Direction Of Arrival Estimation Algorithm Research Articles

Grid-Free DOD and DOA Estimation for MIMO Radar via Duality-Based 2D Atomic Norm Minimization

Atomic norm minimization (ANM) has recently become a powerful tool for gridless compressed sensing (CS). In this paper, the issue of joint estimation of direction-of-departure (DOD) and direction-of-arrival (DOA) for bistatic multiple-input-multiple-output (MIMO) radar is investigated via two dimensional (2D) ANM. However, a major problem of the primal 2D-ANM is that the direct conversion of 2D-ANM into its semi-definite programming (SDP) problem is not strictly established theoretically and is just an approximation, which results in a decline in estimation performance. Besides, the primal 2D-ANM is limited to a single measurement vector (SMV) model. We propose a duality-based 2D-ANM algorithm for grid-free DOD and DOA estimation in MIMO radar, in which the 2D-ANM problem is effectively solved over its optimal variables in the dual-domain with SDP. Thus it retains the benefits of 2D-ANM and holds in theory. Also, it is applicable for SMV as well as multiple measurement vectors (MMV) models and appropriate for non-uniform linear arrays. The simulation results show that the proposed algorithm avoids the grid mismatch effect in DOD and DOA estimation in contrast to the conventional CS methods, and is robust to target correlation and the single-snapshot environment in comparison with the traditional subspace methods.

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

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

Computational Efficient DOA, DOD, and Doppler Estimation Algorithm for MIMO Radar

Joint direction-of-arrival (DOA), direction-of-departure (DOD), and Doppler estimation for multiple-input multiple-output (MIMO) radar usually are too time-consuming to implement because of high-dimensional searching procedures. This letter proposes a computational efficient algorithm for MIMO radar joint DOA, DOD, and Doppler estimation, which adopts an unstructured maximum likelihood method to sequentially estimate the Doppler, DOD, and DOA by three one-dimensional searching procedures based on the extended invariance principle. Numerical results validate the effectiveness together with its superiorities over conventional maximum likelihood algorithms.

Extrapolation-RELAX Estimator Based on Spectrum Partitioning for DOA Estimation of FMCW Radar

This paper proposes an extrapolation-RELAX estimator based on spectrum partitioning (SP) for the direction of arrival (DOA) estimation of frequency-modulated continuous-wave (FMCW) radar. The FMCW radar employs fast Fourier transform (FFT)-based digital beamforming (DBF) for the DOA estimation owing to its low complexity and easy implementation. However, the DBF algorithm has a disadvantage of low angle resolution. To improve the angle resolution, super-resolution algorithms such as multiple signal classification (MUSIC) and estimation of signal parameters via rotational invariance techniques (ESPRIT) are proposed. However, these algorithms require the high signal-to-noise ratio (SNR) to meet the required performance. To overcome this drawback of super-resolution algorithms, the SP-based extrapolation method has been proposed. However, this algorithm still has the problem that the resolution performance degrades owing to the insufficient number of actual antenna arrays. To solve this problem, we propose the SP-based extrapolation-RELAX algorithm for DOA estimation of FMCW radar. Through extrapolation, the proposed structure solves the problem of insufficient number of arrays, resulting in high reliability of SP results. When the extrapolation algorithm is used to generate the input signal of the RELAX algorithm, the RELAX method improves the performance of the DOA estimation. To confirm the effectiveness of the proposed estimation, we compare the Monte Carlo simulation and root-mean-square error results of the proposed and conventional algorithms. To verify the performance of the proposed algorithm in practical conditions, experiments were performed using the FMCW radar module within a chamber and in an indoor environment.

Joint DOD and DOA Estimation in Bistatic MIMO Radar With Distributed Nested Arrays

In this paper, we investigate the problem of joint direction of departure (DOD) and the direction of arrival (DOA) estimation in bistatic MIMO radar. A new bistatic MIMO radar with the distributed nested array is proposed. Based on the new array, the DOD and DOA estimation algorithm called automatically paired DR-ESPRIT based on the angle disambiguation algorithm by using the range information of targets is proposed. By designing distributed nested array and using Khatri-Rao product processing, the long baseline and short baseline in the transceiver arrays are virtually extended simultaneously. The non-ambiguous and high-accuracy sine estimations of the DOD and DOA can be accomplished using DR-ESPRIT algorithm and the range information of targets and the geometry of bistatic MIMO radar. The virtual extension of array aperture and high angle estimation accuracy can be achieved for the MIMO radar with automatic pairing and without increasing the number of antennas compared with traditional uniform linear MIMO array. And, the proposed corresponding algorithm gives significant improvement in the DOD and DOA estimation performance. The simulation results validate the theoretical algorithm.

A PARAFAC Decomposition Algorithm for DOA Estimation in Colocated MIMO Radar With Imperfect Waveforms

In this paper, we focus on the problem of direction-of-arrival (DOA) estimation for a colocated multiple-input multiple-output radar with imperfect waveforms, and a parallel factor (PARAFAC)-based algorithm is proposed. First, the spatial cross-correlation technique is adopted to eliminate the spatially colored noise caused by the nonorthogonal waveforms. To utilize the inherent tensor structure of the array data, the covariance matrix is rearranged into a fourth-order PARAFAC decomposition model. Thereafter, a quadrilinear decomposition algorithm is developed, which obtain the direction matrices via alternating least squares strategy. Finally, the DOAs are achieved through solving a least squares fitting problem. The proposed scheme does not require the prior knowledge of the waveform correlation matrix, and it is computationally more efficient than the state-of-the-art matrix completion (MC) approach. Furthermore, the proposed method may offer more accurate DOA estimation performance than the MC approach. The numerical experiments are provided to show the improvement of our algorithm.

Unitary Matrix Completion-Based DOA Estimation of Noncircular Signals in Nonuniform Noise

In this paper, a novel direction-of-arrival (DOA) estimation algorithm is proposed for noncircular signals with nonuniform noise by using the unitary matrix completion (UMC) technique. First, the proposed method utilizes the noncircular property of signals to design a virtual array for approximately doubling the array aperture. Then, the virtual complex-valued covariance matrix with the unknown nonuniform noise is transformed into the real-valued one by utilizing the unitary transformation to improve the computational efficiency. Next, a novel UMC method is formulated for the DOA estimation to remove the influence of nonuniform noise. Finally, the DOA without the influence of the unknown noncircularity phase is obtained by using the modified estimation of signal parameters via rotational invariance technique (ESPRIT). Especially, for handling the coherent sources, the forward–backward spatial smoothing technique is utilized to reconstruct a full-rank covariance matrix so that the signal subspace and the noise subspace can be correctly separated. Due to utilizing the extended array aperture and the unitary transformation, the proposed method can identify more sources than the number of physical sensors and provides higher angular resolution and better estimation performance. Compared with the existing DOA estimation algorithms for noncircular signals, the proposed one can effectively suppress the influence of the nonuniform noise. The simulation results are provided to verify the effectiveness and superiority of the proposed method.

DOA Estimation Using Single or Dual Reception Channels Based on Cyclostationarity

This paper addresses the problem of direction-of-arrival (DOA) estimation for cyclostationary signals using less reception channel in comparison with the number of sensors. The system is considered to be realized by using the reception channel(s) to receive the signal reached each sensor in turn. Such simplification results in a cost reduction of the system and the effect of inconsistency among different channels are removed. However, non-synchronized sampling also makes the traditional DOA estimation algorithms ineffective. To cope with the problem, the signal models for DOA estimation using a single channel and dual channels are formulated based on signal cyclostationary, and the single channel cyclic MUSIC (SC-Cyclic-MUSIC) algorithm and the dual channels cyclic MUSIC (DC-Cyclic-MUSIC) algorithm are proposed correspondingly. This paper shows that both SC-Cyclic-MUSIC algorithm and DC-Cyclic-MUSIC algorithm work well when the switching interval is known, and a satisfied performance can also be obtained by DC-Cyclic-MUSIC algorithm when the uncertainty of the switching interval exists. Moreover, the proposed estimators are suitable for both narrow-band and wide-band signals. The computer simulations are provided to verify the effectiveness of the proposed algorithms.

Combined root‐MUSIC algorithms for multi‐carrier MIMO radar with sparse uniform linear arrays

In this study, sparse uniform linear arrays are used to improve the direction-of-arrival (DOA) estimation accuracy for the multiple-input multiple-output radar. With a suitable choice of multi-carrier frequencies, the DOA estimation ambiguity problem caused by spatial under-sampling can be resolved. Two kinds of search-free DOA estimation algorithms based on root-multiple signal classification (MUSIC) are proposed. The first algorithm directly applies the root-MUSIC to each carrier frequency separately for the true DOAs as well as their spurious DOAs, then, a novel DOA replicas matching algorithm is proposed to obtain the true DOAs from the ambiguous ones. The second algorithm utilises the manifold separation technique (MST) to align the noise subspaces of all multi-carrier frequencies. Using the MST, the separable representation of the array manifold vector of each carrier frequency is obtained, then the root-MUSIC polynomials of all multi-carrier frequencies are combined to construct a new polynomial, the true DOAs can be obtained directly by applying polynomial rooting without any matching processing. The two proposed algorithms are both practical, computationally efficient and robust. Numerical simulations verify the effectiveness of the proposed algorithms in terms of root-mean-squared error.

Codebook-Aided DOA Estimation Algorithms for Massive MIMO System

The conventional direction of arrival (DOA) estimation algorithm is not effective with the tremendous complexity due to the large-scale array antennas in a massive multiple-input multiple-output (MIMO) system. A new frame structure for downlink transmission is presented. Then, codebook-aided (C-aided) algorithms are proposed based on this frame structure that can fully exploit the priori information under channel codebook feedback mechanism. An oriented angle range is scoped through the codebook feedback, which is drastically beneficial to reduce computational burden for DOA estimation in massive MIMO systemss. Compared with traditional DOA estimation algorithms, our proposed C-aided algorithms are computationally efficient and meet the demand of future green communication. Simulations show the estimation effectiveness of C-aided algorithms and advantage for decrement of computational cost.

Non-coherent direction of arrival estimation utilizing linear model approximation

Abstract This fast communication presents a non-coherent direction of arrival (DOA) estimation algorithm utilizing the elements squared of the array covariance. Very different from previous non-coherent DOA estimation algorithms, the nonlinear model produced by the squared operation is approximately cast as a linear model, under a high-power reference source. And then, the DOA estimation is efficiently obtained via the mature l1-norm minimization. The proposed algorithm can be applied to arbitrary arrays. Focused on the estimation accuracy, the nested coprime array with displaced subarrays (CADiS) is exploited. To resolve the ambiguity problems in the scenario that the sources impinging on the array from the range [ − 90 ∘ , 90 ∘ ] , a simple but effective strategy is introduced. The proposed algorithm performs independent of the phase errors and can provide improved DOA estimation accuracy with reduced computational complexity in large snapshot case. Simulation results demonstrate the effectiveness and superiority of the proposed algorithm.

Efficient Beamspace-Based Algorithm for Two-Dimensional DOA Estimation of Incoherently Distributed Sources in Massive MIMO Systems

In massive multiple-input multiple-output (MIMO) systems, accurate direction-of-arrival (DOA) estimation is critical for the transmitters to conduct downlink precoding. In this paper, we focus on the problem of two-dimensional DOA estimation of incoherently distributed sources in massive MIMO systems using uniform rectangular arrays (URAs). First, with the generalized array manifold, we obtain the beamspace array manifold by performing beamspace transformation on the observed vector of the URA, and establish one beamspace shift invariance structure via appropriate beamforming matrix design and array manifold selection. Second, from the beamspace array manifold, we extract two array manifolds, and derive the other beamspace shift invariance structure. Final, the total least squares approach is used to estimate the nominal azimuth and elevation DOAs. With the DOA estimates, the corresponding angular spreads are given in closed-form solutions. Our approach avoids spectral search and reduces the dimensions in matrix operations, thus, it is more computationally attractive than the existing techniques. Numerical results show that the proposed algorithm achieves performance comparable to that of the conventional estimators in massive MIMO systems.

Estimation of Direction of Arrival by Time Reversal for Low-Angle Targets

In a low-angle target parameter estimation scenario, the backscattered signals from targets are often distorted due to clutter and multipath, which significantly degrades the performance of direction-of-arrival (DOA) estimation. In general, the backscattered multipaths are modeled as coherent signals with respect to the direct path. Decorrelation algorithms such as spatial smoothing and matrix reconstruction can mitigate the effect of multipath. However, most of these methods will perform poorly or even fail for solving parameter estimation problem of low-angle targets in complex terrain where there are rich multipath scatterings. This paper presents a novel method that combines time reversal (TR) technique, coherent signal-subspace method (CSM), and multiple signal classification algorithm to perform DOA estimation in a low-angle target scenario. The TR technique takes advantage of multipath echoes recorded by a sensor array and adaptively adjusts TR probing waveforms to increase the signal-to-noise ratio in a rich scattering environment. Moreover, the CSM method compresses the energy of a signal into a predefined subspace to exploit the full time-bandwidth product of signal sources and cope with coherent wavefronts. As a result, the proposed new DOA estimation algorithm outperforms significantly the conventional methods. The Cramer–Rao bounds analysis and numerical simulations commendably validate the accuracy and robustness of the proposed method.

An Improved Inverse Beamforming Method: Azimuth Resolution Analysis for Weak Target Detection.

The inverse beamforming (IBF) is a mature method to improve azimuth resolution. However, for weak targets it is not applicable as IBF enhances side lobes. In this paper, an improved IBF algorithm is proposed to raise the azimuth resolution under the premise of ensuring the detection ability for weak targets. Firstly, from the point of phase compensation, we analyze the cause of side lobes when IBF is applied. Then the improved IBF algorithm recorded as GIBF (the improved inverse beamforming) is proposed by changing the Toeplitz average into the phase construction. The theoretical derivation and simulation data processing show the proposed method can improve the resolution of the N sensors to the standard of 2N − 1 sensors under different signal-to-noise ratios. Compared with IBF, GIBF has great advantages in detecting weak targets. Passive sonar data are used to further verify the advantages of GIBF; the trajectories on azimuth history diagrams become clear, the azimuth resolution is improved, and the detection ability for weak targets is still robust. In addition, GIBF is combined with the common DOA (direction of arrival) estimation algorithms, such as conventional beamforming and minimum variance distortionless signal response, which proves the applicability of the algorithm.

Direction-of-Arrival Estimation for Coprime Array via Virtual Array Interpolation

Coprime arrays can achieve an increased number of degrees of freedom by deriving the equivalent signals of a virtual array. However, most existing methods fail to utilize all information received by the coprime array due to the non-uniformity of the derived virtual array, resulting in an inevitable estimation performance loss. To address this issue, we propose a novel virtual array interpolation-based algorithm for coprime array direction-of-arrival (DOA) estimation in this paper. The idea of array interpolation is employed to construct a virtual uniform linear array such that all virtual sensors in the non-uniform virtual array can be utilized, based on which the atomic norm of the second-order virtual array signals is defined. By investigating the properties of virtual domain atomic norm, it is proved that the covariance matrix of the interpolated virtual array is related to the virtual measurements under the Hermitian positive semi-definite Toeplitz condition. Accordingly, an atomic norm minimization problem with respect to the equivalent virtual measurement vector is formulated to reconstruct the interpolated virtual array covariance matrix in a gridless manner, where the reconstructed covariance matrix enables off-grid DOA estimation. Simulation results demonstrate the performance advantages of the proposed DOA estimation algorithm for coprime arrays.

Direction of Arrival Estimation Using Augmentation of Coprime Arrays

Recently, direction of arrival (DOA) estimation premised on the sparse arrays interpolation approaches, such as co-prime arrays (CPA) and nested array, have attained extensive attention because of the effectiveness and capability of providing higher degrees of freedom (DOFs). The co-prime array interpolation approach can detect O(MN) paths with O(M + N) sensors in the array. However, the presence of missing elements (holes) in the difference coarray has limited the number of DOFs. To implement co-prime coarray on subspace based DOA estimation algorithm namely multiple signal classification (MUSIC), a reshaping operation followed by the spatial smoothing technique have been presented in the literature. In this paper, an active coarray interpolation (ACI) is proposed to efficiently recovering the covariance matrix of the augmented coarray from the original covariance matrix of source signals with no vectorizing and spatial smoothing operation; thus, the computational complexity reduces significantly. Moreover, the numerical simulations of the proposed ACI approach offers better performance compared to its counterparts.

Off-Grid Direction-of-Arrival Estimation Using Coprime Array Interpolation

In this letter, we propose a coprime array interpolation approach to provide an off-grid direction-of-arrival (DOA) estimation. Through array interpolation, a uniform linear array (ULA) with the same aperture is generated from the deterministic non-uniform coprime array. Taking the observed correlations calculated from the signals received at the coprime array, a gridless convex optimization problem is formulated to recover all the rows and columns of the unknown correlation matrix entries corresponding to the interpolated sensors. The optimized Hermitian positive semidefinite Toeplitz matrix functions as the covariance matrix of the interpolated ULA, which enables to resolve off-grid sources. Simulation results demonstrate that the proposed array interpolation-based DOA estimation algorithm achieves improved performance as compared to existing coarray-based DOA estimation algorithms in terms of the number of achievable degrees-of-freedom and estimation accuracy.

Direction of Arrival Estimation With the Received Signal Strength Gradient

Direction of arrival (DoA) estimation has wide-ranging applications and is particularly challenging in complex propagation environments. Conventional approaches estimate the DoA based on the phase of the impinging signal on a sensor array. This approach has several challenges: for example, it requires tight synchronization among array elements and the estimated DoA is sensitive to multipath and to correct specification of the array geometry. In this paper, we develop a principled Bayesian DoA estimation algorithm based on the received signal strength gradient. We present algorithms for clustering, spatial- and model-based outlier detection and removal, and proper uncertainty quantification, which yield an estimator robust to non-uniform shadowing, multipath, and errors in antenna position. Physics-based full-wave simulations and experiments in the 2.4 GHz and 40 MHz bands illustrate the utility of our approach.

Two-Dimensional Angle Estimation of Two-Parallel Nested Arrays Based on Sparse Bayesian Estimation.

To increase the number of estimable signal sources, two-parallel nested arrays are proposed, which consist of two subarrays with sensors, and can estimate the two-dimensional (2-D) direction of arrival (DOA) of signal sources. To solve the problem of direction finding with two-parallel nested arrays, a 2-D DOA estimation algorithm based on sparse Bayesian estimation is proposed. Through a vectorization matrix, smoothing reconstruction matrix and singular value decomposition (SVD), the algorithm reduces the size of the sparse dictionary and data noise. A sparse Bayesian learning algorithm is used to estimate one dimension angle. By a joint covariance matrix, another dimension angle is estimated, and the estimated angles from two dimensions can be automatically paired. The simulation results show that the number of DOA signals that can be estimated by the proposed two-parallel nested arrays is much larger than the number of sensors. The proposed two-dimensional DOA estimation algorithm has excellent estimation performance.

A low-complexity RARE-based 2-D DOA estimation algorithm for a mixture of circular and strictly noncircular sources

A new rank reduction (RARE)-based two-dimensional (2-D) direction of arrival (DOA) estimation algorithm is proposed considering a mixture of circular and strictly noncircular sources. To enhance array aperture, a geometry of three uniform linear arrays is considered and then treated as displaced arrays from a virtual array using a simple linear transformation. The received data and the conjugated counterpart are combined together, exploiting the noncircular property. Both sources can be estimated separately by designing and exploiting the distinctive nature of circular and noncircular steering vectors. However, a 2-D spectrum search would lead to a high computational complexity burden. To reduce this high computational complexity burden, a novel RARE-based method is proposed, which plays a vital role by decomposing 2-D observation space into two successive 1-D peak search functions. The proposed method has some distinctive advantages: it can enhance the array aperture utilization, it can provide better estimation accuracy when mixed sources are greater than the number of sensors, it can estimate a larger number of mixed sources than the number of sensors, and finally it can automatically pair 2-D DOAs without any complicated pairing formulation. Extensive simulation results are provided to demonstrate the effectiveness of the proposed method.