The problem of gridless direction of arrival (DOA) estimation is addressed in the non-uniform array (NUA) case. Traditionally, gridless DOA estimation and root-MUSIC are only applicable for measurements from a uniform linear array (ULA). This is because the sample covariance matrix of ULA measurements has Toeplitz structure, and both algorithms are based on the Vandermonde decomposition of a Toeplitz matrix. The Vandermonde decomposition breaks a Toeplitz matrix into its harmonic components, from which the DOAs are estimated. First, we present the `irregular' Toeplitz matrix and irregular Vandermonde decomposition (IVD), which generalizes the Vandermonde decomposition to apply to a more general set of matrices. It is shown that the IVD is related to the MUSIC and root-MUSIC algorithms. Next, gridless DOA is generalized to the NUA case using IVD. The resulting non-convex optimization problem is solved using alternating projections (AP). A numerical analysis is performed on the AP based solution which shows that the generalization to NUAs has similar performance to traditional gridless DOA.
We present a gridless sparse iterative covariance-based estimation method based on alternating projections for direction-of-arrival (DOA) estimation. The gridless DOA estimation is formulated in the reconstruction of Toeplitz-structured low rank matrix, and is solved efficiently with alternating projections. The method improves resolution by achieving sparsity, deals with single-snapshot data and coherent arrivals, and, with co-prime arrays, estimates more DOAs than the number of sensors. We evaluate the proposed method using simulation results focusing on co-prime arrays.
This paper focuses on the gridless direction-of-arrival (DoA) estimation for data acquired by non-uniform linear arrays (NLAs) in automotive applications. Atomic norm minimization (ANM) is a promising gridless sparse recovery algorithm under the Toeplitz model and solved by convex relaxation, thus it is only applicable to uniform linear arrays (ULAs) with array manifolds having a Vandermonde structure. In automotive applications, it is essential to apply the gridless DoA estimation to NLAs with arbitrary geometry with efficiency. In this paper, a fast ANM-based gridless DoA estimation algorith…
To reduce the adverse impacts of the unknown colored noise on the performance degradation of the direction-of-arrival (DOA) estimation, we propose a new gridless DOA estimation method based on fourth-order cumulant (FOC)in this letter. We first introduce the non-redundancy single measurement vector (SMV) through FOC, which is capable of suppressing the Gaussian colored noise. Next, we analyze the distribution of the estimation error and design an estimation error tolerance scheme for it. We then combine the atomic norm minimization of the non-redundancy SMV with the above constraint scheme. Th…
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 continuous (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 lo…
Low-Complexity Gridless Single-Snapshot DoA Estimation via Truncated Hankel Newton-MUSIC
The Hong Kong University of Science and Technology（香港科技大学）；Southern University of Science and Technology（南方科技大学）；The University of British Columbia（不列颠哥伦比亚大学）
We develop a direction of arrival (DoA) and channel estimation algorithm for the one-bit quantized millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) system. By formulating the estimation problem as a noisy one-bit compressed sensing problem, we propose a computationally efficient gridless solution based on the expectation-maximization generalized approximate message passing (EMGAMP) approach. The proposed algorithm does not need the prior knowledge about the number of DoAs and outperforms the existing methods in distinguishing extremely close DoAs for the case of one-bit q…
Due to the increasing demand for low power and higher sampling rates, low resolution quantization for data acquisition has drawn great attention recently. Consequently, line spectral estimation (LSE) with multiple measurement vectors (MMVs) from coarsely quantized samples is of vital importance in cutting edge array signal processing applications such as range estimation and DOA estimation in millimeter wave radar systems. In this paper, we combine the low complexity gridless variational line spectral estimation (VALSE) and expectation propagation (EP) and propose an MVALSE-EP algorithm to est…
We focus on developing an effective Direction Of Arrival (DOA) estimation method for wideband sources based on the gridless sparse concept. Previous coherent methods have been designed by dividing wideband frequencies into a few subbands which are transferred to a reference subband using focusing matrices. In this work, as opposed to the previous techniques, we propose a convex optimization problem that leads to an accurate wideband DOA estimation method with no need for any focusing matrix. Moreover, in this method, no initial DOA estimates are required and it can be used for any arbitrary li…
In this paper, an algorithm of multiple signal classification (MUSIC) is proposed for two-dimensional (2-D) direction of- arrival (DOA) and polarization estimation of non-circular signal in three-dimensional (3-D) millimeter wave polarized largescale/ massive multiple-input-multiple-output (MIMO) systems. The traditional MUSIC-based algorithms can estimate either the DOA and polarization for circular signal or the DOA for non-circular signal by using spectrum search. By contrast, in the proposed algorithm only the DOA estimation needs spectrum search, and the polarization estimation has a clos…
Robust Quantum-MUSIC for DoA Estimation Using Rydberg Atomic Receiver Arrays
Indian Institute of Technology (IIT) Delhi（印度理工学院德里分校）；Bharti School of Telecommunication Technology and Management, IIT Delhi（印度理工学院德里分校电信技术与管理学院）；University of Melbourne（墨尔本大学）
In this letter, we consider the problem of direction-of-arrival (DOA) estimation with one-bit quantized array measurements. With analysis, it is shown that, under mild conditions the one-bit covariance matrix can be approximated by the sum of a scaled unquantized covariance matrix and a scaled identity matrix. Although the scaling parameters unknown because of the extreme quantization, they do not affect the subspace-based DOA estimators. Specifically, the signal and noise subspaces can be straightforwardly determined through the eigendecomposition of the one-bit covariance matrix, without pre…
Inspection robots are widely used in the field of smart grid monitoring in substations, and partial discharge (PD) is an important sign of the insulation state of equipments. PD direction of arrival (DOA) algorithms using conventional beamforming and time difference of arrival (TDOA) require large-scale antenna arrays and high computational complexity, which make them difficult to implement on inspection robots. To address this problem, a novel directional multiple signal classification (Dir-MUSIC) algorithm for PD direction finding based on signal strength is proposed, and a miniaturized dire…
A general non-Gaussian semiparametric model is adopted to characterize the measurement vectors, i.e.\ the \textit{snapshots}, collected by a linear array. Moreover, the recently derived \textit{robust semiparametric efficient} $R$-estimator of the data covariance matrix is exploited to implement an original version of the MUSIC estimator. The efficiency of the resulting $R$-MUSIC algorithm is investigated by comparing its Mean Squared Error (MSE) in the estimation of the source spatial frequencies with the relevant Semiparametric Stochastic Cramér-Rao Bound (SSCRB).
Multiple-input multiple-output (MIMO) systems play an essential role in direction-of-arrival (DOA) estimation. A large number of antennas used in a MIMO system imposes a huge complexity burden on the popular DOA estimation algorithms, such as MUSIC and ESPRIT due to the implementation of eigenvalue decomposition. This renders those algorithms impractical in applications requiring quick DOA estimation. Consequently, we theoretically derive several useful noise subspace vectors when the number of signal sources is less than the number of elements in both the transmitter and receiver sides. Those…
Sparse array arrangement has been widely used in vector-sensor arrays because of increased degree-of-freedoms for identifying more sources than sensors. For large-size sparse vector-sensor arrays, one-bit measurements can further reduce the receiver system complexity by using low-resolution ADCs. In this paper, we present a sparse cross-dipole array with one-bit measurements to estimate Direction of Arrivals (DOA) of electromagnetic sources. Based on the independence assumption of sources, we establish the relation between the covariance matrix of one-bit measurements and that of unquantized m…
For a sub-connected hybrid multiple-input multiple-output (MIMO) receiver with $K$ subarrays and $N$ antennas, there exists a challenging problem of how to rapidly remove phase ambiguity in only single time-slot. First, a DOA estimator of maximizing received power (Max-RP) is proposed to find the maximum value of $K$-subarray output powers, where each subarray is in charge of one sector, and the center angle of the sector corresponding to the maximum output is the estimated true DOA. To make an enhancement on precision, Max-RP plus quadratic interpolation (Max-RP-QI) method is designed. In the…
This paper aims at presenting a numerical investigation of the statistical efficiency of the MUSIC (with different covariance matrix estimates) and the IAA-APES Direction of Arrivals (DOAs) estimation algorithms under a general Complex Elliptically Symmetric (CES) distributed measurement model. Specifically, the density generator of the CES-distributed data snapshots is considered as an additional, infinite-dimensional, nuisance parameter. To assess the efficiency in the considered semiparametric setting, the Semiparametric Stochastic Cramér-Rao Bound (SSCRB) is adopted as lower bound for the …
Conventional direction of arrival (DOA) estimation algorithms suffer from performance degradation due to antenna pattern distortion and substantial computational complexity in real-time execution. The support vector regression (SVR) approach is a possible solution to overcome those limitations. In this work, we propose a sequential DOA estimation technique that combines the reduced dimension SVR (for the azimuthal plane) with a closed form approach (for the elevation plane). Thus, the training and testing are only required for the azimuthal angles which makes it very attractive from the implem…
Geometry-Decoupled Deep Unfolding for Gridless Super-Resolution TomoSAR Under Nonuniform Baselines
Wuhan Electronic Information Institute（武汉电子信息学院）；School of Earth Sciences and Engineering, Hohai University（河海大学地球科学与工程学院）；School of Medical Information Engineering, Guangzhou University of Chinese Medicine（广州中医药大学医学信息工程学院）；Technical University of Munich（慕尼黑工业大学）
本文提出DUSG-Tomo-Net，一种深度解折叠网格less框架，通过学习Toeplitz结构协方差表示，解决非均匀基线下空间borne SAR Tomography的超分辨率问题。
We address the problem of search-free DOA estimation from a single noisy snapshot for sensor arrays of arbitrary geometry, by extending a method of gridless super-resolution beamforming to arbitrary arrays with noisy measurements. The primal atomic norm minimization problem is converted to a dual problem in which the periodic dual function is represented with a trigonometric polynomial using truncated Fourier series. The number of terms required for accurate representation depends linearly on the distance of the farthest sensor from a reference. The dual problem is then expressed as a semidefi…
Institute of Digital Communication Systems, Ruhr University Bochum（鲁尔大学波鸿数字通信系统研究所）；Department of Electrical and Computer Engineering, Purdue University（普渡大学电气与计算机工程系）
We present a MUSIC-based Direction of Arrival (DOA) estimation strategy using small antenna arrays, via employing deep learning for reconstructing the signals of a virtual large antenna array. Not only does the proposed strategy deliver significantly better performance than simply plugging the incoming signals into MUSIC, but surprisingly, the performance is also better than directly using an actual large antenna array with MUSIC for high angle ranges and low test SNR values. We further analyze the best choice for the training SNR as a function of the test SNR, and observe dramatic changes in …
High data rate communication with Unmanned Aerial Vehicles (UAV) is of growing demand among industrial and commercial applications since the last decade. In this paper, we investigate enhancing beam forming performance based on signal Direction of Arrival (DoA) estimation to support UAV-cellular network communication. We first study UAV fast moving scenario where we found that drone's mobility cause degradation of beam forming algorithm performance. Then, we propose a DoA estimation algorithm and a steering vector adaptive receiving beam forming method. The DoA estimation algorithm is of high …
An Fluid Antenna Array-Enabled DOA Estimation Method: End-Fire Effect Suppression
Ningbo University（宁波大学）；Hong Kong Metropolitan University（香港都会大学）；City University of Hong Kong（香港城市大学）；Hong Kong Polytechnic University（香港理工大学）；University College London（伦敦大学学院）
The report focuses on three areas in particular: the first is the Received Signal Strength indicator technique, Direction of Arrival technique, and the integration of two algorithms, RSS and DOA, in order to build a hybrid, more robust algorithms. In the Received Signal Strength (RSS), the unknown node location is estimated using trilateration. This report examines the performance of different estimators such as Least Square, Weighted Least Square, and Huber robustness in order to obtain the most robust performance. In the direction of arrival (DOA) method, the estimation is carried out using …
Self-Calibration DOA Estimation for Movable Antenna Systems with Antenna Position Errors
Nanjing University of Science and Technology（南京理工大学）；Qian Xuesen College, Nanjing University of Science and Technology（南京理工大学钱学森学院）；Seoul National University（首尔大学）
Multiple signal classification (MUSIC) has been widely applied in multiple-input multiple-output (MIMO) receivers for direction-of-arrival (DOA) estimation. To reduce the cost of radio frequency (RF) chains operating at millimeter-wave bands, hybrid analog-digital structure has been adopted in massive MIMO transceivers. In this situation, the received signals at the antennas are unavailable to the digital receiver, and as a consequence, the spatial covariance matrix (SCM), which is essential in MUSIC algorithm, cannot be obtained using traditional sample average approach. Based on our previous…
In this paper, we address the problem of direction finding using coprime array, which is one of the most preferred sparse array configurations. Motivated by the fact that non-uniform element spacing hinders full utilization of the underlying information in the receive signals, we propose a direction-of-arrival (DoA) estimation algorithm based on low-rank reconstruction of the Toeplitz covariance matrix. The atomic-norm representation of the measurements from the interpolated virtual array is considered, and the equivalent dual-variable rank minimization problem is formulated and solved using a…
Electromagnetic (EM) vector sensor arrays can track both the polarisation and direction of arrival (DOA) of the impinging signals. For linear crossed-dipole arrays, as shown by our analysis, due to inherent limitation of the structure, it can only track one DOA parameter and two polarisation parameters. For full four-dimensional (4-D, 2 DOA and 2 polarization parameters) estimation, we could extend the linear crossed-dipole array to the planar case. In this paper, instead of extending the array geometry, we replace the crossed-dipoles by tripoles and construct a linear tripole array. It is pro…
To improve the accuracy of direction-of-arrival (DOA) estimation, a deep learning (DL)-based method called CDAE-DNN is proposed for hybrid analog and digital (HAD) massive MIMO receive array with overlapped subarray (OSA) architecture in this paper. In the proposed method, the sample covariance matrix (SCM) is first input to a convolution denoise autoencoder (CDAE) to remove the approximation error, then the output of CDAE is imported to a fully-connected (FC) network to get the estimation result. Based on the simulation results, the proposed CDAE-DNN has great performance advantages over trad…
An algorithm called MUSIC-like algorithm was originally proposed as an alternative method to the MUltiple SIgnal Classification (MUSIC) algorithm for direction-of-arrival (DOA) estimation. Without requiring explicit model order estimation, it was shown to have robust performance particularly in low signal-to-noise ratio (SNR) scenarios. In this letter, the working principle of a relaxation parameter β, a parameter which was introduced into the formulation of the MUSIC-like algorithm, is provided based on geometrical interpretation. To illustrate its robustness, the algorithm will be examined u…
This work analyses the performance-complexity tradeoff for different direction of arrival (DoA) estimation techniques. Such tradeoff is investigated taking into account uniform linear array structures. Several DoA estimation techniques have been compared, namely the conventional Delay-and-Sum (DS), Minimum Variance Distortionless Response (MVDR), Multiple Signal Classifier (MUSIC) subspace, Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT), Unitary-ESPRIT and Fourier Transform method (FT-DoA). The analytical formulation of each estimation technique as well the compar…
Apart from the conventional parameters (such as signal-to-noise ratio, array geometry and size, sample size), several other factors (e.g. alignment of the antenna elements, polarization parameters) influence the performance of direction of arrival (DOA) estimating algorithms. When all the antenna elements are identically aligned, the polarization parameters do not affect the steering vectors, which is the underlying assumption of all the conventional DOA algorithms. Unfortunately, in this case, for a given set of DOA angles there exists a range of polarization parameters which could result in …
