Direction of Arrival (DoA) estimation using Sparse Linear Arrays (SLAs) has recently gained considerable attention in array processing thanks to their capability to provide enhanced degrees of freedom in resolving uncorrelated source signals. Additionally, deployment of one-bit Analog-to-Digital Converters (ADCs) has emerged as an important topic in array processing, as it offers both a low-cost and a low-complexity implementation. In this paper, we study the problem of DoA estimation from one-bit measurements received by an SLA. Specifically, we first investigate the identifiability conditions for the DoA estimation problem from one-bit SLA data and establish an equivalency with the case when DoAs are estimated from infinite-bit unquantized measurements. Towards determining the performance limits of DoA estimation from one-bit quantized data, we derive a pessimistic approximation of the corresponding Cramér-Rao Bound (CRB). This pessimistic CRB is then used as a benchmark for assessing the performance of one-bit DoA estimators. We also propose a new algorithm for estimating DoAs from one-bit quantized data. We investigate the analytical performance of the proposed method through deriving a closed-form expression for the covariance matrix of the asymptotic distribution of the DoA estimation errors and show that it outperforms the existing algorithms in the literature. Numerical simulations are provided to validate the analytical derivations and corroborate the resulting performance improvement.
With a careful design of sample spacings either in temporal and spatial domain, co-prime sensing can reconstruct the autocorrelation at a significantly denser set of points based on Bazout theorem. However, still restricted from Bazout theorem, it is required O(M1 + M2) samples to estimate frequencies in the case of co-prime sampling, where M1 and M2 are co-prime down-sampling rates. Besides, for Direction-of-arrival (DOA) estimation, the sensors can not be arbitrarily sparse in co-prime arrays. In this letter, we restrain our focus on complex waveforms and present a framework under multiple s…
In this work, we consider the Direction-of-Arrival (DOA) estimation problem in a low-cost architecture where only one antenna as the receiver is aided by a reconfigurable intelligent surface (RIS). We introduce the one-bit RIS as a signal reflector to enhance signal transmission in non-line-of-sight (NLOS) situations and substantially simplify the physical hardware for DOA estimation. We optimize the beamforming scheme called measurement matrix to focus the echo power on the receiver with the coarse localization information of the targets as the prior. A beamforming scheme based on the modifie…
Sparse arrays have attracted a lot of interests recently for their capability of providing more degrees of freedom than traditional uniform linear arrays. For a mixture of circular and noncircular signals, most of the existing direction of arrival (DOA) estimation methods are based on various uniform arrays. Recently, a class of DOA estimation algorithms based on sparse arrays was developed for a mixture of circular and noncircular signals. To further improve its performance, in this work, a modified algorithm is presented, which can resolve the same number of signals, and simulation results a…
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…
The direction of arrival (DOA) estimation problem is addressed in this letter. A reconfigurable intelligent surface (RIS) aided system for the DOA estimation is proposed. Unlike traditional DOA estimation systems, a low-cost system with only one complete functional receiver is given by changing the phases of the reflected signals at the RIS elements to realize the multiple measurements. Moreover, an atomic norm-based method is proposed for the DOA estimation by exploiting the target sparsity in the spatial domain and solved by a semi-definite programming (SDP) method. Furthermore, the RIS elem…
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…
The paper considers direction of arrival (DOA) estimation from long-term observations in a noisy environment. In such an environment the noise source might evolve, causing the stationary models to fail. Therefore a heteroscedastic Gaussian noise model is introduced where the variance can vary across observations and sensors. The source amplitudes are assumed independent zero-mean complex Gaussian distributed with unknown variances (i.e. the source powers), inspiring stochastic maximum likelihood DOA estimation. The DOAs of plane waves are estimated from multi-snapshot sensor array data using s…
In the practical radar with multiple antennas, the antenna imperfections degrade the system performance. In this paper, the problem of estimating the direction of arrival (DOA) in multiple-input and multiple-output (MIMO) radar system with unknown mutual coupling effect between antennas is investigated. To exploit the target sparsity in the spatial domain, the compressed sensing (CS)-based methods have been proposed by discretizing the detection area and formulating the dictionary matrix, so an \emph{off-grid} gap is caused by the discretization processes. In this paper, different from the pre…
This letter addresses the estimation of directions-of-arrival (DoA) by a sensor array using a sparse model in the presence of array calibration errors and off-grid directions. The received signal utilizes previously used models for unknown errors in calibration and structured linear representation of the off-grid effect. A convex optimization problem is formulated with an objective function to promote two-layer joint block-sparsity with its second-order cone programming (SOCP) representation. The performance of the proposed method is demonstrated by numerical simulations and compared with the …
This paper proposes a new sparse array geometry for 2-D (azimuth and elevation) DOA (direction-of-arrival) estimation. The proposed array geometry is V-shaped sparse array and it is composed of two linear portions which are crossing each other. The degrees of freedom of the sparse array is enhanced by sparse sampling property. In this respect, V-shaped coprime (VCA) and V-shaped nested array (VNA) structures are developed. VCA can resolve both azimuth and elevation angles up to MN sources with 2M + N -1 sensors in each portion and the total number of sensors is 4M+2N-3. VNA can resolve O(N^2) …
Directions of arrival (DOA) estimation or localization of sources is an important problem in many applications for which numerous algorithms have been proposed. Most localization methods use block-level processing that combines multiple data snapshots to estimate DOA within a block. The DOAs are assumed to be constant within the block duration. However, these assumptions are often violated due to source motion. In this paper, we propose a signal model that captures the linear variations in DOA within a block. We applied conventional beamforming (CBF) algorithm to this model to estimate linear …
In this paper, a new signal processing framework is proposed, in which the array time samples are represented in DOA-frequency domain through a single stage problem. It is shown that concatenated array data is well represented in a $\mathbf{G}$ dictionary atoms space, where $\mathbf{G}$ columns correspond to pixels in the DOA-frequency image. We present two approaches for the $\mathbf{G}$ formation and compare the benefits and disadvantages of them. A mutual coherence guaranteed $\mathbf{G}$ manipulation technique is also proposed. Furthermore, unlike most of the existing methods, the proposed…
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…
In this work, combined calibration and DoA estimation is approached as an extension of the formulation for the Single Measurement Vector (SMV) model of self-calibration to the Multiple Measurement Model (MMV) case. By taking advantage of multiple snapshots, a modified nuclear norm minimization problem is proposed to recover a low-rank larger dimension matrix. We also give the definition of a linear operator for the MMV model, and give its corresponding matrix representation to generate a variant of a convex optimization problem. In order to mitigate the computational complexity of the approach…
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…
For a massive multiple-input-multiple-output (MIMO) system using intelligent reflecting surface (IRS) equipped with radio frequency (RF) chains, the multi-channel RF chains are expensive compared to passive IRS, especially, when the high-resolution and high-speed analog to digital converters (ADC) are used in each RF channel. In this letter, a direction of angle (DOA) estimation problem is investigated with low-cost ADC in IRS, and we propose a deep neural network (DNN) as a recovery method for the low-resolution sampled signal. Different from the existing denoising convolutional neural networ…
Estimating the directions of arrival (DOAs) of multiple sources from a single snapshot obtained by a coherent antenna array is a well-known problem, which can be addressed by sparse signal reconstruction methods, where the DOAs are estimated from the peaks of the recovered high-dimensional signal. In this paper, we consider a more challenging DOA estimation task where the array is composed of non-coherent sub-arrays (i.e., sub-arrays that observe different unknown phase shifts due to using low-cost unsynchronized local oscillators). We formulate this problem as the reconstruction of a joint sp…
A recent trend of research on direction-of-arrival (DOA) estimation is to localize more uncorrelated sources than sensors by using a proper sparse linear array (SLA) and the Toeplitz covariance structure, at a cost of robustness to source correlations. In this paper, we make an attempt to achieve the two goals simultaneously by using a single algorithm. In order to statistically efficiently localize a maximal number of uncorrelated sources, we propose an effective algorithm for the stochastic maximum likelihood (SML) method based on elegant problem reformulations and the alternating direction …
The problem of direction of arrival (DOA) estimation has been studied for decades as an essential technology in enabling radar, wireless communications, and array signal processing related applications. In this paper, the DOA estimation problem in the scenario with gain-phase errors is considered, and a sparse model is formulated by exploiting the signal sparsity in the spatial domain. By proposing a new atomic norm, named as GP-ANM, an optimization method is formulated via deriving a dual norm of GP-ANM. Then, the corresponding semidefinite program (SDP) is given to estimate the DOA efficient…
In this paper, we study the problem of estimating the direction of arrival (DOA) using a sparsely sampled uniform linear array (ULA). Based on an initial incomplete ULA measurement, our strategy is to choose a sparse subset of array elements for measuring the next snapshot. Then, we use a Hankel-structured matrix completion to interpolate for the missing ULA measurements. Finally, the source DOAs are estimated using a subspace method such as Prony on the fully recovered ULA. We theoretically provide a sufficient bound for the number of required samples (array elements) for perfect recovery. Th…
In this paper, we consider a reconfigurable intelligent surface (RIS)-assisted 3D direction-of-arrival (DoA) estimation system, in which a uniform planar array (UPA) RIS is deployed to provide virtual line-of-sight (LOS) links and reflect the uplink pilot signal to sensors. To overcome the mutually coupled problem between the beamforming design at the RIS and DoA estimation, we explore the separable sparse representation structure and propose an alternating optimization algorithm. The grid-based DoA estimation is modeled as a joint-sparse recovery problem considering the grid bias, and the Joi…
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.
Direction of Arrival (DOA) estimation of mixed uncorrelated and coherent sources is a long existing challenge in array signal processing. Application of compressive sensing to array signal processing has opened up an exciting class of algorithms. The authors investigated the application of orthogonal matching pursuit (OMP) for direction of Arrival (DOA) estimation for different scenarios, especially to tackle the case of coherent sources and observed inconsistencies in the results. In this paper, a modified OMP algorithm is proposed to overcome these deficiencies by exploiting maximum variance…
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…
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…
The purpose of this research is to employ non-uniform arrays in different active and passive sensing applications for both narrowband and wideband operations, while providing a multitude of array processing methodologies that assist in dealing with the different encountered challenges. The problem of direction-of-arrival (DOA) estimation using non-uniform arrays is considered. The different challenges that are treated include the reduction of the available degrees-of-freedom (DOFs), the presence of coherent targets, and the mutual coupling effect in practical antenna arrays. Multi-frequency op…
This paper proposes a compressed sensing-based high-resolution direction-of-arrival estimation method called gradient orthogonal matching pursuit (GOMP). It contains two main steps: a sparse coding approximation step using the well-known OMP method and a sequential iterative refinement step using a newly proposed gradient-descent method. To enhance the recoverability, we further propose an efficient projection matrix design method, which considers the constant modulus constraints imposed by the projection matrix hardware components. Simulation results show the effectiveness of the proposed met…
In this paper, we present a new scenario of direction of arrival (DOA) estimation using massive multiple-input multiple-output (MIMO) receive array with low-resolution analog-to-digital convertors (ADCs), which can strike a good balance between performance and circuit cost. Based on the linear additive quantization noise model (AQNM), the effect of low-resolution ADCs on the methods, such as Root-MUSIC method, is analyzed. Also, the closed-form expression of Cramer-Rao lower bound (CRLB) is derived to evaluate the performance loss caused by the low-resolution ADCs. The simulation results show …
Reconfiguring Sparse Apertures: Partial-Mobility Planar FAS for 2-D DOA Estimation
South China University of Technology（华南理工大学）；Queen Mary University of London（伦敦大学玛丽女王学院）；University of Missouri（密苏里大学）；Hong Kong Metropolitan University（香港都会大学）
In large-scale antenna systems, using one-bit analog-to-digital converters (ADCs) has recently become important since they offer significant reductions in both power and cost. However, in contrast to high-resolution ADCs, the coarse quantization of one-bit ADCs results in an irreversible loss of information. In the context of channel estimation, studies have been developed extensively to combat the performance loss incurred by one-bit ADCs. Furthermore, in the field of array signal processing, direction-of-arrival (DOA) estimation combined with one-bit ADCs has gained growing interests recentl…
