Fast Direction-of-arrival Estimation Research Articles

Direction‐of‐arrival estimation via coarray‐domain RELAX algorithm with source number estimation

AbstractA modified RELAX algorithm based on iterative coarray‐domain beamforming for fast source direction‐of‐arrival (DOA) estimation with fully augmentable sparse arrays is proposed. The authors exploit the deterministic centralised nature of the noise in the coarray domain and the Hermitian symmetry of the spatial autocorrelation function to efficiently incorporate source number estimation within the iterative framework. In doing so, the proposed algorithm allows low‐complexity, fast DOA estimation of more sources than sensors, without resorting to computationally expensive implementations of source number estimation using information theoretic criteria. Three variants of the proposed algorithm are presented, each differing in terms of the specific method employed for source number estimation. Extensive simulations are performed with a minimum redundancy array to compare and contrast the performance of the three variants in terms of their accuracy in estimating the number of sources in the field‐of‐view of the array. The results demonstrate that the modified RELAX algorithm can provide accurate estimates of the number and directions of sources, especially when the number of uncorrelated sources is equal to or higher than the number of sensors.

Direction-of-Arrival Estimation Method Based on Neural Network with Temporal Structure for Underwater Acoustic Vector Sensor Array.

Acoustic vector sensor (AVS) is a kind of sensor widely used in underwater detection. Traditional methods use the covariance matrix of the received signal to estimate the direction-of-arrival (DOA), which not only loses the timing structure of the signal but also has the problem of weak anti-noise ability. Therefore, this paper proposes two DOA estimation methods for underwater AVS arrays, one based on a long short-term memory network and attention mechanism (LSTM-ATT), and the other based on Transformer. These two methods can capture the contextual information of sequence signals and extract features with important semantic information. The simulation results show that the two proposed methods perform much better than the multiple signal classification (MUSIC) method, especially in the case of low signal-to-noise ratio (SNR), the DOA estimation accuracy has been greatly improved. The accuracy of the DOA estimation method based on Transformer is comparable to that of the DOA estimation method based on LSTM-ATT, but the computational efficiency is obviously better than that of the DOA estimation method based on LSTM-ATT. Therefore, the DOA estimation method based on Transformer proposed in this paper can provide a reference for fast and effective DOA estimation under low SNR.

Direction-of-arrival estimation in half-space from single sample array snapshot.

Most existing direction-of-arrival (DOA) estimation algorithms are intended for single-frequency use. However, the majority of real sound fields are wideband, and the application of these techniques then becomes computationally expensive. In this paper, a fast DOA estimation method for use with wideband sound fields is constructed from only a single observation of the array signal based on the properties of a space of spherically band-limited functions. The proposed method can be applied to any element arrangement and spatial dimensions, and the computational load is only dependent on the number of microphones in the array. However, because this method does not use time information, forward-backward identification of the arriving waves is not possible. Therefore, the proposed DOA estimation method is limited to a half-space. Numerical simulations of multiple sound waves arriving from a half-space show that the proposed method offers good processing performance when applied to pulse-like broadband sound fields. The results also indicate that the method is capable of tracking DOAs in real time, even when these DOAs vary rapidly.

Fast and Accurate Single-Snapshot DOA Estimation: Iterative Interpolated Approaches

Estimating the Direction of Arrival (DOA) of a single source signal from a single observation of an array data still plays an important part in practical application scenarios. To address the problem, this letter proposes two iterative, fast and accurate approaches namely Q-Shift based DOA Estimation Algorithm (QS-DOAEA) and Tradeoff between A&M and Q-Shift based DOA Estimation Algorithm (TAQ-DOAEA). QS-DOAEA adopts the interpolation of shifted DFT coefficients to iteratively obtain the near-optimal estimation. TAQ-DOAEA employs the error function by simultaneously mixing the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -shifted and half-shifted DFT coefficients, which only requires two iterations. Numerical results reveal that QS-DOAEA achieves significant improvement in terms of estimation accuracy and TAQ-DOAEA expedites the convergence. The proposed estimation algorithms demonstrate that they have an asymptotic variance that is at least 1.0013 times asymptotic Cramér-Rao bound (ACRB), and provide more than 80× reduction in the computational cost, compared to the baseline method. All our proposed algorithms and code are available at https://github.com/jn-z/.

Advanced direction of arrival estimation using step‐learnt iterative soft‐thresholding for frequency‐modulated continuous wave multiple‐input multiple‐output radar

The number of antennas in automotive frequency-modulated continuous wave (FMCW) multiple-input multiple-output (MIMO) radar systems is increasing. Existing greedy or subspace-based methods cannot quickly and accurately estimate the direction of arrival (DoA) of the target. Therefore, we propose a fast and accurate DoA estimation algorithm for the automotive FMCW MIMO radar. To achieve both fastness and accuracy, we exploit the group sparsity in DoA estimation by defining the problem as a multiple measurement vector (MMV) compressive sensing and extend the step-learnt iterative soft-thresholding algorithm (SLISTA) to the MMV problem. To apply the extended SLISTA, we train the network in an unsupervised manner and normalise the input. We conduct experiments to evaluate the performance of the proposed method. Compared to the algorithms such as ISTA/FISTA/MFOCUSS that solve the same optimisation problem, the extended SLISTA exhibits the most accurate DoA estimation results for actual targets, with less execution time than a subspace-based method. Moreover, the results show that the extended SLISTA prevents false detections, whereas greedy and subspace-based methods do not.

Lens-Loaded Cavity Antenna With Detector Diode as a Direction-of-Arrival Estimator

This letter proposes a novel direction-of-arrival (DoA) estimation approach that uses a lens-loaded, coded aperture antenna connected to a detector diode for millimeter-wave (mmWave) frequencies. The presented approach exploits three distinct but closely related properties of mmWave communication front-end hardware: First, the quasi-random radiation modes created by a lens-loaded cavity antenna; Second, the frequency-diverse impulse response of oversized metallic cavities; Third, the sensitivity of detector diodes at mmWave frequencies. Critically, we use a combination of the synthesis approach and experimental results to demonstrate that DoA estimation is possible with less complex hardware as compared to conventional methods, where an array of mmWave antennas is typically employed for DoA estimation. Bandwidth-to-accuracy tradeoff is thoroughly studied, which is an important commercial matrix. It is demonstrated that the lens-loaded cavity antenna with a detector diode circuit can be an apt choice for DoA estimation. Finally, it is shown that the proposed approach provides fast and accurate DoA estimation, thus inherently suitable for DoA estimation in future mmWave systems.

Two-Stage Fast DOA Estimation Based on Directional Antennas in Conformal Uniform Circular Array.

In conformal array radar, due to the directivity of antennas, the responses of the echo signals between different antennas are distinct, and some antennas cannot even receive the target echo signal. These phenomena significantly affect the accuracy of direction-of-arrival (DOA) estimation. To implement accurate DOA estimation in a conformal uniform circular array (UCA) composed of directional antennas, the two-stage fast DOA estimation algorithm is proposed. In the pre-processing stage, multi-target decoupling and target detection are mainly used to obtain the targets’ range bin indexes set; in the rough-precise DOA estimation stage, the amplitude and phase information of each antenna are used for rough DOA estimation and precise DOA estimation, respectively. Based on simulation and actual anechoic chamber radar experiments, and through quantitative analyses of the accuracy, validity and elapsed time of the two-stage fast DOA estimation algorithm compared with the directional antenna MUSIC (DA-MUSIC), sub-array MUSIC (S-MUSIC) and Capon-like algorithms, results indicate that the two-stage fast DOA estimation algorithm can rapidly and accurately estimate DOAs in a multi-target scenario without the range-angle pair-matching procedure. Lower computational complexity and superior estimation accuracy provide the two-stage fast DOA estimation algorithm a broader application prospect in the practical engineering field.

Fast detection and DOA estimation of the unknown wideband signal sources

SummaryThe direction of arrival (DOA) estimation analysis requires prior knowledge of frequency‐related information of the incident wideband signals, eg, center frequency and bandwidth, which are not available in many cases. This research is based on applications where DOA estimation of the wideband signal source is unknown, eg, in astronomy and unauthorized transmissions. Therefore, this paper has two major contributions. The first contribution is to identify the frequency spectrum of the wideband signals transmitted from an unknown source. The method use edge detection prestage to identify the frequency spectrum of the received signal. The second contribution is to estimate the DOA of the wideband signal at higher accuracy while keeping a minimum computational cost. The estimation of the DOAs was analyzed by measuring the orthogonal relationship between the signal and the noise subspaces of multiple frequency components of the sources. The introduced method utilizes subband as a reference frequency based on the extracted frequency‐related information rather than examining the complete incoming signal spectrum and exploits the spatial information of a few subbands. The introduced algorithm is implemented based on the well‐known method, test of orthogonality of projected subspaces (TOPS). Tests are conducted on a range of wideband signals with extreme values of signal‐to‐noise ratio (SNR). Considerable performance improvement is obtained.

A Real-Valued Polynomial Rooting Method for Fast Direction of Arrival Estimation With Large Uniform Linear Arrays

When used for direction of arrival (DOA) estimation with large uniform linear arrays (ULAs), both root-MUSIC and unitary root-MUSIC (U-root-MUSIC) involve high-dimension eigenvalue decomposition (EVD) and high-degree polynomial rooting computations. In this paper, we propose a novel real-valued modification of root-MUSIC to reduce the computational complexity. We first divide the large ULA into two moderate subarrays and exploit the subarray structure to extract a real noise matrix with reduced-dimension EVD. Using this real noise matrix, we construct a real polynomial, and further employ a variable substitution technique to transform the real polynomial to a new one with reduced degree equivalently. As such, both tasks of EVD and polynomial rooting can be computed efficiently. We finally show by numerical simulations that with significantly reduced computational complexity, the proposed method sacrifices statistically nonsignificant accuracy that is acceptable.

Fast DOA Estimation Algorithms for Sparse Uniform Linear Array With Multiple Integer Frequencies

The sparse uniform linear array (SULA) with larger array aperture is adopted to improve the accuracy of direction of arrival (DOA) estimation with a limited number of physical antennas. In the case of single working frequency configuration, spatial aliasing problem occurs due to the spatial under-sampling. However, with a sufficient anti-aliasing condition for multiple frequencies, the unique DOA estimations can be obtained without ambiguity by using multiple integer frequencies. The multiple equivalent array structures of the multiple integer frequencies are analyzed. To perform DOA estimation, in the first part of the paper, a pair of fast DOA estimation methods are proposed. Based on the fact that a real DOA and its ambiguous positions are periodic distributed in the sine domain, the two proposed methods are applied to each equivalent array separately to obtain the real DOA positions as well as their replica positions. Then, an effective matching algorithm is proposed to pick out the real DOAs from the ambiguous ones. The first algorithm is a partial spectral search-based algorithm, and the second algorithm is a search-free-based method. These two algorithms are referred to as matching partial spectral search-based algorithm (matching PPS) and matching root-multiple signal classification algorithm (matching root-MUSIC), respectively. Our third proposed algorithm is a combined root-MUSIC which is applied to the multiple equivalent arrays by taking them as sub-arrays of a common filled ULA. The combined root-MUSIC algorithm utilizes the MUSIC null-spectrum functions of all equivalent arrays to form a new polynomial, and the DOA estimations can be obtained efficiently without any spatial ambiguity by applying polynomial rooting to the new polynomial. Simulations are provided to verify the validity of the proposed algorithms.

Joint Smoothed l₀-Norm DOA Estimation Algorithm for Multiple Measurement Vectors in MIMO Radar.

Direction-of-arrival (DOA) estimation is usually confronted with a multiple measurement vector (MMV) case. In this paper, a novel fast sparse DOA estimation algorithm, named the joint smoothed -norm algorithm, is proposed for multiple measurement vectors in multiple-input multiple-output (MIMO) radar. To eliminate the white or colored Gaussian noises, the new method first obtains a low-complexity high-order cumulants based data matrix. Then, the proposed algorithm designs a joint smoothed function tailored for the MMV case, based on which joint smoothed -norm sparse representation framework is constructed. Finally, for the MMV-based joint smoothed function, the corresponding gradient-based sparse signal reconstruction is designed, thus the DOA estimation can be achieved. The proposed method is a fast sparse representation algorithm, which can solve the MMV problem and perform well for both white and colored Gaussian noises. The proposed joint algorithm is about two orders of magnitude faster than the -norm minimization based methods, such as -SVD (singular value decomposition), RV (real-valued) -SVD and RV -SRACV (sparse representation array covariance vectors), and achieves better DOA estimation performance.

Fast Direction of Arrival Estimation with the Coexistence of both Uncorrelated and Coherent Signals

Fast Direction of Arrival Estimation with the Coexistence of both Uncorrelated and Coherent Signals

Fast 2D DOA Estimation Algorithm by an Array Manifold Matching Method with Parallel Linear Arrays.

In this paper, the problem of two-dimensional (2D) direction-of-arrival (DOA) estimation with parallel linear arrays is addressed. Two array manifold matching (AMM) approaches, in this work, are developed for the incoherent and coherent signals, respectively. The proposed AMM methods estimate the azimuth angle only with the assumption that the elevation angles are known or estimated. The proposed methods are time efficient since they do not require eigenvalue decomposition (EVD) or peak searching. In addition, the complexity analysis shows the proposed AMM approaches have lower computational complexity than many current state-of-the-art algorithms. The estimated azimuth angles produced by the AMM approaches are automatically paired with the elevation angles. More importantly, for estimating the azimuth angles of coherent signals, the aperture loss issue is avoided since a decorrelation procedure is not required for the proposed AMM method. Numerical studies demonstrate the effectiveness of the proposed approaches.

Fast DOA estimation based on a split subspace decomposition on the array covariance matrix

A novel real-valued root multiple signal classification (RV-root-MUSIC) algorithm for estimating the direction-of-arrival (DOA) of multiple narrow-band signals is presented. Compared with the conventional root-MUSIC with a complex subspace decomposition on the entire array covariance matrix (ACM), RV-root-MUSIC exploited a split subspace decomposition on either the real-part of ACM (R-ACM) or the imaginary-part of ACM (I-ACM) with real-valued computations. Unlike the unitary root-MUSIC (U-root-MUSIC) with exploitations on the centro-Hermitian property of ACM, the proposed method developed a new result showing that R-ACM shares the same null subspace with I-ACM, which collides with the intersection of the original noise subspace and its conjugate one. Thanks to the real coefficients, the roots of RV-root-MUSIC appear in conjugate pairs, which allows fast rooting with only real-valued computations. Therefore, both subspace decomposition and polynomial rooting can be implemented with real-valued computations, which hence results in a significant reduction in computational cost as compared to root-MUSIC and U-root-MUSIC. Simulations are conducted to verify the effectiveness of the new technique.

Fast and efficient DOA estimation method for signals with known waveforms using nonuniform linear arrays

In this paper, a new approach is proposed to estimate the direction of arrival (DOA) of multiple non-coherent source signals with known waveforms but unknown gains based on a nonuniform linear sensor array. Unlike some previous methods, which estimate the DOA using spatial signatures of the signals with known waveforms, the proposed method first uses the known waveforms and mutually independent sensor measurement noises to establish a maximum likelihood estimation problem corresponding to multiple linear regression models, each containing the DOA and the gain information of all the source signals. Then, regression analysis is performed to estimate the coefficients of each linear regression model, and the well-known generalized least squares is used to obtain the estimates of the angles and gains from the estimated regression coefficients. The proposed method does not require a search over a large region of the parameter space, which is normally needed in ML-based DOA estimation methods. The effect of correlated sources on the performance of the parameter estimation is also studied. It is shown that the DOA and gain estimates are asymptotically optimal as the sources tend to be uncorrelated. Finally, simulation results that demonstrate the estimation performance of the proposed method are given.

Fast DOA estimation for coherent wideband sources based on symmetrical spectrum

A new fast algorithm was proposed to solve the heavy computational load of coherent wideband signal DOA(Direction Of Arrival) estimation. Firstly,through Toeplitz technique of matrix,incoherent wideband signals were obtained without any division for the array. Secondly,according to the character of Hermitian matrix of received data,utilized the unitary transformation matrix,the real matrix could be acquired and the computation of eigendecomposition could be decreased. Finally,through the orthogonality technique of projected subspaces,new space spectrum was acquired with noise subspace and conjugate noise subspace,and the DOA could be obtained just through the angle search from zero to ninety degree in semi-spectrum according to the symmetrical spectrum,while the computational complexity for the search of spectrum peak was reduced by half. The theoretical analysis and simulation results show that the new algorithm has higher precision and smaller computational load,and it is effective for wideband coherent signals.

Precise and Fast GNSS Signal Direction of Arrival Estimation

This paper proposes a precise and fast direction of arrival estimation method using Global Navigation Satellite System (GNSS) carrier phase measurements. Single-epoch, single-satellite integer cycle ambiguities are reliably resolved by making use of constraints and taking advantages of antenna arrays. The algorithm shows good robustness in cases where signal interruption or corruption occurs on some antenna elements as long as four antenna elements in a non-planar array have uncorrupted observables. The algorithm is demonstrated by field tests where antenna elements are connected to multiple receivers with an external common clock. The results indicate a high success rate of single-epoch ambiguity resolution and high direction of arrival accuracy.

Source localization based on symmetrical MUSIC and its statistical performance analysis

In this paper, a new method for fast direction-of-arrival (DOA) estimation with no dependance on array configurations is proposed, which is referred to as the symmetrical multiple signal classification (SMUSIC). Unlike the standard MUSIC, the S-MUSIC spatial spectrum is constructed by the intersection of the noise subspace and the conjugate noise subspace, and it hence generates spectral peaks at the true DOAs and the symmetrical virtual DOAs simultaneously. Such a characteristic allows fast DOA estimation by spectral search over only half of the total angular filed-of-view. Therefore, the new approach has a much lower computational complexity than the standard MUSIC. The statistical performance of S-MUSIC is studied and a close-form expression for the MSEs (mean square errors) of DOA estimation by the proposed estimator is derived. Numerical simulations are conducted to demonstrate the effectiveness of the new algorithm and to verify the theoretical analysis, and it is indicated that S-MUSIC makes a trade-off between MSEs and lower computational complexity as well as an improved resolution for closely-spaced sources as compared to the standard MUSIC.

Novel Direction Findings for Cyclostationary Signals in Impulsive Noise Environments

We consider the problem of direction-of-arrival (DOA) estimation for cyclostationary signals in impulsive noise modeled as a complex symmetric α-stable (SαS) process. Since the DOA estimation based on second-order cyclic statistics degrades seriously in an α-stable distribution noise environment, we define a novel pth-order cyclic correlation by fusing the fractional lower order statistics and second-order cyclic correlation. After briefly introducing the statistical characteristics of pth-order cyclic correlation and building the extended data model, we first propose a novel extended pth-order cyclic MUSIC algorithm (EX-POC-MUSIC) by exploiting both pth-order cyclic correlation and pth-order cyclic conjugate correlation. The algorithm allows us to select desired signals and to ignore interference in the communication system. Second, in order to increase the resolution capabilities and the noise robustness significantly, an improved EX-POC-MUSIC algorithm called the extended pth-order cyclic Root-MUSIC (EX-POC-RMUSIC) algorithm is also presented. This algorithm has all the merits of the EX-POC-MUSIC algorithm, and it is also a fast DOA estimation algorithm because it avoids spatial spectrum searching. Under some conditions, both proposed algorithms are able to handle more sources than the number of sensors. Simulation results strongly verify the effectiveness of the two algorithms.

Fast maximum likelihood DOA estimation in the two-target case with applications to automotive radar

Direction-of-arrival (DOA) estimation of two targets using a single snapshot plays an important role in automotive radar for advanced driver assistance systems. Conventional Fourier methods have a limited resolution and generally yield biased estimates. Subspace methods involve a numerically complex eigendecomposition and require multiple snapshots or a suboptimal pre-processing for reliable estimation. We therefore consider the maximum likelihood (ML) DOA estimator, which is applicable with a single snapshot and shows good statistical properties. To reduce the computational burden, we propose a grid search procedure with a simplified calculation of the objective function. The required projection operators are pre-calculated off-line and stored. To save storage space and computations, we further propose a rotational shift of the field-of-view such that the relevant angular sector, which has to be evaluated, is delimited and centered with respect to broadside. The final estimates are obtained using a quadratic interpolation. The developed method is demonstrated with an example. Simulations are designed to assess the performance of the considered ML estimator with grid search and interpolation, and to compare it among selected representative methods. We further present results obtained with experimental data from a typical application in automotive radar.