Super-Resolution DOA Estimation for Multi Frequency Signals of Polarization Sensitive Array Based on Atomic Norm Minimization

This paper introduces a low complexity wideband direction-of-arrival (DOA) estimation algorithm on the co-prime array. To increase the number of the detectable signal sources and to prevent an unnecessary increase in complexity, the low dimensional co-prime array vector is constructed by arranging elements of the correlation matrix at every frequency bin. The atomic norm minimization (ANM)-based approach resolves the grid-mismatch, which causes an inevitable error in the compressive sensing (CS)-based DOA estimation. However, the complexity surges when the ANM is exploited to the wideband DOA estimation on the co-prime array. The surging complexity of the ANM-based wideband DOA estimation on the co-prime array is handled by solving the time-saving semidefinite programming (SDP) motivated by the ANM for multiple measurement vector (MMV) case. Simulation results show that the proposed algorithm has high accuracy and low complexity compared to compressive sensing (CS)-based wideband DOA estimation algorithms that exploit the co-prime array.

This paper presents an efficient optimization technique for super-resolution two-dimensional (2D) direction of arrival (DOA) estimation by introducing a new formulation of atomic norm minimization (ANM). ANM allows gridless angle estimation for correlated sources even when the number of snapshots is far less than the antenna size, yet it incurs huge computational cost in 2D processing. This paper introduces a novel formulation of ANM via semi-definite programming, which expresses the original high-dimensional problem by two decoupled Toeplitz matrices in one dimension, followed by 1D angle estimation with automatic angle pairing. Compared with the state-of-the-art 2D ANM, the proposed technique reduces the computational complexity by several orders of magnitude with respect to the antenna size, while retaining the benefits of ANMin terms of super-resolution performance with use of a small number of measurements, and robustness to source correlation and noise. The complexity benefits are particularly attractive for large-scale antenna systems such as massive MIMO and radio astronomy.

Direction-of-arrival (DOA) estimation is widely applied in acoustic source localization. A multi-frequency model is suitable for characterizing the broadband structure in acoustic signals. In this paper, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">continuous</i> (gridless) DOA estimation problem with multiple frequencies is considered. This problem is formulated as an atomic norm minimization (ANM) problem. The ANM problem is equivalent to a semi-definite program (SDP) which can be solved by an off-the-shelf SDP solver. The dual certificate condition is provided to certify the optimality of the SDP solution so that the sources can be localized by finding the roots of a polynomial. We also construct the dual polynomial to satisfy the dual certificate condition and show that such a construction exists when the source amplitude has a uniform magnitude. In multi-frequency ANM, spatial aliasing of DOAs at higher frequencies can cause challenges. We discuss this issue extensively and propose a robust solution to combat aliasing. Numerical results support our theoretical findings and demonstrate the effectiveness of the proposed method.

In underwater acoustic signal processing, direction of arrival (DOA) estimation can provide important information for target tracking and localization. To address underdetermined wideband signal processing in underwater passive detection system, this paper proposes a novel underdetermined wideband DOA estimation method equipped with the nested array (NA) using focused atomic norm minimization (ANM), where the signal source number detection is accomplished by information theory criteria. In the proposed DOA estimation method, especially, after vectoring the covariance matrix of each frequency bin, each corresponding obtained vector is focused into the predefined frequency bin by focused matrix. Then, the collected averaged vector is considered as virtual array model, whose steering vector exhibits the Vandermonde structure in terms of the obtained virtual array geometries. Further, the new covariance matrix is recovered based on ANM by semi-definite programming (SDP), which utilizes the information of the Toeplitz structure. Finally, the Root-MUSIC algorithm is applied to estimate the DOAs. Simulation results show that the proposed method outperforms other underdetermined DOA estimation methods based on information theory in term of higher estimation accuracy.

The performance of the existing direction of arrival (DOA) estimation algorithms for source localization in the wireless sensor networks (WSN) degrades when the sources are correlated. The degradation is due to the rank deficiency of the source covariance matrix which is reflected in the high cramer-Rao lower bound (CRLB) for correlated sources. Unlike subspace based techniques, maximum likelihood (ML) based technique does not require any preprocessing technique for DOA estimation of correlated signals. Hence ML technique can be directly applied for WSN with arbitrary array geometry. The DOA estimation accuracy for correlated signals is improved by employing distributed ML approach in this paper. The subarray formed at a particular node which is experiencing highest CRLB can improve its estimation accuracy by receiving better DOA estimates from its neighbors. The corresponding distributed CRLB is derived and found a substantial improvement in the distributed scenario. The distributed CRLB lies between that of local CRLB for the subarray formed at the node and global CRLB for the array formed by all sensors in the WSN. Diffusion quantum particle swarm optimization is used to optimize ML estimator for fully correlated signals as it has only a single parameter for tuning. Simulation results show that the estimation accuracy improves at a node even for correlated signals yielding highest CRLB using distributed approach. The root mean square error at a specific node using distributed algorithm approaches to the derived distributed CRLB.

The coprime array provides the possibility of resolving more signals than the sensors for the directionof-arrival (DOA) estimation application. However, the non-consecution of its virtual array raises challenges for making full use of the degree of freedom (DOF). In this paper, we propose a new underdetermined DOA estimation method with coprime array where the non-consecutive virtual array can be converted into a virtual uniform linear array (ULA) with the same aperture. Firstly, all elements in the vectorized signal covariance matrix corresponding to the same virtual array positions are averaged to construct the output signals of the virtual array. Then, an atomic norm minimization (ANM) based optimization problem is formed for denoising the output signals of the virtual array and for interpolating the missing signals at the virtual array holes. At last, the ANM problem is solved by the semidefinite programming (SDP) and the DOAs are obtained by applying the subspace method on the reconstructed signal covariance matrix of the interpolated virtual ULA. The proposed algorithm is gridless and makes full use of the DOF and the information provided by the coprime array. The simulation results compared with the other representative methods are given to demonstrate the superiority of the proposed method with respect to the resolution and estimation accuracy.

Estimating the direction of arrival (DOA) has been a crucial problem in a wide range of applications. Current research predominantly focuses on narrow-band, 1-D signals, which are not directly applicable to practical scenarios involving wideband and multidimensional signals. To deal with this drawback, we propose a 2-D multiple frequency atomic norm minimization (2DMFANM) algorithm to estimate the elevation and azimuth angles of wideband signals in a grid-less manner. To be specific, we exploit the multiple frequency model to describe the wideband signals and derive the corresponding signal model. Based on the structure of the signal model, we formulated an atomic norm minimization (ANM) problem that allows for the gridless joint estimation of elevation and azimuth angles. The ANM problem is further converted into semidefinite programming (SDP) via analysis of the dual problem. To reduce the computational burden that hinders the deployment of 2DMFANM, we propose two fast algorithms called 2DMFDANM and 2DMFANM_SizeRedu. Specifically, 2DMFDANM reduces the size of the original algorithm by decoupling the information of spatial angular frequencies, while 2DMFANM_SizeRedu achieves fast speed by removing the redundancy in the original algorithm. Theoretical and numerical analyses indicate that these two algorithms significantly enhance the speed of computation with minor degradation in the estimation accuracy. Numerical simulations and experimental data analysis demonstrate the superior performance of the proposed methods compared to state-of-the-art algorithms.

Atomic norm minimization (ANM) has recently become a powerful tool for gridless compressed sensing (CS). In this paper, the issue of joint estimation of direction-of-departure (DOD) and direction-of-arrival (DOA) for bistatic multiple-input-multiple-output (MIMO) radar is investigated via two dimensional (2D) ANM. However, a major problem of the primal 2D-ANM is that the direct conversion of 2D-ANM into its semi-definite programming (SDP) problem is not strictly established theoretically and is just an approximation, which results in a decline in estimation performance. Besides, the primal 2D-ANM is limited to a single measurement vector (SMV) model. We propose a duality-based 2D-ANM algorithm for grid-free DOD and DOA estimation in MIMO radar, in which the 2D-ANM problem is effectively solved over its optimal variables in the dual-domain with SDP. Thus it retains the benefits of 2D-ANM and holds in theory. Also, it is applicable for SMV as well as multiple measurement vectors (MMV) models and appropriate for non-uniform linear arrays. The simulation results show that the proposed algorithm avoids the grid mismatch effect in DOD and DOA estimation in contrast to the conventional CS methods, and is robust to target correlation and the single-snapshot environment in comparison with the traditional subspace methods.

Joint parameter estimation algorithm for polarization-sensitive channel compression arrays based on atomic norm minimization

Gridless direction-of-arrival (DOA) estimation with multiple frequencies can be applied in acoustics source localization problems.We formulate this as an atomic norm minimization (ANM) problem and derive an equivalent <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">regularization-free</i> semi-definite program (SDP) thereby avoiding regularization bias. The DOA is retrieved using a Vandermonde decomposition on the Toeplitz matrix obtained from the solution of the SDP. We also propose a fast SDP program to deal with non-uniform array and frequency spacing. For non-uniform spacings, the Toeplitz structure will not exist, but the DOA is retrieved via irregular Vandermonde decomposition (IVD), and we theoretically guarantee the existence of the IVD. We extend ANM to the multiple measurement vector (MMV) cases and derive its equivalent regularization-free SDP. Using multiple frequencies and the MMV model, we can resolve more sources than the number of physical sensors <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">for a uniform linear array</i> . Numerical results demonstrate that the regularization-free framework is robust to noise and aliasing, and it overcomes the regularization bias.

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.

Sparse scatterer identification with atomic norm minimization (ANM) techniques in the delay-Doppler domain is investigated for a vehicle-to-infrastructure millimeter wave propagation channel. First, a two-dimensional ANM is formulated for jointly estimating the time-delays and Doppler frequencies associated with individual multipath components (MPCs) from short-time Fourier transformed measurements. The two-dimensional ANM is formulated as a semi-definite program and promotes sparsity in the delay-Doppler domain. The numerical complexity of the two-dimensional ANM limits the problem size which results in processing limitations on the time-frequency sample matrix size. Subsequently, a decoupled form of ANM is used together with a matrix pencil, allowing a larger sample matrix size. Simulations show that spatial clusters of a point-scatterers with small cluster spread are suitable to model specular reflection which result in significant MPCs and the successful extraction of their delay-Doppler parameters. The decoupled ANM is applied to vehicle-to-infrastructure channel sounder measurements in a sub-urban street in Vienna at 62 GHz. The obtained results show that the decoupled ANM successfully extracts the delay-Doppler parameters in high resolution for the channel’s significant MPCs.

To perform multi-user multiple-input and multipleoutput transmission in millimeter-wave (mmWave) cellular systems, the high-dimensional channels need to be estimated for designing the multi-user precoder. Conventional grid-based Compressed Sensing (CS) methods for mmWave channel estimation suffer from the basis mismatch problem, which prevents accurate channel reconstruction and degrades the precoding performance. This paper formulates mmWave channel estimation as an Atomic Norm Minimization (ANM) problem. In contrast to grid-based CS methods which use discrete dictionaries, ANM uses a continuous dictionary for representing the mmWave channel. We consider a continuous dictionary based on sub-sampling in the antenna domain via a small number of radio frequency chains. We show that mmWave channel estimation using ANM can be formulated as a Semidefinite Programming (SDP) problem, and the channel can be accurately estimated via off-the-shelf SDP solvers in polynomial time. Simulation results indicate that ANM can achieve much better estimation accuracy compared to grid-based CS, and significantly improves the spectral efficiency provided by multi-user precoding.

This paper deals with the computation of the Cramer-Rao lower bound (CRB) for direction of arrival (DOA) estimation of ultra wideband-orthogonal frequency division multiplexing (UWB-OFDM) signals detected by antenna arrays for millimetre-wave applications. The CRB on DOA estimation of UWB-OFDM sources is evaluated by extending the mathematical model of DOA estimation of narrow band signals to wideband orthogonal multicarrier signals. Specific results are presented for the case of a uniform linear array (ULA) and line-of-sight (LOS) scenario. After a comparison of our results for OFDM with the case of wideband single carrier signals, we use the CRB for DOA to substantiate the design of medium access controllers protocols that make use of DOA information.

The ocean acoustic tomography (OAT) is frequently used to the estimation of sound speed variations in the shallow ocean waveguide. As the first step of OAT, acoustic wideband rays along the different paths are exactly separated with two particular parameters of direction of arrival (DOA) and time of arrival (TOA). However, the multipath propagation of ray paths induces interferences between different rays, which makes the OAT impossible to identify these raypaths. In this paper, a two-dimensional wideband grid-free algorithm is proposed for separating acoustic raypaths by using their DOAs and TOAs. Firstly, a continuous formulation of the raypath separation problem is presented. Then, an atomic norm minimization (ANM) problem is designed by exploiting an atomic norm which promotes signal sparsity in the continuous domain. To solve such a ANM problem, an equivalent maximization problem is introduced, which can be solved efficiently with semidefinite programming. Finally, the certain parameters of DOA and TOA achieved through an optimization variable of the maximization problem. The experimental results show that the proposed method obtains more accurate separation performance compared to conventional compressive sensing-based algorithms.