Modified Eigendecomposition DOA EstimateAlgorithms and Field Test Studiesfor Super-Resolution

The signal direction of arrival (DOA) estimate algorithm based on the eigendecomposition of the modified covariance matrix is introduced in this paper. A field test system consisting of a 4-element linear array and a meter band radar is also presented, which is applied to the experimental studies of the algorithms in the practical performances. The results of the test indicate that when SNR is only 5.85 dB, two airplanes being 0.25 beam width apart in azimuth can be resolved clearly.

一种基于迭代近端投影的被动声纳探测离网格DOA估计方法

Traditional direction of arrival(DOA)estimation methods based on sparse reconstruction commonly use convex or smooth functions to approximate non-convex and non-smooth sparse representation problems.This approach often introduces errors into the sparse representation model,necessitating the development of improved DOA estimation algorithms.Moreover,conventional DOA estimation methods typically assume that the signal coincides with a predetermined grid.However,in reality,this assumption often does not hold true.The likelihood of a signal not aligning precisely with the predefined grid is high,resulting in potential grid mismatch issues for the algorithm.To address the challenges associated with grid mismatch and errors in sparse representation models,this article proposes a novel high-performance off-grid DOA estimation approach based on iterative proximal projection(IPP).In the proposed method,we employ an alternating optimization strategy to jointly estimate sparse signals and grid offset parameters.A proximal function optimization model is utilized to address non-convex and non-smooth sparse representation problems in DOA estimation.Subsequently,we leverage the smoothly clipped absolute deviation penalty(SCAD)function to compute the proximal operator for solving the model.Simulation and sea trial experiments have validated the superiority of the proposed method in terms of higher resolution and more accurate DOA estimation performance when compared to both traditional sparse reconstruction methods and advanced off-grid techniques.

High-Precision DOA Estimation Method Based on Synthetic Aperture Technique

The existing direction-of-arrival(DOA)estimation methods only utilize the current received signals,which are susceptible to noise.In this paper,a method for DOA estimation based on a motion platform is proposed to achieve high-precision DOA estimation by utilizing past and present signals.The concept of synthetic aperture is introduced to construct a linear DOA estima-tion model.A DOA fine-tuning method based on the linear model is proposed to eliminate the lin-ear DOA variation,achieving a non-coherent accumulation of DOA estimations.Moreover,the baseband modulation and the phase modulation caused by the range history are compensated to achieve the coherent accumulation of all the DOA estimations.Simulation results show that the proposed method can significantly improve the DOA estimated accuracy at low signal-to-noise ratios(SNR).

Improved Capon Estimator for High-Resolution DOA Estimation and Its Statistical Analysis

Despite some efforts and attempts have been made to improve the direction-of-arrival(DOA)estimation performance of the standard Capon beamformer(SCB)in array processing,rigorous statistical performance analyses of these modified Capon estimators are still lacking.This paper studies an improved Capon estimator(ICE)for estimating the DOAs of multiple uncorrelated narrowband signals,where the higherorder inverse(sample)array covariance matrix is used in the Capon-like cost function.By establishing the relationship between this nonparametric estimator and the parametric and classic subspace-based MUSIC(multiple signal classification),it is clarified that as long as the power order of the inverse covariance matrix is increased to reduce the influence of signal subspace components in the ICE,the estimation performance of the ICE becomes equivalent to that of the MUSIC regardless of the signal-to-noise ratio(SNR).Furthermore the statistical performance of the ICE is analyzed,and the large-sample mean-squared-error(MSE)expression of the estimated DOA is derived.Finally the effectiveness and the theoretical analysis of the ICE are substantiated through numerical examples,where the Cramer-Rao lower bound(CRB)is used to evaluate the validity of the derived asymptotic MSE expression.

Exploration on 2D DOA Estimation of Linear Array Motion:Uniform Linear Motion

Generally,due to the limitation of the dimension of the array aperture,linear arrays cannot achieve two-dimensional(2D)direction of arrival(DOA)estimation.But the emergence of array motion provides a chance for that.In this paper,a generalized motion scheme and a novel method of 2D DOA estimation are proposed by exploring the linear array motion.To be specific,the linear arrays are controlled to move along an arbitrary direction at a constant velocity and snap per fixed time delay.All the received signals are processed to synthesize the comprehensive observation vector for an extended 2D virtual aperture.Subsequently,since most of 2D DOA estimation methods are not universal to our proposed motion scheme and the reduced-dimensional(RD)method fails to handle the case of the coupled parameters,a decoupled reduced-complexity multiple signals classification(DRC MUSIC)algorithm is designed specifically.Simulation results demonstrate that:a)our proposed scheme can achieve underdetermined 2D DOA estimation just by the linear arrays;b)our designed DRC MUSIC algorithm has the good properties of high accuracy and low complexity;c)our proposed motion scheme with the DRC method has better universality in the motion direction.

Computationally efficient MUSIC based DOA estimation algorithm for FMCW radar

This paper proposes low-cost yet high-accuracy direction of arrival(DOA)estimation for the automotive frequency-modulated continuous-wave(FMcW)radar.The existing subspace-based DOA estimation algorithms suffer fromeither high computational costs or low accuracy.We aim to solve such contradictory relation between complexity and accuracy by using randomizedmatrix approximation.Specifically,we apply an easily-interpretablerandomized low-rank approximation to the covariance matrix(CM)and R∈C^(M×M)throughthresketch maties in the fom of R≈OBQ^(H).Here the approximately compute its subspaces.That is,we first approximate matrix Q∈C^(M×z)contains the orthonormal basis for the range of the sketchmatrik C∈C^(M×z)cwe whichis etrated fom R using randomized unifom counsampling and B∈C^(z×z)is a weight-matrix reducing the approximation error.Relying on such approximation,we are able to accelerate the subspacecomputation by the orders of the magnitude without compromising estimation accuracy.Furthermore,we drive a theoretical error bound for the suggested scheme to ensure the accuracy of the approximation.As validated by the simulation results,the DOA estimation accuracy of the proposed algorithm,eficient multiple signal classification(E-MUSIC)s high,closely tracks standardMUSIC,and outperforms the well-known algorithms with tremendouslyreduced time complexity.Thus,the devised method can realize high-resolutionreal-time target detection in the emerging multiple input and multiple output(MIMO)automotive radar systems.

Triad-displaced ULAs configuration for non-circular sources with larger continuous virtual aperture and enhanced degrees of freedom

Non-uniform linear array(NULA)configurations are well renowned due to their structural ability for providing increased degrees of freedom(DOF)and wider array aperture than uniform linear arrays(ULAs).These characteristics play a significant role in improving the direction-of-arrival(DOA)estimation accuracy.However,most of the existing NULA geometries are primarily applicable to circular sources(CSs),while they limitedly improve the DOF and continuous virtual aperture for noncircular sources(NCSs).Toward this purpose,we present a triaddisplaced ULAs(Tdis-ULAs)configuration for NCS.The TdisULAs structure generally consists of three ULAs,which are appropriately placed.The proposed antenna array approach fully exploits the non-circular characteristics of the sources.Given the same number of elements,the Tdis-ULAs design achieves more DOF and larger hole-free co-array aperture than its sparse array competitors.Advantageously,the number of uniform DOF,optimal distribution of elements among the ULAs,and precise element positions are uniquely determined by the closed-form expressions.Moreover,the proposed array also produces a filled resulting co-array.Numerical simulations are conducted to show the performance advantages of the proposed Tdis-ULAs configuration over its counterpart designs.

DOA Estimation Algorithm Based on Adaptive Filtering in Spatial Domain

In this paper, a novel DOA estimation methodology based upon the technology of adaptive nulling antenna is proposed. Initially, the nulling antenna obtains the weight vector by LMS algorithm and power inversion criterion.Afterwards, reciprocal of the antenna pattern is defined as the spatial spectrum and the extracted peak values are corresponded to the estimated DOA. Through observation of the spectrum and data analysis of variable steps and SNRs, the simulation results demonstrate that the proposed method can estimate DOA above board. Furthermore, the estimation error of the proposed technique is directly proportional to step size and is inversely proportional to SNR. Unlike the existing MUSIC algorithm, the proposed algorithm has less computational complexity as it eliminates the need of estimating the number of signals and the eigenvalue decomposition of covariance matrix. Also it outperforms MUSIC algorithm, the recently proposed MUSIC-Like algorithm and classical methods by achieving better resolution with narrow width of peaks.

Blind identification and DOA estimation for array sources in presence of scattering

A novel identification method for point source,coherently distributed（CD） source and incoherently distributed（ICD） source is proposed.The differences among the point source,CD source and ICD source are studied.According to the different characters of covariance matrix and general steering vector of the array received source,a second order blind identification method is used to separate the sources,the mixing matrix could be obtained.From the mixing matrix,the type of the source is identified by using an amplitude criterion.And the direction of arrival for the array received source is estimated by using the matching pursuit algorithm from the vectors of the mixing matrix.Computer simulations validate the efficiency of the method.

Novel algorithm on DOA estimation for correlated sources under complex symmetric Toeplitz noise

To cope with the scenario where both uncorrelated sources and coherent sources coexist, a novel algorithm to direction of arrival （DOA） estimation for symmetric uniform linear array is presented. Under the condition of stationary colored noise field, the algorithm employs a spatial differencing method to eliminate the noise covariance matrix and uncorrelated sources, then a Toeplitz matrix is constructed for the remained coherent sources. After preprocessing, a propagator method （PM） is employed to find the DOAs without any eigendecomposition. The number of sources resolved by this approach can exceed the number of array elements at a lower computational complexity. Simulation results demonstrate the effectiveness and efficiency of the proposed method.

DOA estimation of coexisted noncoherent and coherent signals via sparse representation of cleaned array covariance matrix

A new direction finding method is presented to deal with coexisted noncoherent and co- herent signals without smoothing operation. First the direction-of-arrival （DOA） estimation task is herein reformulated as a sparse reconstruction problem of the cleaned array covariance matrix, which is processed to eliminate the affection of the noise. Then by using the block of matrices, the information of DOAs which we pursuit are implied in the sparse coefficient matrix. Finally, the sparse reconstruction problem is solved by the improved M-FOCUSS method, which is applied to the situation of block of matrices. This method outperforms its data domain counterpart in terms of noise suppression, and has a better performance in DOA estimation than the customary spatial smoothing technique. Simulation results verify the efficacy of the proposed method.

Underdetermined DOA estimation via multiple time-delay covariance matrices and deep residual network

Higher-order statistics based approaches and signal sparseness based approaches have emerged in recent decades to resolve the underdetermined direction-of-arrival(DOA)estimation problem.These model-based methods face great challenges in practical applications due to high computational complexity and dependence on ideal assumptions.This paper presents an effective DOA estimation approach based on a deep residual network(DRN)for the underdetermined case.We first extract an input feature from a new matrix calculated by stacking several covariance matrices corresponding to different time delays.We then provide the input feature to the trained DRN to construct the super resolution spectrum.The DRN learns the mapping relationship between the input feature and the spatial spectrum by training.The proposed approach is superior to existing model-based estimation methods in terms of calculation efficiency,independence of source sparseness and adaptive capacity to non-ideal conditions(e.g.,low signal to noise ratio,short bit sequence).Simulations demonstrate the validity and strong performance of the proposed algorithm on both overdetermined and underdetermined cases.

A Modified Root-MUSIC Algorithm for Signal DOA Estimation

This paper presents a modified Root-MUSIC algorithm by which the signal DOA estimation performance can be improved when the snapshot number is limited. The operation principlesof this algorithm are described in detail. It is also pointed out theoretically that this is equivalentto have increased the snapshot number and can make the DOA estimation better. Finally, somesimulating results to verify the theoretical analyses are presented.

2D DOA Estimation Algorithm with Increased Degrees of Freedom for Two Parallel Linear Arrays

In this paper,a two-dimensional(2 D)direction-of-arrival(DOA)estimation algorithm with increased degrees of freedom for two parallel linear arrays is presented.Being different from the conventional two-parallel linear array,the proposed two-parallel linear array consists of two uniform linear arrays with non-equal inter-element spacing.Propagator method(PM)is used to obtain a special matrix which can be utilized to increase the virtual elements of one of uniform linear arrays.Then,the PM algorithm is used again to obtain automatically paired elevation and azimuth angles.The simulation results and complexity analysis show that the proposed method can increase the number of distinguishable signals and improve the estimation precision without increasing the computational complexity.

Low complexity DOA estimation for massive UCA with single snapshot

In this paper, a low complexity direction of arrival(DOA) estimation method for massive uniform circular array(UCA) with single snapshot is proposed.Firstly, the coarse DOAs are estimated by finding the peaks from the circular convolution between a fixed coefficient vector and the received data vector.Thereafter, in order to refine coarse DOA estimates, we reconstruct the direction matrix based on the coarse DOA estimations and take the first order Taylor expansion with DOA estimation offsets into account.Finally, the refined estimations are obtained by compensating the offsets, which are obtained via least squares(LS) without any complex searches.In addition, the refinement can be iteratively implemented to enhance the estimation results.Compared to the offset search method, the proposed method achieves a better estimation performance while requiring lower complexity.Numerical simulations are presented to demonstrate the effectiveness of the proposed method.

DOA ESTIMATION USING A SPARSE LINEAR MODEL BASED ON EIGENVECTORS

To reduce high computational cost of existing Direction-Of-Arrival(DOA) estimation techniques within a sparse representation framework,a novel method with low computational com-plexity is proposed.Firstly,a sparse linear model constructed from the eigenvectors of covariance matrix of array received signals is built.Then based on the FOCal Underdetermined System Solver(FOCUSS) algorithm,a sparse solution finding algorithm to solve the model is developed.Compared with other state-of-the-art methods using a sparse representation,our approach also can resolve closely and highly correlated sources without a priori knowledge of the number of sources.However,our method has lower computational complexity and performs better in low Signal-to-Noise Ratio(SNR).Lastly,the performance of the proposed method is illustrated by computer simulations.

DOA estimation based on multi-frequency joint sparse Bayesian learning for passive radar

This paper considers multi-frequency passive radar and develops a multi-frequency joint direction of arrival(DOA)estimation algorithm to improve estimation accuracy and resolution.The developed algorithm exploits the sparsity of targets in the spatial domain.Specifically,we first extract the required frequency channel data and acquire the snapshot data through a series of preprocessing such as clutter suppression,coherent integration,beamforming,and constant false alarm rate(CFAR)detection.Then,based on the framework of sparse Bayesian learning,the target’s DOA is estimated by jointly extracting the multi-frequency data via evidence maximization.Simulation results show that the developed algorithm has better estimation accuracy and resolution than other existing multi-frequency DOA estimation algorithms,especially under the scenarios of low signalto-noise ratio(SNR)and small snapshots.Furthermore,the effectiveness is verified by the field experimental data of a multi-frequency FM-based passive radar.

Generalized Array Architecture with Multiple Sub-Arrays and Hole-Repair Algorithm for DOA Estimation

Arranging multiple identical sub-arrays in a special way can enhance degrees of freedom(DOFs)and obtain a hole-free difference co-array(DCA).In this paper,by adjusting the interval of adjacent sub-arrays,a kind of generalized array architecture with larger aperture is proposed.Although some holes may exist in the DCA of the proposed array,they are distributed uniformly.Utilizing the partial continuity of the DCA,an extended covariance matrix can be constructed.Singular value decomposition(SVD)is used to obtain an extended signal sub-space,by which the direction-of-arrival(DOA)estimation algorithm for quasi-stationary signals is given.In order to eliminating angle ambiguity caused by the holes of DCA,the estimation of signal parameters via rotational invariance techniques(ESPRIT)is used to construct a matrix that includes all angle information.Utilizing this matrix,a secondary extended signal sub-space can be obtained.This signal sub-space is corresponding to a hole-free DCA.Then,dealing with the further extended signal sub-space by multiple signal classification(MUSIC)algorithm,the unambiguous DOAs of all incident signals can be estimated.Some simulation results are shown to prove the improved performance of proposed generalized array architecture in DOA estimation and the effectiveness of corresponding hole-repair algorithm in eliminating angle ambiguity.

Joint Estimation of 2-D DOA and Polarization by Using the Linear Array with Diverse Polarizations

A linear array of diversely polarized antennas with one pair of identical sensors is used to obtain closed-form unambiguous estimation of 2-D direction of arrival （DOA） and polarization. Spatial phase information together with weighted 3-D polarization-angular coherence structure （PACS） are first recovered with fourth-order cumulants manipulation via a new 2-D ESPRIT variant. Spatial filtering is performed to obtain the scaled PACS, from which the closed-form 2-D DOA and polarization estimates can be derived with only quadrant ambiguity involved. The undesired quadrant ambiguity can be further resolved by using the acquired estimate of spatial phase factor.

MULTI-INVARIANCE ESPRIT-LIKE ALGORITHMS FOR COHERENT DOA ESTIMATION

Estimation of Signal Parameters via Rotational Invariance Technique(ESPRIT) algorithm can estimate Direction-Of-Arrival(DOA) of coherent signal,but its performance can not reach full satisfaction.We reconstruct the received signal to form data model with multi-invariance property,and multi-invariance ESPRIT algorithm for coherent DOA estimation is proposed in this paper.The proposed algorithm can resolve the DOAs of coherent signals and performs better in DOA estimation than that of ESPRIT-like algorithm.Meanwhile,it identifies more DOAs than ESPRIT-like algorithm.The simulation results demonstrate its validity.