Direction Of Arrival Estimation Algorithm Research Articles

Weighted Block Sparse Recovery Algorithm for High Resolution DOA Estimation with Unknown Mutual Coupling

Based on weighted block sparse recovery, a high resolution direction-of-arrival (DOA) estimation algorithm is proposed for data with unknown mutual coupling. In our proposed method, a new block representation model based on the array covariance vectors is firstly formulated to avoid the influence of unknown mutual coupling by utilizing the inherent structure of the steering vector. Then a weighted l 1 -norm penalty algorithm is proposed to recover the block sparse matrix, in which the weighted matrix is constructed based on the principle of a novel Capon space spectrum function for increasing the sparsity of solution. Finally, the DOAs can be obtained from the position of the non-zero blocks of the recovered sparse matrix. Due to the use of the whole received data of array and the enhanced sparsity of solution, the proposed method effectively avoids the loss of the array aperture to achieve a better estimation performance in the environment of unknown mutual coupling in terms of both spatial resolution and accuracy. Simulation experiments show the proposed method achieves better performance than other existing algorithms to minimize the effects of unknown mutual coupling.

Efficient DOA Estimation Algorithm for Noncircular Sources Under Unknown Mutual Coupling

Mutual coupling effects may seriously degrade the direction-of-arrival (DOA) estimation performance in practical sensor arrays. In this article, a computationally efficient DOA estimation algorithm is proposed for noncircular sources in the presence of mutual coupling. Utilizing the noncircularity of the sources, we first construct an extended covariance matrix. Then, based on the banded symmetric Toeplitz structure of the mutual coupling matrix, the extended covariance matrix is divided into two submatrices. By simultaneous singular-value decomposition (SVD) of the two submatrices, the DOA parameter is obtained in a closed form. The proposed algorithm can improve the DOA estimation performance. Moreover, it is computationally efficient since it does not require any spectral search and avoids high-order statistics. Simulation results demonstrate both the efficiency and the effectiveness of our proposed algorithm under unknown mutual coupling.

Off-Grid Direction-of-Arrival Estimation Based on Steering Vector Approximation

In this paper, a novel off-grid direction-of-arrival (DOA) estimation algorithm is proposed based on steering vector approximation. The conventional multiple signal classification (MUSIC) technique estimates the DOA with a uniformly discretized grid by assuming that the true DOAs lie on the grids. In practice, this assumption is rarely satisfied. In order to improve the estimation accuracy, a dense sampling grid is required for the MUSIC technique. Besides the higher computational complexity, it is still not guaranteed that the dense sampling grids will cover the true DOAs. In order to address the off-grid problem with a lower computational complexity, we use the Taylor series expansion to approximate the steering vectors. We first construct a two-dimensional spectrum searching method to simultaneously estimate the nearest on-grid DOA and the corresponding off-grid error. To further improve the estimation accuracy, we then solve an optimization problem to obtain the accurate DOA estimation, which is formulated by the fact that the signal and noise subspaces are orthogonal to each other. Simulation results demonstrate the effectiveness of the proposed off-grid DOA estimation algorithm.

An optimum 2-D DOA estimation algorithm with uniform circular array and its performance analysis

ABSTRACTThis paper presents an optimum algorithm for two-dimensional (2-D) direction of arrival (DOA) estimation of a single source with uniform circular arrays (UCAs). The algorithm is computationally efficient due to its algebraic formulations for 2-D DOA estimation. It exploits Fourier transforms to expand the phase distribution and reformulate the underlying DOA estimation problem as an equivalent expansion coefficient extraction problem. Avoiding Fourier spectrum aliasing ensures that the minimum number of elements for 2-D DOA estimation is 3. Accuracy analysis demonstrates that it approaches the Cramer–Rao bound. In addition, mathematical insights into the relation between the estimation accuracy and the element number of a UCA are observed by employing Parseval’s theorem in the Fourier domain. Performance comparisons are made between a UCA and a linear array (LA) interferometer of the same aperture, showing that the ratio of accuracy of the UCA to that of the LA is , with N being the number of elements.

DOA estimation method of weak sources for an array antenna under strong interference conditions

ABSTRACTThe concept of a preserving source orthogonality and characteristic beam is defined according to an array data model. It is proven theoretically that the corresponding eigenvectors maintain the preserving orthogonality when the powers and the angle intervals between the signals are large. The theory is then applied to the direction of arrival (DOA) estimation for the array antenna in the presence of strong interference. A novel DOA estimation algorithm based on the elimination of the eigenvectors of interference is proposed. The simulation results and comparison of the jamming jam method (JJM) algorithm show that the proposed algorithm does not require the position of the interference source to be known. Moreover, its interference suppression ability and statistical estimation performance are superior to those of the JJM, and thus, it is more suitable for low SNR and small angle intervals.

DOA Estimation for a Mixture of Uncorrelated and Coherent Sources Based on Hierarchical Sparse Bayesian Inference with a Gauss-Exp-Chi2 Prior

Direction of arrival (DOA) estimation algorithms based on sparse Bayesian inference (SBI) can effectively estimate coherent sources without recurring to extra decorrelation techniques, and their estimation performance is highly dependent on the selection of sparse prior. Specifically, the specified sparse prior is expected to concentrate its mass on the zero and distribute with heavy tails; otherwise, these algorithms may suffer from performance degradation. In this paper, we introduce a new sparse-encouraging prior, referred to as “Gauss-Exp-Chi2” prior, and develop an efficient DOA estimation algorithm for a mixture of uncorrelated and coherent sources under a hierarchical SBI framework. The Gauss-Exp-Chi2 prior distribution exhibits a sharp peak at the origin and heavy tails, and this property makes it an appropriate prior to encourage sparse solutions. A three-layer hierarchical sparse Bayesian model is established. Then, by exploiting variational Bayesian approximation, the model parameters are estimated by alternately updating until Kullback-Leibler (KL) divergence between the true posterior and the variational approximation becomes zero. By constructing the source power spectra with the estimated model parameters, the number and locations of the highest peaks are extracted to obtain source number and DOA estimates. In addition, some implementation details for algorithm optimization are discussed and the Cramér-Rao bound (CRB) of DOA estimation is derived. Simulation results demonstrate the effectiveness and favorable performance of the proposed algorithm as compared with the state-of-the-art sparse Bayesian algorithms.

Joint DOD and DOA estimation for bistatic multiple‐input multiple‐output radar target discrimination based on improved unitary ESPRIT method

Target position estimation of radar system has attracted much attention. Researchers have proposed a variety of joint direction-of-departure (DOD) and direction-of-arrival (DOA) estimation algorithms over the last few decades for this well-known problem. However, traditional estimation algorithms require a pairing process between the DOD and DOA estimation. In this study, the authors propose an improved unitary estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm for joint DOD and DOA estimation without a pairing operation. The waveforms are transmitted by an array with M sensors and received by two detached sub-arrays with and sensors, respectively. Specifically, the proposed algorithm eliminates a pairing process via sharing the eigenvectors of DOD and DOA. Theoretical derivation demonstrates that the proposed algorithm requires less computational complexity than two-dimensional multiple signal classification (MUSIC), reduced-dimension MUSIC, and ESPRIT. Simulation results show that the proposed algorithm can effectively enhance the accuracy of identifying and locating targets for the bistatic multiple-input multiple-output radar system.

Integrated polarisation and diversity smoothing algorithm for DOD and DOA estimation of coherent targets

This study proposes a novel integrated polarisation and diversity smoothing (IPDS) algorithm to solve the direction estimation problem of coherent targets in bistatic multiple-input multiple-output (MIMO) radar with electromagnetic vector sensors (EVSs). The IPDS algorithm partitions the transmit and receive arrays into multiple subarrays based on the sensor elements and the spatial phase shift factors. Then the covariance matrices of the received signals from coherent targets associated with these subarrays are smoothened to restore the rank inadequacy of the reflection coefficient covariance matrix. After applying the IPDS algorithm, the direction of departure (DOD) and the direction of arrival (DOA) are estimated using the estimation of signal parameters via rotational invariance technique and the multiple signal classification methods. The effectiveness of the proposed algorithm in terms of decorrelation factor, estimation accuracy, precision and the spatial spectrum is evaluated through computer simulations. Cramér–Rao lower bound is derived for the bistatic MIMO radar with EVSs to substantiate the proposed algorithm. The simulation results are compared with the diversity smoothing and the polarisation smoothing algorithms available in literature. The results obtained by using the proposed algorithm were found to be impressive.

Novel Diagonal Reloading Based Direction of Arrival Estimation in Unknown Non-Uniform Noise

Nested array can expand the degrees of freedom (DOF) from difference coarray perspective, but suffering from the performance degradation of direction of arrival (DOA) estimation in unknown non-uniform noise. In this paper, a novel diagonal reloading (DR) based DOA estimation algorithm is proposed using a recently developed nested MIMO array. The elements in the main diagonal of the sample covariance matrix are eliminated; next the smallest MN-K eigenvalues of the revised matrix are obtained and averaged to estimate the sum value of the signal power. Further the estimated sum value is filled into the main diagonal of the revised matrix for estimating the signal covariance matrix. In this case, the negative effect of noise is eliminated without losing the useful information of the signal matrix. Besides, the degrees of freedom are expanded obviously, resulting in the performance improvement. Several simulations are conducted to demonstrate the effectiveness of the proposed algorithm.

Design and analysis of direction of arrival using hybrid expectation-maximization and MUSIC for wireless communication

As multiple signal classification (MUSIC) algorithm is unable to estimate the direction of arrival (DOA) of highly correlated or coherent signal, based on array processing and decomposition of covariance matrix of incident signals due to its lack of source identification. In the proposed hybrid model, we have considered expectation maximization (EM) algorithm for precise identification of the DOA of highly correlated signals in wireless communication applications. The proposed model is analysed, simulated and verified using two different source signals. The mathematical analysis shows substantial closeness with the simulated results. The robustness of the proposed algorithm is further verified by adding noise to the incident signals. The utilization of the EM algorithm in the proposed hybrid approach reduces the time requirement and mathematical complexity of MUSIC algorithm for DOA estimation. By exploiting the EM algorithm, the original transmitted signal and its arriving angle on the antenna element are estimated from the mixture of interferer’s signal, transmitted signal, multipath component and noise. Hence it is straightforward to recognise the desired signal.

Sparsity-Based Off-Grid DOA Estimation With Uniform Rectangular Arrays

Conventional sparsity-based direction of arrival (DOA) estimation algorithms suffer from performance degradation due to the off-grid problem. To address it, several research studies focused on 1-D off-grid problem have been conducted. However, due to the bias coupling between the azimuth and elevation directions, those works cannot be directly extended to the uniform rectangular array. In this paper, we propose an effective sparsity-based 2-D DOA estimation algorithm. The proposed algorithm provides the following benefits: 1) we introduce a more accurate observation model where the bias coupling problem is eliminated and each grid bias can be compensated individually and 2) besides the sparsity constraint, we engage additional energy constraint over the biases to improve the estimation performance. Due to the presence of multiple unknown parameters, an alternating descent method is adopted to solve the associated joint optimization problem. Finally, simulational results demonstrate that the proposed algorithm, compared with competitors, exhibits superior performance including high precision DOA estimation and low computational complexity.

Unitary Direction of Arrival Estimation Based on A Second Forward/Backward Averaging Technique

A second forward/backward (SFB) averaging technique is presented to transform the real symmetrical covariance matrix of the popular unitary root-MUSIC (U-root-MUSIC) into a real bisymmetrical one, based on which a SFB-U-root-MUSIC direction of arrival estimation algorithm with reduced computational complexity is developed. The proposed SFB-U-root-MUSIC algorithm reduces the computational complexity in the eigenvalue decomposition (EVD) stage by a factor about four because it performs real-valued EVDs on two sub-matrices of about half sizes. The proposed SFB averaging technique is further extended as a generalized dimension reduction method to other unitary DOA estimators for low-complexity EVD computation, and numerical simulations are conducted to demonstrate, such a dimension reduction technique sacrifices statistically nonsignificant root mean square performance that is acceptable.

A Direction of Arrival Estimation Algorithm Based on Orthogonal Matching Pursuit

The results show that the modified DSM is able to predict local buckling capacity of hot-rolled RHS and SHS accurately. In order to solve the problem of the weak ability of anti-radiation missile against active decoy in modern electronic warfare, a direction of arrival estimation algorithm based on orthogonal matching pursuit is proposed in this paper. The algorithm adopts the compression sensing technology. This paper uses array antennas to receive signals, gets the sparse representation of signals, and then designs the corresponding perception matrix. The signal is reconstructed by orthogonal matching pursuit algorithm to estimate the optimal solution. At the same time, the error of the whole measurement system is analyzed and simulated, and the validity of this algorithm is verified. The algorithm greatly reduces the measurement time, the quantity of equipment and the total amount of the calculation, and accurately estimates the angle and strength of the incoming signal. This technology can effectively improve the angle resolution of the missile, which is of reference significance to the research of anti-active decoy.

Spatial Differencing Reconstruction Based Low-Angle DOA Estimation with MIMO Radar

Due to the multipath effect, the direction of arrival (DOA) estimation performance for low-angle targets decreases greatly. To overcome this problem, this paper proposes a spatial differencing reconstruction based DOA estimation algorithm by using the received signal model of multiple input multiple output (MIMO) radar. Combining with the spatial diversity of MIMO radar, the proposed method can first use the multipath echo power to select the best signal. Then, a spatial differencing based iterative scheme is developed to reduce the effect of additive noise, resulting in a better estimation performance for low-angle targets. Simulation results show that the proposed method has better advantages in suppressing noise and improving estimation accuracy.

Narrowband and Wideband Off-Grid Direction-of-Arrival Estimation via Sparse Bayesian Learning

The sparse Bayesian learning based relevance vector machine (SBLRVM) algorithm is a promising algorithm to estimate the directions-of-arrival (DOAs) of multiple narrowband signals. The parameters involved in the DOA estimation model are automatically estimated by the algorithm that makes it more attractive than the deterministic sparsity based DOA estimation algorithms in which fine-tuning of parameters is necessary. However, one limitation of the algorithm is that it assumes the DOAs of the signals to be exactly aligned with the angular grids, which may not be true in practice. In this paper, we first propose an off-grid version of the narrowband SBLRVM algorithm. Next, we propose an off-grid wideband SBLRVM algorithm. The algorithms assume that the true scenario DOAs of the signals are not exactly aligned with the angular grids and the parameters of the algorithms are automatically estimated by the expectation maximization approach. In the wideband DOA estimation algorithm, we estimate one spatial power spectrum by simultaneously exploiting sparsity from all frequency bins. We demonstrate the application of the proposed algorithms by analyzing data from the shallow water HF $\mathbf {97}$ ocean acoustic experiment. The estimated DOAs of a narrowband tonal from the experiment by using our proposed narrowband DOA estimation algorithm are consistent with the nonadaptive conventional beamformer. Processing a wideband chirp from the experiment shows that estimating one spatial power spectrum by simultaneously exploiting sparsity from all frequency bins using the proposed wideband DOA estimation algorithm is a more valuable processor than an incoherent combination of the power spectra from the individual frequency bins estimated using the proposed narrowband DOA estimation algorithm. Moreover, since our proposed algorithms are off-grid algorithms, an empirical analysis for the choice of the discretization interval of the angular spread is not required as opposed to the on-grid DOA estimation algorithms. This results in a reduced computational complexity.

An improved algorithm for multiple source direction of arrival estimation

Based on MUSIC-LIKE algorithm, an improved algorithm for multiple source direction of arrival estimation was proposed to resolve the problem, the enabled estimation number of source for traditional direction of arrival estimation algorithm restricted by the size of the antenna array. The computations and the matrix dimension were reduced by constructed new fourth cumulate matrix, the number of direction estimation was increased by smoothing computation snapshots based on MFOCMUSIC algorithm. The spatial spectrum measuring error was decreased by smoothing the virtual array extended by fourth order cumulate. Simulation results proved that the proposed algorithm can find more direction of arrival than MFOC-MUSIC algorithm, improve the direction of arrival resolution ratio, and inhibit the influence of gaussian white noise to direction of arrival estimation

FPGA Hardware Implementation of DOA Estimation Algorithm Employing LU Decomposition

In this paper, authors present their work on field-programmable gate array (FPGA) hardware implementation of proposed direction of arrival estimation algorithms employing LU factorization. Both L and U matrices were considered in computing the angle estimates. Hardware implementation was done on a Virtex-5 FPGA and its experimental verification was performed using National Instruments PXI platform which provides hardware modules for data acquisition, RF down-conversion, digitization, etc. A uniform linear array consisting of four antenna elements was deployed at the receiver. LabVIEW FPGA modules with high throughput math functions were used for implementing the proposed algorithms. MATLAB simulations of the proposed algorithms were also performed to validate the efficacy of the proposed algorithms prior to hardware implementation of the same. Both MATLAB simulation and experimental verification establish the superiority of the proposed methods over existing methods reported in the literature, such as QR decomposition-based implementations. FPGA compilation results report low resource usage and faster computation time compared with the QR-based hardware implementation. Performance comparison in terms of estimation accuracy, percentage resource utilization, and processing time is also presented for different data and matrix sizes.

Direction Finding Using Compressive One-Bit Measurements

In this paper, we propose a novel direction-of-arrival (DOA) estimation scheme, which is named the compressive one-bit measurement scheme. In the proposed scheme, the one-bit quantization technique is used to reduce the system cost in terms of the analog-to-digital converter (ADC). However, the one-bit quantization leads to a serious information loss, thus compromising the estimation accuracy. Inspired by the compressive sensing theory, the compressive measurement method is used to expand the receive array aperture. To be specific, the compressive measurement allows more sensors than the number of front-end circuit chains to be used. Thus, the additional information is obtained, and the estimation performance can be improved from the system structure layer. It is noted that by introducing the compression operation, the relationship between the normalized and the original covariance matrix is different to the conventional one-bit quantization structure. Thus, two DOA estimation algorithms, i.e., the iterative compressive measurement-based multiple signal classification (CM-MUSIC) and the compressive sensing (CS)-based algorithm, are proposed for the compressive one-bit measurement scheme. The iterative CM-MUSIC can achieve a high-resolution estimation, whereas the CS-based algorithm can resolve more sources than the sensors. Numerical simulations validate the effectiveness of the proposed scheme.

Decoupled two-dimensional direction of arrival estimation of single distributed source by vectoring differential phases

In practical applications such as radar, sonar, and mobile communications, transmitted signals are often affected by the scattering and reflection phenomena, which causes the signal energy received by the antenna array to be distributed into a certain space. In this case, a distributed source model will be more applicable. In general, the distributed sources have been classified as coherently distributed (CD) source and incoherently distributed (ID) source, which prove to be suitable for the cases of slowly time-varying and rapidly time-varying channels, respectively.In this paper, we consider the two-dimensional direction of arrival (DOA) estimation of distributed sources (including CD source or ID source). Specifically, uniform circular array (UCA) is widely used because of its ability to measure full azimuth angle and high resolution. However, the existing estimation algorithms all require spectral peak searching and the eigenvalue decomposition, which can bring a large computational complexity. To solve this problem, a decoupled rapid two-dimensional DOA estimation algorithm is proposed based on vectoring differential phases considering the two cases of single CD source and ID source. Firstly, based on spatial frequency approximation model, it is proved that none of differential phases between the received signals of different sensors in the UCA is affected by angle spread parameters when there is only a single distributed source. Under the premise of such a property, the central DOAs can be decoupled through obtaining the differential phases. Next, we can obtain the phase angles of strictly upper triangular elements in the sample covariance matrix, which correspond to differential phases between different sensors. Finally, by vectoring these differential phases, the central azimuth and elevation DOAs are estimated in the closed form from a least-squared problem, where the spectral peak searching and eigenvalue decomposition can be avoided, hence the computational complexity is reduced greatly. Theoretical analysis and simulation results show that the proposed algorithm has higher estimation accuracy and does not require prior information about the distribution of angular signals. With both low computational complexity and low hardware complexity, the proposed algorithm is beneficial to the engineering practice of array direction finding in complex environment.

Efficient Real-Valued Rank Reduction Algorithm for DOA Estimation of Noncircular Sources Under Mutual Coupling

Noncircular sources are widely used in wireless communication array systems, which can offer more accurate estimates and detect more sources. However, in practical array systems, the direction-of-arrival (DOA) estimation performance may be severely degraded by mutual coupling effects. To solve this problem, we propose a real-valued DOA estimation algorithm for noncircular sources under unknown mutual coupling. Based on the sources’ noncircularity, an augmented real-valued covariance matrix is constructed. Then, utilizing the banded symmetric and Toeplitz property of the mutual coupling matrix, the middle subarray elements are considered as ideal ones, which have the same array gains. Finally, according to the subspace principle, a rank reduction-based virtual steering vector parameterizing method is derived, which extracts the DOAs from other nuisance parameters. Compared with conventional algorithms, the proposed one not only improves the estimation accuracy but also resolves more sources. Moreover, it is computationally efficient, since it only requires real-valued computations and 1-D spectral search. Numerical simulations demonstrate that the proposed method performs well under unknown mutual coupling and outperforms some of the existing approaches in resolution capability, estimation accuracy, and computational loads.