Joint Direction Of Arrival Estimation Research Articles

Advanced Interference Mitigation Method Based on Joint Direction of Arrival Estimation and Adaptive Beamforming for L-Band Digital Aeronautical Communication System

The L-band digital aeronautical communication system (LDACS) is one of the candidate technologies for future broadband digital aeronautical communications, utilizing the unused L-band spectrum between distance measuring equipment (DME) channels. However, the higher signal power of DME complicates LDACS implementation. This paper proposes an advanced DME mitigation approach for the LDACS, integrating joint direction of arrival (DOA) estimation with adaptive beamforming techniques. The proposed method begins by exploiting the cyclostationary characteristics of signals, accurately obtaining the preliminary direction of the LDACS signal using the Cyclic-MUSIC method. Subsequent precise steering vectors (SVs) are selected through Capon spectrum search, followed by the reconstruction of the interference plus noise covariance matrix (INCM). Using the obtained SV and INCM, the weight vector is calculated and beamforming is performed. Simulation results validate that the proposed method not only accurately estimates the direction of LDACS signal but also efficiently mitigates DME interference, demonstrating a superior performance and reduced algorithmic complexity, even in scenarios with lower signal-to-noise ratios (SNRs) and the presence of DOA estimation errors. Additionally, the proposed method achieves a low bit error rate (BER), further validating its ability to ensure communication quality and enhance the reliability of LDACS.

Алгоритм оценки углов прихода сигналов в системе распределенных некогерентных автомобильных радаров

The present paper is focused on processing of signals from multiple sensors in non-coherent mode that provide improvement of angular resolution of close targets compared to single radar. The low-complexity technique of Direction-of-Arrival (DoA) estimation in Automotive Distributed Non-Coherent Multi-Radar Systems in the case of short length of snapshots is proposed. This technique consists of three main stages: beam-scanning procedure, transformation of the received signals of two radars to the unified coordinate system, and joint DoA estimation algorithm. The DoA method is represented by two approaches: (i) the Capon method modified for joint signal processing; (ii) low-complexity algorithm based on theory of auto-compensator. Performance of the system is investigated on the base of Monte-Carlo simulation. Current algorithm shows improvement of system performance of distributed non-coherent multi-radar systems compared to single radar.

DOA estimation using two independent convolutional neural networks with residual blocks

Acoustic source localization in the spherical harmonic domain with reverberation has hitherto not been investigated extensively. When the joint direction-of-arrival (DOA) estimation is treated as a classification task, it needs a lot of different classes and large-scale dataset, which is time-consuming and less cost-effective. Thus, a novel learning-based method is proposed in this paper, which separately estimates azimuths and elevations by two independent convolution neural networks (CNNs) with residual blocks. First, a mapping matrix is adopted to transform the spherical harmonic function into the Kronecker product of two Vandermonde vectors. Based on the special structure, features dependent on azimuth and elevation, respectively, are extracted as inputs to neural networks. This can divide the joint DOA estimation into two sub-tasks completed by two independent CNNs with residual blocks, which can be realized in parallel. Furthermore, the performance of the model learned by CNNs with residual blocks is better than ordinary CNNs. Simulations are conducted both on the simulated and real speech data for evaluating the performance of the proposed method. The results show that the method has higher accuracy. Moreover, the method is time-saving and effectively reduces the computational complexity.

Joint estimation of DOA and mutual coupling via imposing an annihilation constraint

The mutual coupling between elements degrades the direction-of-arrival (DOA) estimation performance. This paper considers jointly estimating the DOA and mutual coupling. Firstly, based on the fact that the noiseless array output without mutual coupling consists of complex exponential sums, an annihilation relation is obtained. Then, an optimization problem is proposed by combining a cost function derived from the maximum likelihood principle and a constraint formed by the annihilation relation. The optimization problem is solved by the sequential quadratic programming (SQP) method, where the Jacobian matrix is derived via exploiting the symmetric Toeplitz structure of the mutual coupling matrix. At last, a post-processing method is proposed for further improving the accuracy of mutual coupling estimation. The new method can handle single snapshot estimation, and it is gridless while utilizing the whole aperture. It is also insensitive to overestimation of the degree of mutual coupling. The method has been verified by simulations and compared with representative methods regarding accuracy and efficiency.

Estimation Method for Mixed Near-Field and Far-Field Sources Based on Four-Order Cumulant and Polarization Sensitive Array

A new multidimensional parameters joint estimation method of mixed near-field and far-field sources based on polarization sensitive array, fourth-order cumulant, joint diagonalization technology, and propagator method is presented, which can realize the joint estimation of DOA (Direction of Arrival), range, frequency, polarization auxiliary angle, and polarization phase difference without multidimensional spectral peak searching and parameter pairing, and it is suitable for any additive Gaussian noise environment and effective for reducing the loss of array aperture. The algorithm skillfully constructs the fourth-order cumulant matrix by using the output on the label of specific dipole pairs of the received array, which effectively avoids the matrix rank reduction caused by the far-field sources coexistence situation. In addition, the presented algorithm utilizes the orthogonal propagation algorithm for subspace decomposition and uses the total least square solution to replace the orthogonal solution of singular value decomposition, which effectively reduces the computational complexity. The experiment proved the effectiveness of the proposed algorithm.

Efficient Joint Estimation of DOA, Range and Reflectivity in Near-Field by Using Mixed-Order Statistics and a Symmetric MIMO Array

Most works in the literature on parameter estimation with multiple-input multiple-output (MIMO) systems are limited to estimating only the direction of arrival (DOA), and/or based on the far-field assumption. However, the joint estimation of DOA and range is an important challenge for near-field (NF) applications. In addition, backscatter coefficient estimation, as one of the most important parameters of radar systems, has been neglected in existing works. In this paper, the joint estimation of the DOA, range and reflectivity is presented for a MIMO array in the NF. By employing the symmetry property in the array, first, two special spatial expressions based on fourth-order and second-order statistics from the received data are defined so that the output of the first expression lacks targets’ range information. By collecting the information of all the sensors and calculating all the interactions between the transmit and receive sensors based on the first expression, a spatial cumulant matrix is constructed. In two different approaches, with/without the use of eigendecomposition, the virtual steering vectors are extracted. Next, DOAs are estimated by a one-dimensional (1D) spectral search. The second expression, which contains both angle and range information, is used to construct several covariance submatrices and then to construct a covariance matrix with a size corresponding to the array’s dimensions. Then, corresponding ranges are estimated by employing estimated DOAs, eigendecomposition and 1D spectral searches. Finally, the equations required to estimate the reflectivity are derived. The simulation results show the remarkable performance of the proposed method in terms of computational time and estimation accuracy.

Robust Reweighted ℓ2,1-Norm Based Approach for DOA Estimation in MIMO Radar Under Array Sensor Failures

To alleviate the direction of arrival (DOA) estimation performance degradation under array sensor failures in multiple input multiple output (MIMO) radar, joint DOA estimation and missing data recovery is dealt with by a reweighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{2,1}$ </tex-math></inline-formula> -norm framework. Firstly, we employ a technique based on singular value decomposition (SVD) to reduce the dimension of the array data matrix and the sensitivity to observation noise. Then, a novel reweighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{2,1}$ </tex-math></inline-formula> -norm minimization framework is introduced to improve the robustness against model mismatch caused by sensor failures, which incorporates the recovery of the complete array data matrix into the sparse reconstruction and constructs the weight matrix for reweighting the mixed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{2,1}$ </tex-math></inline-formula> -norm minimization. Thereafter, the alternative direction method of multipliers (ADMM) under the augmented Lagrange multiplier (ALM) framework is applied to solve this multivariable optimization problem with multiple constraints, in which the sparse solution is iteratively obtained along with the recovery of the complete array data matrix. Finally, the estimation of DOAs can be achieved by finding the non-zero rows in the reconstructed sparse matrix. Simulations demonstrate that the proposed method has better estimation performance than the existing methods for handling array sensor failures and exhibits robustness in the face of a wide range of faulty sensor number.

A Deep Learning Framework for Robust DOA Estimation Using Spherical Harmonic Decomposition

Spherical harmonic decomposition facilitates decomposing the sound pressure at different microphones into independent functions of frequency, azimuth and elevation of the source and microphone locations. This decomposition facilitates the extraction of two sets of features containing different information about elevation and azimuth of the source for the direction of arrival (DOA) estimation. These features can be given as input to a learning approach for the estimation of azimuth and elevation separately. This approach aims at breaking down the problem of DOA estimation into azimuth and elevation estimation separately. An advantage of this is the reduction in computational complexity when compared with the joint DOA estimation. This facilitates a straightforward extension of this approach to denser DOA search grids. The contribution of this paper is threefold. First, we propose spherical harmonic magnitude and phase features and discuss the information present in these features regarding the azimuth and elevation of the source. Second, we propose the convolutional neural network architectures for DOA estimation. Third, we analyse the training, run-time computational complexities and propose to extend the DOA estimation approach to dense DOA search grid rather than restricting to a sparse DOA search grid. The performance of conventional DOA estimation approaches degrades in case of a noisy and reverberant environment. Several advancements to the existing DOA estimation approaches have been recently proposed. However, to the best of the authors’ knowledge, learning approaches to DOA estimation with dense DOA search grids with few frames in the context of spherical arrays have not been proposed. Performance evaluation is carried out using simulated as well as real datasets. The proposed approach is also evaluated on LOCATA dataset in the context of a moving source. The results are motivating enough to consider the application of the proposed method in practical scenarios.

An Intelligent Deep Learning-Based Direction-of-Arrival Estimation Scheme Using Spherical Antenna Array With Unknown Mutual Coupling

Spherical antenna array (SAA) has become highly attractive where hemispherical scan coverage is required as it can provide uniform directivity in all the scan directions. Various direction-of-arrival (DoA) estimation methods suffer from different problems, such as low accuracies in mismatched conditions, high computational complexity and poor estimation in a harsh environment. Another critical concern is mutual coupling (MC) characteristics between the array elements. These problems affect the quality of the navigation signal in harsh environments. This paper presents a robust DoA estimation and mutual coupling compensation technique based on convolutional neural network (CNN) for Spherical Array. Spherical harmonic decomposition (SHD) is used to facilitate feature extraction in two sets, which contains different features about the elevation and azimuth of the source for DoA estimation. The features serve as input to the learning technique for separate estimation of elevation and azimuth, which consequently reduce computational complexity as against the joint estimation of DoA. Learning methods for DoA estimation with few frames and dense search grids within the spherical array configuration are presented. To solve the MC error, the DoA estimation scheme is also used to obtain accurate spectrum peak in the multipath scenario with unknown MC and sharper spectrum peak via the unique structure of the MC matrix and spatial smoothing algorithms. In all, experimental results, which is the ground truth to test any procedure, show the effectiveness, validity, and potential practical application of the proposed technique.

Joint estimation of DOA and channel errors with sparse recovery for SKA low‐frequency array

Here, the authors present an improved and fast sparse recovery method for joint estimation of channel errors and direction of arrival (DOA) for square kilometre antennas low-frequency array. Since this array is formed of a large number of antennas and distributed in a very large space, array calibration is a vital step to provide accurate signal information. Then, channel errors are the concerns here, which are assumed to be localised in a priori known interval. To achieve the joint estimation, an approach is proposed by using the alternative optimisation strategy, which theoretically gives convergence results. In detail, the basis pursuit de-noising (BPDN) algorithm and the proximal algorithm are used to estimate the DOA and the array errors, respectively, and the final results are obtained by alternatively solving these two algorithms. Finally, numerical simulation results are presented to demonstrate the effectiveness of their proposed method.

Joint Estimation of DOA and Frequency of Multiple Sources with Orthogonal Coprime Arrays.

A two-stage method is proposed to jointly estimate the direction-of-arrival (DOA) and carrier frequency (CF) of multiple sources, by using two orthogonal coprime arrays (CPAs). The DOAs of CF-known sources are estimated first by applying a spatial smoothing MUSIC algorithm. The contribution of these source signals is then removed from the originally received signal by applying an orthogonal complement projector. Next, a joint-ESPRIT algorithm is applied to estimate the DOAs and CFs of the remaining CF-unknown sources. With two orthogonal CPA(5, 6), the RMSE of DOA and CF of applying the proposed method to 30 sources, 13 of which have unknown CF, is less than 1% at SNR dB.

Joint Estimation of DOA and TDOA of Multiple Reflections by Matrix Pencil in Mobile Communications

This paper presents the joint estimation of the direction of arrival (DOA) and the time difference of arrival (TDOA) for multipath signals, which is the central issue for mobile communications. The estimator decouples the multi-dimensional problem for realizing the high resolution of DOA and TDOA based on the matrix pencil method without the computation of the correlation matrix. First, the data are transformed into the frequency domain to deconvolution by the known channel model, which maps delays into phase shifts in the frequency domain. Then, a two-dimensional matrix pencil algorithm yields the joint DOA and TDOA estimation based on the double Vandermonde structure data obtained. A closed-form solution without searching is given with the DOA and TDOA of incidence that can be paired automatically without an additional matching algorithm. The simulation results show that the proposed algorithm is not only suitable for the case that the elements’ number is less than the source number but also for the case that multipath rays have equal DOA or TDOA.

Joint DOA estimation and source number detection for arrays with arbitrary geometry

In this paper, we focus on the problem of joint direction-of-arrival (DOA) estimation and source number detection for an array of sensors. We propose a CLEAN-based sequential algorithm that uses a sequential hypothesis testing procedure. This method can be employed for any array with an arbitrary geometry. We also manage to reduce the computational complexity of the proposed method. Additionally, we derive an analytical performance bound for the source number detection algorithm. Our simulation results show that the proposed method achieves an appropriate performance even for low SNR or small number of snapshots. It is shown that the proposed method is applicable to both correlated and uncorrelated sources. Unlike popular methods, the algorithm does not require to know the number of sources for the DOA estimation and is able to estimate the number and the DOA of sources jointly.

Joint estimation of DOA and TOA for MB‐OFDM UWB signals based on frequency‐domain processing

This study proposes a new joint direction of arrival (DOA) and time of arrival (TOA) estimation (JDTE) scheme for multi-band orthogonal frequency-division multiplexing (MB-OFDM) ultra-wideband systems with a two-antenna receiver based on frequency-domain processing. Prior joint TOA and DOA estimation (JTDE) schemes first measure the TOAs from the received waveforms at all antennas and then obtain the DOA from the TOA measurements. The proposed JDTE method estimates parameters directly from the waveforms received at all antennas, where the channel frequency response associated with the two antenna elements can be considered as a 2D (frequency and space) ‘virtual array’. The DOA is estimated by exploiting the spatial dimension of the virtual array first, and then the TOA is estimated by exploiting the frequency dimension of the virtual array. The use of the virtual array enables the number of resolvable paths to exceed the number of antennas. More importantly, the Cramer–Rao bound (CRB) of DOA estimation that is derived from the received waveforms is significantly lower than that obtained from the TOA metric, and the CRB of the estimated TOA is also slightly lower than that obtained using the JTDE scheme. Numerical simulations verify the superiority of the proposed method.

A Sparse-Based Approach for DOA Estimation and Array Calibration in Uniform Linear Array

This paper aims at achieving a joint estimation of direction-of-arrival (DOA) and array perturbations, such as gain and phase uncertainty, mutual coupling, and sensor location error, which deteriorate the performance of the DOA estimation if not carefully handled. To that end, in this paper, the array perturbations represented by a perturbation matrix as multiplicative noise to the array manifold are then reformulated to facilitate the perturbation compensations. One great finding on the perturbation matrix is that it is a sparse matrix, which contains a lot of zero elements and only few nonzero elements. With this reformulation, the perturbation compensation problems turn into sparse matrix completion problems. Then, by utilizing the sparsity of both the DOAs and perturbation matrix, a joint estimation of DOAs and array perturbations is proposed under a unified optimization framework. In addition, numerical studies are presented to demonstrate the effectiveness of the joint estimation.

Joint Estimation of DOA and TDOA of Multiple Reflections in Mobile Communications

In a multipath communication scenario, it is often relevant to estimate the directions and relative delays of each multipath signal. We present an effect algorithm for the simultaneous estimation of these parameters by re-iterative super-resolution, beamforming, and MUSIC-like searching techniques. The algorithm first separates and estimates direction of arrival (DOA) of the multipath signals. Linear constrained minimum power beamforming is used to obtain the transmitted time function of the desired signal in certain incident angle. Then, time difference of arrival (TDOA) for the incident signals are mapped into phase shifts in the frequency domain. Using the DFT of the desired signal and the received data, we can separate the phase shifts in the frequency domain due to time delay by MUSIC-like searching. At the same time, the pairing of the estimated DOA and TDOA is automatically determined. Computer simulations illustrating the performance of the proposed algorithm with the Cramer–Rao bound are included.

Off-grid direction of arrival estimation based on joint spatial sparsity for distributed sparse linear arrays.

In the design phase of sensor arrays during array signal processing, the estimation performance and system cost are largely determined by array aperture size. In this article, we address the problem of joint direction-of-arrival (DOA) estimation with distributed sparse linear arrays (SLAs) and propose an off-grid synchronous approach based on distributed compressed sensing to obtain larger array aperture. We focus on the complex source distribution in the practical applications and classify the sources into common and innovation parts according to whether a signal of source can impinge on all the SLAs or a specific one. For each SLA, we construct a corresponding virtual uniform linear array (ULA) to create the relationship of random linear map between the signals respectively observed by these two arrays. The signal ensembles including the common/innovation sources for different SLAs are abstracted as a joint spatial sparsity model. And we use the minimization of concatenated atomic norm via semidefinite programming to solve the problem of joint DOA estimation. Joint calculation of the signals observed by all the SLAs exploits their redundancy caused by the common sources and decreases the requirement of array size. The numerical results illustrate the advantages of the proposed approach.

Joint angle and Doppler frequency estimation of coherent targets in monostatic MIMO radar

This paper discusses the problem of joint direction of arrival (DOA) and Doppler frequency estimation of coherent targets in a monostatic multiple-input multiple-output radar. In the proposed algorithm, we perform a reduced dimension (RD) transformation on the received signal first and then use forward spatial smoothing (FSS) technique to decorrelate the coherence and obtain joint estimation of DOA and Doppler frequency by exploiting the estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm. The joint estimated parameters of the proposed RD-FSS-ESPRIT are automatically paired. Compared with the conventional FSS-ESPRIT algorithm, our RD-FSS-ESPRIT algorithm has much lower complexity and better estimation performance of both DOA and frequency. The variance of the estimation error and the Cramer–Rao Bound of the DOA and frequency estimation are derived. Simulation results show the effectiveness and improvement of our algorithm.

Joint Estimation of DOA and Polarization with CLD Pair Cylindrical Array Based on Quaternion Model

This paper proposes a quaternion-ESPRIT algorithm for closed-form estimation of direction of arrival (DOA) and polarization, using a cylindrical conformal array configuration. First, the array steering vector and the elevation are estimated using a quaternion eigenvalue decomposition of the data covariance matrix. Second, the azimuth is estimated. Finally, the polarization parameters are estimated using the relationships between the dipoles and the loops. These estimates are automatically matched. Simulation results show that the performance of quaternion method is obviously better than that of the long-vector method.

Joint DOA Estimation and Source Signal Tracking With Kalman Filtering and Regularized QRD RLS Algorithm

In this brief, we present a nontraditional approach for estimating and tracking signal direction-of-arrival (DOA) using an array of sensors. The proposed method consists of two stages: in the first stage, the sources modeled by autoregressive (AR) processes are estimated by the celebrated Kalman filter, and in the second stage, the efficient QR-decomposition-based recursive least square (QRD-RLS) technique is employed to estimate the DOAs and AR coefficients in each observed time interval. The AR-modeled sources can provide useful temporal information to handle cases such as the number of sources being larger than the number of antennas. In addition, the symmetric array enables one to transfer a complex-valued nonlinear problem to a real-valued linear one, which can reduce the computational complexity. Simulation results demonstrate the superior performance of the algorithm for estimating and tracking DOA under different scenarios.