rectangular array DOA of the millimeter-wave radar, it is necessary to reshape the two-dimensional (2D) signal into a long one-dimensional (1D) signal. However, the long 1D signal will greatly increase the number and length of atoms in the complete dictionary of the OMP algorithm, which will greatly increase the amount of computation. Taking advantage of the sparsity of targets in the DOA space, an efficient 2D DOA estimation algorithm based on OMP for rectangular array is proposed. The main idea is to reduce the number of atoms in the complete dictionary of the OMP algorithm, thereby greatly reducing the amount of computation required. A simulation verifies that the efficiency of the proposed algorithm is much higher than the conventional algorithm with almost the same estimation accuracy.

Decomposed CNN for Sub-Nyquist Tensor-Based 2-D DOA Estimation

Direction-of-arrival (DOA) estimation using sub-Nyquist tensor signals benefits from enhanced performance by extracting structural angular information with multi-dimensional sparse arrays. Although convolutional neural network (CNN) has been employed to achieve efficient DOA estimation in challenging conditions, conventional methods demand excessive memory storage and computation power to process sub-Nyquist tensor statistics. In this letter, we propose a decomposed CNN for sub-Nyquist tensor-based 2-D DOA estimation, where an augmented coarray tensor is derived and used as the network input. To compress convolution kernels for efficient coarray tensor propagation, we develop a convolution kernel decomposition approach. This enables the acquisition of canonical polyadic (CP) factors containing compressed parameters. Performing decomposable convolution between the coarray tensor and the CP factors leads to resource-efficient DOA estimation. Our simulation results indicate that the proposed method conserves system resources while maintaining competitive performance.

Efficient DOA and Polarization Estimation for Dual-Polarization Synthetic Nested Arrays

To obtain a larger aperture for improving parameter estimation performance, we present a novel polarization sensitive array with dual-polarization synthetic nested structure, and then propose a low-complexity method for direction of arrival (DOA) and polarization estimation with two steps. There is a systematic procedure to determine the number and positions of antennas in each single-polarization subarray used for the synthetic nested array, in order to achieve more degrees of freedom (DOFs) and larger aperture for difference coarray with limited physical antennas. The increased DOFs of cross- and self-difference coarrays are quantitatively provided. To handle underdetermined parameter estimation with the resulting DOFs, the proposed method first estimates initial DOA and polarization state by using root-MUSIC and oblique projection operator, based on hole-free cross-difference coarray from cross-correlation matrix between subarrays. In the second step, holes in self-difference coarray, which is from autocorrelation matrix of single-polarization subarray, are filled with initial estimation. By exploiting both hole-free self- and cross-difference coarrays, an efficient search-based algorithm with initially estimated parameters is explored for refined estimation. The Cramér–Rao bound for the array and computational complexity of the method are provided. Simulation results are given to demonstrate the superior performance of the proposed array and method.

Efficient DOA Estimation Under Partially Impaired Antenna Array Elements

Partially impaired antenna array is one of the challenges for estimating the accurate directions of the signals impinging upon antenna arrays. It causes random loss of the signal information, resulting in the poor direction of arrival (DOA) estimation performance. In this paper, we propose an efficient DOA estimation method under partially impaired antenna array elements, which work randomly. We first devise a strategy to detect the positions of randomly lost signal information corresponding to partially impaired antenna array elements and then formulate the problem of received signal recovery as low rank matrix completion. Afterwards, we utilize the recursive least squares (RLS) with the nulling antenna array for DOA estimation due to its fast convergence and low mean square error properties and place the nulls in the directions of received signals by adjusting the weight vectors adaptively. The reciprocal of the antenna array defines the output spatial spectrum, and the directions of the signals are estimated by finding the high peaks. We also investigate the mean and mean square performance of the RLS after <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">recovering</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">de-noising</i> the received signal. Simulation results show that the proposed method converges to optimal solution fast and outperforms the existing DOA estimation methods.

DOA Estimation for Transmit Beamspace MIMO Radar via Tensor Decomposition With Vandermonde Factor Matrix

We address the problem of tensor decomposition in application to direction-of-arrival (DOA) estimation for transmit beamspace (TB) multiple-input multiple-output (MIMO) radar. A general 4-order tensor model that enables computationally efficient DOA estimation is designed. Whereas other tensor decomposition-based methods treat all factor matrices as arbitrary, the essence of the proposed DOA estimation method is to fully exploit the Vandermonde structure of the factor matrices to take advantage of the shift-invariance between and within different subarrays. Specifically, the received signal of TB MIMO radar is expressed as a 4-order tensor. Depending on the target Doppler shifts, the constructed tensor is reshaped into two distinct 3-order tensors. A computationally efficient tensor decomposition method is proposed to decompose the Vandermonde factor matrices. The generators of the Vandermonde factor matrices are computed to estimate the phase rotations between subarrays, which can be utilized as a look-up table for finding target DOA. It is further shown that our proposed method can be used in a more general scenario where the subarray structures can be arbitrary but identical. The proposed DOA estimation method requires no prior information about the tensor rank and is guaranteed to achieve precise decomposition result. Simulation results illustrate the performance improvement of the proposed DOA estimation method as compared to conventional DOA estimation techniques for TB MIMO Radar.

Efficient DOA tracking of two dimensional incoherent distributed sources with double parallel linear arrays

ABSTRACT In the field of array processing, the distributed source model can describe more characteristics of a target. Aiming at direction-of-arrival (DOA) tracking of two-dimensional incoherently distributed (TDID) sources, the generalised signal vector (GSV) and generalised array manifold (GAM) matrices of a double parallel linear array (DPLA) are first established. By the rotation relations of GAM matrices, the closed solutions of DOA and angular spread are derived. Then, treating the estimated value as the measurement under the Kalman filter framework, an adaptive DOA tracking algorithm for TDID sources is presented. Finally, the simulation results show that the proposed method can track DOA without spectral search and angles matching and is suitable for multi-source cases. Compared with the subspace updating methods, this method has better tracking accuracy and robustness in the case of model mismatch.

Multi-source off-grid DOA estimation with single snapshot using non-uniform linear arrays

Direction of arrival (DOA) estimation methods suffer from the well-known off-grid problem, that shows up when the true DOAs are not located exactly on the discretized sampling grid points. Existing estimation algorithms should be designed by taking into account the trade-off between density of sampling grids and computational complexity. Moreover, most of the computationally efficient DOA methods cannot be applied to non-uniform linear arrays (NLAs). In order to overcome these drawbacks, we propose a simple but effective off-grid DOA (OGDOA) estimation method that adopts an “estimate and subtract” strategy and then iteratively corrects the DOA estimate of each source based on a closed-form estimator that does not suffer from the off-grid problem. We derived the analytical expression of the mean square error (MSE) of the proposed method and verified that the MSE approaches the Crame´r-Rao lower Bound (CRB) when the signal-to-noise ratio (SNR) increases. We also analyzed the convergence of the proposed OGDOA algorithm. Numerical analyses demonstrated the goodness of the proposed method for OGDOA estimation for single snapshot and NLAs over some existing methods.

Grid-less DOA estimation of coherent sources based on the covariance matrix recovery

A grid-less direction of arrival (DOA) estimation algorithm via covariance matrix recovery is developed to improve the DOA estimation performance under low signal-to-noise ratio (SNR) for coherent and non-coherent sources. Firstly, we propose to recover the covariance matrix by utilizing both the Hermitian Toeplitz structure of the covariance matrix and the noise statistical characters in the multiple measurement vectors (MMVs). An efficient grid-less DOA estimation algorithm based on the covariance matrix’s first column is also presented to reduce grid mismatch effects. The simulation results show that the proposed DOA estimation algorithm can better recover the covariance matrix than the covariance fitting algorithms with non-coherent and coherent sources. Besides, simulations also verify that the proposed algorithm has a smaller root mean square error (RMSE) and higher estimation probability than the state-of-the-art algorithms in low SNR and small angle separation.

An Efficient DOA Estimation Method for Passive Surveillance System Based on Troposcatter

Direction of arrival (DOA) estimation plays an important role in the passive surveillance system based on troposcatter. Rank deficiency and subspace leakage resulting from multipath propagation can deteriorate the performance of the DOA estimator. In this paper, characteristics of signals propagated by troposcatter are analyzed, and an efficient DOA estimation method is proposed. According to our new method, the invariance property of noise subspace (IPNS) is introduced as the main method. To provide precise noise subspace for INPS, forward and backward spatial smoothing (FBSS) is carried out to overcome rank deficiency. Subspace leakage is eliminated by a two-step scheme, and this process can also largely reduce the computational load of INPS. Numerical simulation results validate that our method has not only good resolution in condition of closely spaced signals but also superior performance in case of power difference.

Computationally Efficient DOA and Carrier Estimation for Coherent Signal Using Single Snapshot and Its Time-Delay Replications

In this article, we propose two computationally efficient approaches to jointly estimate direction of arrival (DOA) and carrier for coherent signals using a given single snapshot with uniform linear array. First, the proposed methods construct the Khatri-Rao product-like data vector by introducing P -level delays from the array output. Second, a row elementary transformation is applied to the structured data vector, the rotational invariance structure of the carrier vector is exploited and thereby the carrier is derived. To be able to proceed, the special structure of the data vector is also exploited to estimate the coherent waveform. As a result, the DOA estimation problem can be recast into two Frobenius-norm-based optimization problems: one is referred to as linear search-based covariance-like matrix fitting method, which is suitable for estimating spaced angles that are well separated. The other one is called subspace separation-based covariance-like matrix fitting method, which is suitable for estimating closely spaced angles. The proposed methods develop one-dimensional (1-D) search and K 1-D search procedures, respectively, and hence they are computationally efficient compared to the classical methods. The simulation results illustrate that the performance of the proposed methods is better than the spatial smoothing-based multiple signal classification method under different scenarios.

Robust and Efficient DOA-Steered Adaptive MVDR-FROST Beamforming Model for Multi-source Low SNR Environment

In the last few years, the demand of robust beamforming techniques has been increased significantly to serve numerous purposes. However, beamforming under low Signal to Noise Ratio (SNR) condition has always been a challenging task, which becomes more tedious in case of multiple sources. On the other hand, there are numerous factors such as steering vector error or similar estimation error problems that confine the efficiency of major beamforming techniques. Classical methods employ Eigen-Value Decomposition (EVD) and Singular Value Decomposition (SVD) over covariance matrix of the received signal; however their efficiency is limited under low SNR and multi-source condition, and perform inferiorly in case of steering vector errors. Such approaches are limited to achieve optimal Direction-of-Arrival (DOA) estimation that degrades the overall performance of the beamformer. Considering all these limitations, in this research, the focus is made on designing a robust DOA estimation model, followed by a novel beamformer for 8-element Uniform Linear Array (ULA). The simulation work consists two parts DOA estimation and beamforming. Unlike classical MUSIC and ESPRIT algorithms popular for DOA estimation our proposed model exploits the propagation method based subspace method where at first covariance matrix is obtained for the received signal, which is followed by normalization and Cross-Correlation matrix estimation. The obtained correlation matrix is processed for Generalized Eigen-Value Decomposition (GEVD) that efficiently obtained (orthogonal) subspace and SOI separation to yield DOA information. This approach enables more efficient DOA estimation even under low-SNR and steering vector error conditions. After obtaining DOA information, a novel adaptive beamformer is designed by using MVDR and FROST in parallel. DOA information from proposed model is given as input to the adaptive MVDR FROST beamforming model. Exploiting dynamic Signal-to-Interference ratio (SINR) by each beamformer our proposed method introduces an adaptation model that intends to achieve higher SINR value. MATLAB 2018a based simulation confirmed the robustness of the proposed model in terms of DOA estimation and beamforming results.

TRICE: A Channel Estimation Framework for RIS-Aided Millimeter-Wave MIMO Systems

We consider the channel estimation problem in point-to-point reconfigurable intelligent surface (RIS)-aided millimeter-wave (mmWave) MIMO systems. By exploiting the low-rank nature of mmWave channels in the angular domains, we propose a non-iterative Two-stage RIS-aided Channel Estimation (TRICE) framework, where every stage is formulated as a multidimensional direction-of-arrival (DOA) estimation problem. As a result, our TRICE framework is very general in the sense that any efficient multidimensional DOA estimation solution can be readily used in every stage to estimate the associated channel parameters. Numerical results show that the TRICE framework has a lower training overhead and a lower computational complexity, as compared to benchmark solutions.

Computationally Efficient Two-Dimensional DOA Estimation Algorithm Based on Quaternion Theory

In this letter, we present a novel computationally efficient DOA estimation algorithm based on quaternion theory for two-dimensional (2-D) direction-of-arrival (DOA) estimation. An orthogonal propagator method based on the cross-correlation of the quaternion models (OPM-CQM) is developed to alleviate the computation burden. To eliminate the effect of additive noise, we construct two quaternion-based signal models judiciously. Then, we obtain the statistics of the observed signals by performing the cross-correlation between the quaternion models. Meanwhile, the additive noise is eliminated without introducing other denoising methods. Moreover, the compact modeling approach based on quaternions provides a significant advantage to OPM-CQM in terms of computational effort. Simulations demonstrate that the proposed algorithm offers performance superiority in angular resolution compared with the non-quaternion schemes.

Robust Modified Multiple Signal Classification Algorithm for Direction of Arrival Estimation

A modified robust multiple signal classification (MUSIC) algorithm for direction-of-arrival (DOA) estimation of coherent source signals is devised in this work. Classical and subspace-based methods require large antenna elements and huge computations for the estimation of intended signals. It also deviates from its performance in low signal-to-noise ratio (SNR) conditions. Hence efficient and robust DOA estimators are required to tackle the real-time problems in wireless communication applications. To overcome these problems, the classical MUSIC algorithm is modified by assimilating Jordon canonical matrix in the covariance matrix for the reconstruction of data. With this modification, it is possible to make an accurate estimation of coherent sources even under an extremely low SNR environment. Furthermore, the proposed method requires fewer antenna elements, fewer snapshots, and less computation as compared to the classical MUSIC algorithm. The experimental results signify the effectiveness of the new method.

A new Nystrom approximation based efficient coherent DOA estimator for radar applications

In this work, we present a new method for the direction-of-arrival (DOA) estimation of coherent sources using the symmetric uniform linear array (ULA) without prior source number information. The proposed method constructs a new cost function based on the joint diagonalization structure of the Toeplitz matrix. The estimation of DOAs is made by developing a new spatial spectrum via a 1-D search. Furthermore, we exploit the Nystrom method to diminish the computational complexity of the proposed method. The efficacy of the new estimator is theoretically investigated and the complexity of the computation is also addressed. To examine the efficacy of the proposed method, various experiments are conducted and comparisons with the recent methods are carried out.

Direct Signal Space Construction Luenberger Tracker with Quadratic Least Square Regression for Computationally Efficient DoA Tracking

In this paper, we propose a computationally efficient direction-of-arrival (DoA) tracking scheme called the direct signal space construction Luenberger tracker (DSPCLT) with quadratic least square (QLS) regression. Also, we study analytically how the choice of observer gain affects the algorithm performance and illustrate how we can use the theoretical results in determining optimal observer gain value. The proposed scheme (DSPCLT) has several distinct features compared with existing algorithms. First, it requires only a fraction of computational complexity compared with other schemes. Secondly, it maintains robustness by treating separately the special case of object overlap in which subspace-based algorithms often suffer from lack of resolvability. Thirdly, the proposed scheme achieves enhanced performance by a method of delay compensation, which accounts for observation delay. Through numerical analysis, we show that DSPCLT achieves performance similar or superior to existing algorithms with only a fraction of computational requirement.

Three-Dimensional Coprime Array for Massive MIMO: Array Configuration Design and 2D DOA Estimation

In massive multiple-input multiple-output (MIMO) systems, it is critical to obtain the accurate direction of arrival (DOA) estimation. Conventional three-dimensional array mainly focuses on the uniform array. Due to the dense arrangement of the sensors, the array aperture is limited and severe mutual coupling effects arise. In this paper, a coprime cubic array (CCA) configuration design is presented, which is composed of two uniform cubic subarrays and can extend the interelement spacing with a selection of three pairs of coprime integers. Compared with uniform cubic array (UCA), CCA achieves the larger array aperture and less MC effects. And the analytical expression of Cramer–Rao Bound (CRB) for CCA is derived which verifies that the proposed CCA geometry outperforms the conventional UCA in two-dimensional (2D) DOA estimation performance in massive MIMO systems. Meanwhile, we propose a computationally efficient 2D DOA estimation algorithm with high accuracy for CCA. Specifically, we utilize array mapping to extract two uniform arrays from the nonuniform array by exploiting the relation derived from the signal subspace and the two directional matrices. Then, we operate a reduced dimension process on the uniform arrays and convert the 2D spectrum peak searching (SPS) problem into one-dimensional (1D) one, which significantly reduces the computational complexity. In addition, we employ the polynomial root finding technique with a lower complexity instead of 1D SPS to further relieve the computational complexity. Simultaneously, with coprime property, the phase ambiguity problem is solved, which results from the large interelement spacing. Numerical simulation results demonstrate that the proposed algorithm is very computationally efficient without degradation of DOA estimation performance.