Continuous sparse recovery for direction of arrival estimation with co-prime arrays (original) (raw)
Related papers
Direction of Arrival Estimation Using Co-Prime Arrays: A Super Resolution Viewpoint
IEEE Transactions on Signal Processing, 2014
We consider the problem of direction of arrival (DOA) estimation using a newly proposed structure of nonuniform linear arrays, referred to as co-prime arrays, in this paper. By exploiting the second order statistical information of the received signals, co-prime arrays exhibit O(M N ) degrees of freedom with only M + N sensors. A sparsity based recovery method is proposed to fully utilize these degrees of freedom. Unlike traditional sparse recovery methods, the proposed method is based on the developing theory of super resolution, which considers a continuous range of possible sources instead of discretizing this range into a discrete grid. With this approach, off-grid effects inherited in traditional sparse recovery can be neglected, thus improving the accuracy of DOA estimation. In this paper we show that in the noiseless case one can theoretically detect up to M N 2 sources with only 2M + N sensors. The noise statistics of co-prime arrays are also analyzed to demonstrate the robustness of the proposed optimization scheme. A source number detection method is presented based on the spectrum reconstructed from the sparse method. By extensive numerical examples, we show the superiority of the proposed method in terms of DOA estimation accuracy, degrees of freedom, and resolution ability compared with previous methods, such as MUSIC with spatial smoothing and the discrete sparse recovery method.
Direction of Arrival Estimation Using Augmentation of Coprime Arrays
Information, 2018
Recently, direction of arrival (DOA) estimation premised on the sparse arrays interpolation approaches, such as co-prime arrays (CPA) and nested array, have attained extensive attention because of the effectiveness and capability of providing higher degrees of freedom (DOFs). The co-prime array interpolation approach can detect O(MN) paths with O(M + N) sensors in the array. However, the presence of missing elements (holes) in the difference coarray has limited the number of DOFs. To implement co-prime coarray on subspace based DOA estimation algorithm namely multiple signal classification (MUSIC), a reshaping operation followed by the spatial smoothing technique have been presented in the literature. In this paper, an active coarray interpolation (ACI) is proposed to efficiently recovering the covariance matrix of the augmented coarray from the original covariance matrix of source signals with no vectorizing and spatial smoothing operation; thus, the computational complexity reduce...
Sparse DOA Estimation Based on Multi-Level Prime Array with Compression
IEEE Access, 2019
A signal emitter can be located using diverse types of direction finding (DF) techniques. One of the most widely used techniques is the direction of arrival (DOA) estimation using antenna arrays. An array configuration that can increase the degrees of freedom (DOF) or the number of estimated sources is desired. Multi-level prime array (MLPA) uses multiple uniform linear subarrays where the number of elements in the subarrays is pairwise coprime integer. Compared with nested and coprime arrays, MLPA requires smaller aperture size which is important in mobile applications. Different MLPA configurations can be constructed for a given number of antennas and the one that maximizes the DOF is exploited. These configurations have a difference coarray with large number of consecutive lags and few holes. The number of consecutive lags can be increased by properly compressing the inter-element spacing of one subarray under a fixed number of antennas and without changing the aperture size. This paper proposes a new compressed MLPA configuration and demonstrates its performance in sparse DOA estimation. The resultant array, MLPA with compressed subarray (MLPAC), can have a hole-free difference coarray as in nested array case. MLPAC can estimate larger number of sources using both MUSIC and sparse reconstruction algorithms. Mutual coupling between sensors has also been evaluated. Simulation results confirm the achievable DOF and the advantage of the proposed configuration in DOA estimation.
Journal of telecommunications and information technology, 2021
Regular fully filled antenna arrays have been widely used in direction of arrival (DOA) estimation. However, practical implementation of these arrays is rather complex and their resolutions are limited to the beamwidth of the array pattern. Therefore, higher resolution and simpler methods are desirable. In this paper, the compressed sensing method is first applied to an initial fully filled array to randomly select the most prominent and effective elements which are used to form the sparse array. To keep the dimension of the sparse array equal to that of the fully filled array, the first and the last elements were excluded from the sparseness process. In addition, some constraints on the sparse spectrum are applied to increase estimation accuracy. The optimization problem is then solved iteratively using the iterative reweighted l 1 l 1 l 1 norm. Finally, a simple searching algorithm is used to detect peaks in the spectrum solution that correspond to the directions of the arriving signals. Compared with the existing scanned beam methods, such as the minimum variance distortionless response (MVDR) technique, and with subspace approaches, such as multiple signal classification (MUSIC) and ESPIRT algorithms, the proposed sparse array method offers better performance even with a lower number of array elements and in severely noisy environments. Effectiveness of the proposed sparse array method is verified via computer simulations.
2021
Date of publication (dd/mm/yyyy): 03/04/2021 Abstract – In this paper, a new method for the direction of arrival (DoA) estimation using sparse representation of covariance matrix is proposed by using a non-uniform linear array. By vectoring of covariance matrix of nonuniform linear array, a new vector will be derived. This vector is similar to received vector of a virtual uniform linear array with a large number of antennas. As the covariance matrix of this vector is rank one, then the DoA of one source will be estimated. An approach to solve this problem is spatial smoothing technique. In this method, the obtained array is divided into multiple sub-arrays and the covariance matrix of each sub-array will be estimated. Using the average of sub-arrays covariance matrix, a new full rank covariance matrix will be obtained. By quantizing the continuous angle space into a discrete set, DoA estimation can be modeled as a compressed sensing problem. The DoA of sources will be estimated by m...
Sparse direction-of-arrival estimation for two sources with constrained antenna arrays
2017 10th International Conference on Electrical and Electronics Engineering (ELECO), 2017
Compressive sensing (CS), multiple signal classification (MUSIC), and estimation of signal parameter via rotational invariance techniques (ESPRIT) are among the main used estimation techniques for direction of arrival (DOA). Though, the practical implementation of DOA techniques in handheld wireless devices is limited by the number of antennas and the spacing between them. A robust DOA estimation technique is needed to overcome the different impairments in the communication channel. This paper mainly focuses on DOA estimation of two sources in the presence of practical limitations. A comparison between important DOA estimation algorithms is presented including: Beamforming, Capon, MUSIC, and First-norm singular value decomposition (l1-SVD).
IEEE Transactions on Signal Processing, 2005
We address the problem of maximum likelihood (ML) direction-of-arrival (DOA) estimation in unknown spatially correlated noise fields using sparse sensor arrays composed of multiple widely separated subarrays. In such arrays, intersubarray spacings are substantially larger than the signal wavelength, and therefore, sensor noises can be assumed to be uncorrelated between different subarrays. This leads to a block-diagonal structure of the noise covariance matrix which enables a substantial reduction of the number of nuisance noise parameters and ensures the identifiability of the underlying DOA estimation problem. A new deterministic ML DOA estimator is derived for this class of sparse sensor arrays. The proposed approach concentrates the ML estimation problem with respect to all nuisance parameters. In contrast to the analytic concentration used in conventional ML techniques, the implementation of the proposed estimator is based on an iterative procedure, which includes a stepwise concentration of the log-likelihood (LL) function. The proposed algorithm is shown to have a straightforward extension to the case of uncalibrated arrays with unknown sensor gains and phases. It is free of any further structural constraints or parametric model restrictions that are usually imposed on the noise covariance matrix and received signals in most existing ML-based approaches to DOA estimation in spatially correlated noise.
A Review of Sparse Sensor Arrays for Two-Dimensional Direction-of-Arrival Estimation
IEEE Access, 2021
Two-dimensional (2D) arrays are fundamental to localization applications. Specifically, sparse arrays can provide superior direction-of-arrival (DoA) estimation performance with limited number of sensors. There has been increased interest in the research community in designing 2D sparse arrays with performance improvement and complexity reduction. The research efforts are uncoordinated resulting in some repetitions and sometimes conflicting claims. After introducing 2D sparse arrays and their importance, this paper establishes the 2D-DoA estimation model and consolidates the performance metrics. An extensive literature overview of sparse arrays for 2D-DoA estimation is presented with an attempt to categorize existing works. The examined arrays include parallel arrays, L-shaped, V-shaped, hourglass, thermos, nested planer, and coprime planner, to name a few. Existing designs are compared in terms of required number of sensors, degrees of freedom (DOF), algorithm used, associated complexity and aperture size. The focus is on describing the sparse arrays, yet some specific details on DoA estimation algorithms are provided for selected array geometries. Fundamental problems of 2D-DoA estimation are outlined and existing solutions to alleviate these problems are discussed. This should be useful in predicting the estimation performance and required complexity; thus, aiding the decision of selecting a sensor geometry for DoA estimation. This review serves as a starting point for researchers interested in exploring or designing new 2D sparse arrays. It also helps to identify the gaps in the field and avoids unnecessary minor design modifications.
IEEE Transactions on Aerospace and Electronic Systems, 2000
This work addresses the problem of direction-of-arrival (DOA) estimation of multiple sources using short and dynamic sensor arrays. We propose to utilize compressive sensing (CS) theory to reconstruct the high-resolution spatial spectrum from a small number of spatial measurements. Motivated by the physical structure of the spatial spectrum, we model it as a sparse signal in the wavenumber-frequency domain, where the array manifold is proposed to serve as a deterministic sensing matrix. The proposed spatial CS (SCS) approach allows exploitation of the array orientation diversity (achievable via array dynamics) in the CS framework to address challenging array signal processing problems such as left-right ambiguity and poor estimation performance at endfire. The SCS is conceptually different from well-known classical and subspace-based methods because it provides high azimuth resolution using a short dynamic linear array without restricting requirements on the spatial and temporal stationarity and correlation properties of the sources and the noise. The SCS approach was shown to outperform current superresolution and orientation diversity based methods in single-snapshot simulations with multiple sources.
Sparse Bayesian Learning for DOA Estimation Using Co-Prime and Nested Arrays
2018 IEEE 10th Sensor Array and Multichannel Signal Processing Workshop (SAM), 2018
Sparse Bayesian learning (SBL) has been used to obtain source direction-of-arrivals (DoAs) from uniform linear array (ULA) data. The maximum number of sources that can be resolved using a ULA is limited by the number of sensors in the array. It is known that sparse linear arrays such as co-prime and nested arrays can resolve more sources than the number of sensors. In this paper we demonstrate this using SBL. We compute the mean squared error in source power estimation as various parameters are varied.