Direction Of Arrival Estimation Algorithm Research Articles

Quantum algorithm for MUSIC-based DOA estimation in hybrid MIMO systems

The multiple signal classification (MUSIC) algorithm is a well-established method to evaluate the direction of arrival (DOA) of signals. However, the construction and eigen-decomposition of the sample covariance matrix (SCM) are computationally costly for MUSIC in hybrid multiple input multiple output (MIMO) systems, which limits the application and advancement of the algorithm. In this paper, we present a novel quantum method for MUSIC in hybrid MIMO systems. Our scheme makes the following three contributions. First, the quantum subroutine for constructing the approximate SCM is designed, along with the quantum circuit for the steering vector and a proposal for quantum singular vector transformation. Second, the variational density matrix eigensolver is proposed to determine the signal and noise subspaces utilizing the destructive swap test. As a proof of principle, we conduct two numerical experiments using a quantum simulator. Finally, the quantum labelling procedure is explored to determine the DOA. The proposed quantum method can potentially achieve exponential speedup on certain parameters and polynomial speedup on others under specific moderate circumstances, compared with their classical counterparts.

Robust 2-D DOA Estimation in a Polarization Sensitive Single User Environment

Apart from the conventional parameters (such as signal-to-noise ratio (SNR), array geometry and size, and the number of samples), several other factors (e.g., alignment of the antenna elements, polarization parameters) influence the performance of direction of arrival (DOA) estimation algorithms. When all the antenna elements are aligned in the same direction, the polarization parameters uniformly affect the steering vectors, which is the underlying assumption of almost all conventional DOA algorithms. Unfortunately, in this case, for a given set of DOA angles, there exists a range of polarization parameters resulting in a very low SNR across all the antenna elements in the array and vice versa. To avoid this type of unwanted event, different antenna elements must be aligned differently. However, this fact will make almost all commonly used DOA estimation algorithms inoperable since the steering vectors are contaminated unevenly by the polarization parameters. To the best of our knowledge, no work in the literature handles this issue using simple hardware and signal processing techniques even for a single user environment. In this paper, that line of inquiry is pursued. We consider a circular array with the minimum number (i.e., 4) of short dipole antenna elements and propose an antenna alignment scheme. This ensures that at any given point no more than one element will suffer significantly from low SNR due to the contribution of polarization. A thresholding technique to isolate the antenna element after being seriously contaminated by the polarization parameters is developed and analyzed. Two algorithms that are suited for operating reliably in all possible DOA and polarization environments are addressed. The first algorithm follows the working principle of the popular MUSIC algorithm after cleaning the polarization contributions from the non-signal subspace. The other one, which is found as a byproduct of the process of cleaning the non-signal subspace, can estimate the DOA angles in a closed form manner. The implementations of the above algorithms for an arbitrary number of antenna elements greater than or equal to 4 are also presented. Finally, a thorough performance and complexity analysis are illustrated for those two algorithms considering various polarization and DOA scenarios.

Maximum likelihood DOA estimation based on improved invasive weed optimization algorithm and application of MEMS vector hydrophone array

<abstract><p>Direction of arrival (DOA) estimation based on Maximum Likelihood is a common method in array signal processing, with many practical applications, but the huge amount of calculation limits the practical application. To deal with such an Maximum Likelihood (ML) DOA estimation problem, firstly, the DOA estimation model with ML for acoustic vector sensor array is developed, where the optimization standard in various cases can be unified by converting the maximum of objective function to the minimum. Secondly, based on the Invasive Weed Optimization (IWO) method which is a novel biological evolutionary algorithm, a new Improved IWO (IIWO) algorithm for DOA estimation of the acoustic vector sensor array is proposed by using ML estimation. This algorithm simulates weed invasion process for DOA estimation by adjusting the non-linear harmonic exponent of IWO algorithm adaptively. The DOA estimation accuracy has been improved, and the computation of multidimensional nonlinear optimization for the ML method has been greatly reduced in the IIWO algorithm. Finally, compared with Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE) method and Tuna Swarm Optimization(TSO) algorithm, numerical simulations show that the proposed algorithm has faster convergence rate, improved accuracy in terms of Root Mean Square Error (RMSE), lower computational complexity and more robust estimation performance for ML DOA estimation. The experiment with tracking the orientation of the motorboat by Microelectronic mechanical systems (MEMS) vector hydrophone array shows the superior performance of proposed IIWO algorithm in engineering application. Therefore, the proposed ML-DOA estimation with IIWO algorithm can take into account both resolution and computation. which can meet the requirements of real-time calculation and estimation accuracy in the actual environment.</p></abstract>

Robust DOA estimation of complex correlated signals in non-Gaussian CES distributed models

The sample covariance matrix (SCM) is commonly used in direction-of-arrival (DOA) estimation methods when the noise or observations are circular complex Gaussian (C CG) distributed. However, with a very heavy-tailed non-Gaussian noise model, the SCM-based DOA estimation methods fail to provide an accurate estimate of DOA. This paper presents a numerical analysis of the resolving capability of subspace-based circular (C) and non-circular (NC) multiple signal classification (MUSIC) DOA estimation methods of arbitrarily narrowband correlated signal sources corrupted by circular complex elliptical symmetric (C CES) distributed noise. It evaluates the robustness of these methods for correlated C and NC sources by employing the robust complex M-estimators instead of SCM. It study also the effects of correlation on robust MUSIC-based DOA estimation algorithms accuracy as a function of the magnitude and phase of the correlation coefficients. Simulations results show that the NC MUSIC algorithm which requires fewer sensor elements yields robust estimates of DOA for correlated sources than the C MUSIC algorithm using the M-estimators.

A high-precision 2D DOA estimation algorithm by a large-space three-parallel array for reducing mutual coupling

In this paper, a high-precision two-dimensional (2D) direction of arrival (DOA) estimation algorithm by three parallel uniform linear arrays (ULAs) is proposed. Both the internal spacing of each sub-array and the spacing between two adjacent sub-arrays can exceed the half-wavelength of incident signal. An extended propagator method (PM) algorithm is introduced to obtain a multiple extended propagator matrix by processing the covariance matrix of received signals. Then, by using the extended propagator matrix, unambiguous and high-precision 2D DOA estimation can be obtained without extra pairing process. For the proposed array construction, mutual coupling effect can be ignored as long as the element interval is large enough. The extended PM algorithm based on the proposed array has far higher precision than the existing similar algorithms, which can be proved by some simulation experiments.

An Efficient DOA Estimation Algorithm Based on Diagonal-Symmetric Loading

In order to solve the problem that the subspace-like direction of arrival (DOA) estimation performs poor due to the error of sources number, this paper proposes a new super-resolution DOA estimation algorithm based on the diagonal-symmetric loading (DSL). Specifically, orthogonality principle of the minimum eigenvector of the specific covariance matrix and the source number estimation based on the improved K-means method were adopted to construct the spatial spectrum. Then, by considering the signal-to-interference-to-noise ratio (SINR), the theoretical basis for selecting parameters was given and verified by numerical experiment. To evaluate the effectiveness of the proposed algorithm, this paper compared it with the methods of minimum variance distortionless response (MVDR) and new signal subspace processing (NSSP). Experimental results prove that the proposed DSL has higher resolution and better estimation accuracy than the MVDR and NSSP.

Coarray-domain iterative direction-of-arrival estimation with coprime arrays

In this paper, we consider source direction-of-arrival (DOA) estimation with coprime arrays via coarray domain processing. We present two Fourier-based iterative methods which address the non-uniformity of the corresponding difference coarray, thereby permitting exploitation of all offered degrees-of-freedom. The proposed approaches are based on the fast iterative interpolated beamforming (FIIB), which is a low-complexity algorithm for DOA estimation using uniform linear arrays. The first method specifically accounts for the non-uniformity of the coarray in the FIIB algorithm. The second approach modifies the FIIB to estimate the contributions of the missing elements, thus emulating a uniform coarray. We show that both methods achieve asymptotically unbiased DOA estimates. Extensive simulation results are provided to demonstrate the effectiveness of the proposed approaches.

A recursive expectation-maximization algorithm for speaker tracking and separation

The problem of blind and online speaker localization and separation using multiple microphones is addressed based on the recursive expectation-maximization (REM) procedure. A two-stage REM-based algorithm is proposed: (1) multi-speaker direction of arrival (DOA) estimation and (2) multi-speaker relative transfer function (RTF) estimation. The DOA estimation task uses only the time frequency (TF) bins dominated by a single speaker while the entire frequency range is not required to accomplish this task. In contrast, the RTF estimation task requires the entire frequency range in order to estimate the RTF for each frequency bin. Accordingly, a different statistical model is used for the two tasks. The first REM model is applied under the assumption that the speech signal is sparse in the TF domain, and utilizes a mixture of Gaussians (MoG) model to identify the TF bins associated with a single dominant speaker. The corresponding DOAs are estimated using these bins. The second REM model is applied under the assumption that the speakers are concurrently active in all TF bins and consequently applies a multichannel Wiener filter (MCWF) to separate the speakers. As a result of the assumption of the concurrent speakers, a more precise TF map of the speakers’ activity is obtained. The RTFs are estimated using the outputs of the MCWF-beamformer (BF), which are constructed using the DOAs obtained in the previous stage. Next, using the linearly constrained minimum variance (LCMV)-BF that utilizes the estimated RTFs, the speech signals are separated. The algorithm is evaluated using real-life scenarios of two speakers. Evaluation of the mean absolute error (MAE) of the estimated DOAs and the separation capabilities, demonstrates significant improvement w.r.t. a baseline DOA estimation and speaker separation algorithm.

Real-valued sparse Bayesian learning algorithm for off-grid DOA estimation in the beamspace

In recent years, sparse Bayesian learning (SBL) algorithms in the array element space have become very popular for off-grid direction-of-arrival (DOA) estimation. However, the SBL algorithm in beamspace has not been researched. Therefore, this paper proposes a real-valued SBL algorithm in the beamspace. First, the received data in the array element space is transformed to the beamspace using the receive beamspace matrix. Subsequently, singular value decomposition (SVD) is introduced to reduce the computational burden further. Finally, the SBL algorithm is combined to estimate the off-grid DOA. Compared with the SBL algorithms in the array element space, the proposed algorithm has less computational complexity, better robustness to grid interval, and better DOA estimation performance under certain conditions. In addition, we also show the DOA estimation performance of the proposed algorithm for correlated signals and large-scale arrays. Numerical simulations verify the effectiveness of the proposed algorithm.

Experimental study on the performance of DOA estimation algorithm using a coprime acoustic sensor array without a priori knowledge of the source number

Coprime acoustic sensor arrays have been recently developed to estimate the direction-of-arrival (DOA) of multiple sound sources and may be needed in many acoustic applications because they can provide greater degrees of freedom and better estimation performance. However, most existing DOA estimation algorithms are derived under the assumption that the number of sources is known and have poor robustness due to unknown noise. This paper proposes a robust DOA estimation algorithm without estimating the number of sources using a coprime acoustic sensor array. The solution is based on the multiple signal classification (MUSIC)-like DOA estimation algorithm framework, in which a new spatial covariance model via spatial smoothing of the coprime array output signal is designed. The proposed spatial smoothing generalized MUSIC-like (SS-G-MUSIC-like) algorithm utilizes the diagonal loading technique to reconstruct the spatial smoothed covariance matrix. Results related to one-sound source and two-sound sources DOA estimation experiments show that the proposed algorithm can provide more focused source tracks over the entire data segment and better clutter suppression.

Two-dimensional DOA estimation method of acoustic vector sensor array based on sparse recovery

In order to solve the Direction of Arrival (DOA) estimation of fast-moving targets in a strong noisy environment, an auto-paired two-dimensional (2D) DOA estimation algorithm architecture based on the sparse recovery of acoustic vector sensor arrays is proposed. The structure of the array signal autocorrelation operator is similar to the 2D compressed sampling model. Based on the structure of the autocorrelation operator, a 2D DOA estimation sparse recovery model for the Uniform Line Array (ULA) of the acoustic vector sensors is proposed. Meanwhile, the modified Compressive Sampling Matching Pursuit (CoSaMP) algorithm is used to realize the auto-paired 2D DOA estimation. The simulation results show that the method proposed in this paper can effectively suppress noise, and can be used to realize 2D DOA estimation of acoustic vector sensor ULA under a low Signal-to-Noise Ratio (SNR) and small snapshots.

An Improved OMP-GA Combined Algorithm for Off-grid DOA Estimation

DOA (Direction of Arrival) is used to determine the direction of the targets and is one of the important technologies in array signal processing. To ensure the accuracy of traditional OMP-based DOA estimation algorithm, the over-complete dictionary needs to contain grids that match the real incident angles. However, for off-grid targets, the estimation accuracy will decrease. In this paper, we propose an improved OMP-based DOA estimation algorithm with genetic algorithm (GA), in which GA is introduced to search incident angle of the off-grid target directly, the subsequent traditional OMP steps are remained and the result got by which is used to filter out the false estimation results that deviate from the true target obtained by GA. Compared with the traditional OMP-based DOA estimation algorithm, this proposed algorithm could achieve higher accuracy. Simulation results verify the effectiveness of this proposed algorithm in the case of low signal-to-noise ratio (SNR) and low number of snapshots.

Reverberation aware deep learning for environment tolerant microphone array DOA estimation

By transferring the direction of arrival (DOA) estimation into a problem of spatial sample classification, deep neural network (DNN) driven by large training data have been investigated to achieve significant performance enhancement compared to classic DOA estimation strategies do. However, consider the highly diverse indoor environments that microphone arrays being used, different reverberation pattern under various environment pose extremely significant limitations to the DOA network model, as its performance is dependent on the match between training data and practical data. In order to improve the robustness of DOA estimation, a reverberation aware network (RAN) algorithm is proposed in this paper. The beam cross-correlation (BCC) is defined as the cross-correlation between the beamforming output and the observed multi-channel signal, which carries an approximation of the room impulse response. Adopting covariance matrix of BCC matrix as the DNN input to enable explicit characterization of reverberation in which the speech was captured, a reverberation aware deep learning network is trained to improve the generalization capability. Finally, simulation and experiment are performed to verify the effectiveness of the proposed method in improving the environment tolerance of DOA estimation, by comparing to the classic traditional DOA estimation algorithm and MLP strategy.

DoA Estimation for FMCW Radar by 3D-CNN.

A method of direction-of-arrival (DoA) estimation for FMCW (Frequency Modulated Continuous Wave) radar is presented. In addition to MUSIC, which is the popular high-resolution DoA estimation algorithm, deep learning has recently emerged as a very promising alternative. It is proposed in this paper to use a 3D convolutional neural network (CNN) for DoA estimation. The 3D-CNN extracts from the radar data cube spectrum features of the region of interest (RoI) centered on the potential positions of the targets, thereby capturing the spectrum phase shift information, which corresponds to DoA, along the antenna axis. Finally, the results of simulations and experiments are provided to demonstrate the superior performance, as well as the limitations, of the proposed 3D-CNN.

DOA tracking for seamless connectivity in beamformed IoT-based drones

In recent times, there has been a surge of interest around the usage of adaptive antenna arrays of Internet of Things (IoT) based Drones in the communication systems. Adaptive antenna arrays have the ability to form customized radiation patterns based on the changes in the environment by employing methods for estimating Direction of Arrival (DOA) and adaptive beamforming. Nevertheless, upon deploying adaptive antenna arrays in complex IoT platforms, the radiation patterns that result from the use of such adaptive algorithms may be adjusted to the preceding location of the node and not attuned to the current location. These issues that arise due to mobility can be resolved by continuously tracking the DOA of the intended target. As DOA is time varying in an IoT Drone environment, existing algorithms for estimating the DOA like MUltiple SIgnal Classification (MUSIC) and Estimation of Signal Parameter via Rotational Invariance Techniques (ESPRIT) cannot be used to track the signal subspace recursively, as they are based on batch eigenvalue decomposition which is highly time consuming with a time complexity of O(n3). Furthermore, DOA estimation algorithms do not result in robust subspace estimates when the Signal to Noise Ratio (SNR) is low.The main novelty of the proposed work is a low computational complexity subspace tracking algorithm for tracking DOA in order to provide seamless connectivity. Simulation results show that the proposed DOA tracking takes lesser time for tracking the current location of the drone target as opposed to conventional DOA estimation methods. Furthermore,it is observed that the tracking process remains unaffected by SNR.

Joint spectrum sensing and DOA estimation with sub-Nyquist sampling

This paper addresses the problem of joint spectrum sensing and Direction-of-Arrival (DOA) estimation under array receiver based on modulated wideband converter (MWC) with sub-Nyquist sampling. To simplify the structure of MWC, we connect one identical branch of MWC on each antenna of array receiver, reducing the overhead of hardware resources. Two joint spectrum sensing and DOA estimation (JSS-DOA) algorithms, referred to as CP- and MUSIC-based algorithms, are proposed to improve the robustness of estimation. The proposed approaches utilize Fourier series coefficients of a periodic signal provided by MWC to determine the subband positions where sources are located, and combine the recovered subband spectrum information to obtain estimates of frequencies. This strategy ensures robust frequency estimation accuracy under certain conditions and contributes to a robust DOA estimation under high noise level. We further provide a theoretical analysis of the working conditions for proposed algorithms, based on which the rationale of parameter setting is also reported. Finally, the performance of proposed algorithms is assessed via simulation experiments concerning multiple unknown sources under our receiver with sub-Nyquist sampling.

An Enhanced Smoothed L0-Norm Direction of Arrival Estimation Method Using Covariance Matrix.

An enhanced smoothed -norm algorithm for the passive phased array system, which uses the covariance matrix of the received signal, is proposed in this paper. The SL0 (smoothed -norm) algorithm is a fast compressive-sensing-based DOA (direction-of-arrival) estimation algorithm that uses a single snapshot from the received signal. In the conventional SL0 algorithm, there are limitations in the resolution and the DOA estimation performance, since a single sample is used. If multiple snapshots are used, the conventional SL0 algorithm can improve performance in terms of the DOA estimation. In this paper, a covariance-fitting-based SL0 algorithm is proposed to further reduce the number of optimization variables when using multiple snapshots of the received signal. A cost function and a new null-space projection term of the sparse recovery for the proposed scheme are presented. In order to verify the performance of the proposed algorithm, we present the simulation results and the experimental results based on the measured data.

Fast and robust super-resolution DOA estimation for UAV swarms

Unmanned aerial vehicle (UAV) swarms have shown great potentials in civilian and military applications. Consequently, there is a high demand for accurate UAV swarms detection. In response to resolve the closely spaced UAVs, we propose three super-resolution direction of arrival (DOA) estimation algorithms, i.e., frequency-selective reweighted atomic-norm minimization (FSRAM), fast Fourier transform (FFT)-reweighted atomic-norm minimization (FFT-RAM) and FFT-FSRAM. These proposed three algorithms take full account of advantages of prior knowledge, effective information extraction and gridless sparse technique, i.e., i) the use of prior knowledge can improve the accuracy of DOA estimation; ii) the effective information extraction can improve the signal-to-noise ratio to enhance the robustness and reduce the computational complexity; iii) the gridless sparse technique is insensitive to signal correlations. Complexity analysis and numerical simulations are performed to demonstrate that, compared with the Beamforming method, multiple signal classification (MUSIC) and reweighted atomic-norm minimization (RAM), the proposed three algorithms are insensitive to signal correlations and the FFT-RAM and FFT-FSRAM are more robust and faster for super-resolution DOA estimation of UAV swarms under the noisy environment. Additionally, the real experiment with C-band radar is also conducted to verify the effectiveness of the proposed super-resolution DOA estimation algorithms.

Low-complexity neural network based DOA estimation for wideband signals in massive MIMO systems

Massive multiple-input multiple-output (MIMO) has become one of the most promising technologies for wireless communication systems, in which the direction-of-arrival (DOA) plays an important role in interference cancellation and transmission reliability. However, the challenge of conventional wideband DOA estimation algorithms is that their high computational complexity brings great difficulties for their effective application in massive MIMO systems. In this paper, we propose a wideband low-complexity DOA estimation algorithm based on a principal component analysis (PCA) neural network for massive MIMO systems. First, a new criterion for constructing a focusing matrix is proposed to avoid complex angle pre-estimation. To further reduce the complexity of the eigenvalue decomposition (EVD), we propose a signal subspace estimation algorithm based on PCA, which uses only a limited amount of self-organizing learning to estimate the weights of the network and the signal subspace and does not require prior sample training. Moreover, to increase the estimation accuracy, we use the Akaike information criterion (AIC) to divide signal and noise subspaces accurately. The theoretical analysis and simulation results show that the computational complexity of the proposed algorithm is effectively reduced, and the angles of wideband sources can be accurately estimated in massive MIMO systems.

RxCV-based unitary SBL algorithm for off-grid DOA estimation with MIMO radar in unknown non-uniform noise

As an indispensable part of array signal processing, direction-of-arrival (DOA) estimation has been well investigated over the past few decades, and many excellent DOA estimation methods have been proposed. In this paper, a receiving domain covariance vector (RxCV) based unitary SBL algorithm is proposed for the off-grid DOA estimation of monostatic multiple-input multiple-output (MIMO) radar in unknown non-uniform noise environment. In the proposed algorithm, the data received by MIMO radar is firstly transformed into receiving domain by a reshape operation. Then the RxCV-based unitary off-grid sparse model without non-uniform noise is constructed through unitary transformation and first-order linear approximation, where the unknown non-uniform noise is got rid off by a linear transformation. Based on the RxCV-based unitary off-grid sparse model, the sparse Bayesian learning (SBL) criterion is adopted to estimate the parameters, where signal variance and off-gird error are estimated by using expectation-maximization (EM) strategy. The DOA estimation is ultimately realized through 1-dimensional spectrum search of the received data. Results of the simulation experiments have provided the evidence of that the proposed algorithm is robustness against nonuniform noise and off-grid error, and it can maintain superior DOA estimation performance compared with other reported sparse signal representation based methods.