A Sparse Array DOA Estimation Approach Based on Matrix Completion
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Abstract:
In order to improve the performance of direction of arrival (DOA) estimation for sparse array, this paper applies low-rank matrix completion theory to DOA estimation and proposes an improved matrix completion model and optimization solution. The proposed method utilizes the Hermitian and Toeplitz structural information of the observation matrix as a priori information. We split the augmented Lagrangian function and minimize one of the subproblems by Dykstra alternating projection which makes the completion matrices keep the Toeplitz structure and accomplishes the denoising of the known data. The simulation results show that the proposed method can effectively realize the reconstruction of sparse array, the performance of DOA estimation is excellent, and it can be applied to coherent sources.Keywords:
Matrix (chemical analysis)
Matrix Completion
Augmented Lagrangian method
Rank (graph theory)
Direction of arrival
Sparse array
Sparse linear array has some advantages over uniform linear array in some applications. However, it is well known that sparse array always suffers from manifold ambiguity, which has significant influence on direction‐of‐arrival (DOA) estimation and resolution. In this study, a new method based on the multiple signal classification (MUSIC) for resolving manifold ambiguities of uncorrelated sources by using semi‐circular substrate is proposed for DOA estimation of sparse array. Spurious MUSIC peak spectrums are generated because of a linear combination of the steering vectors of true DOAs. The main idea of the proposed method is to setup one or several semi‐circular medium substrates at the front of some elements. The phases of these elements are changed through the refractive index and the radii of those semi‐circular substrates. This treatment breaks down the previous linearity of the steering vectors for the array without adding the substrates. Thus, true DOA peaks can be discriminated according to this feature. Simulation results show good performance of the proposed method. Trivial and non‐trivial ambiguities are efficiently resolved.
Manifold (fluid mechanics)
Direction of arrival
Circular buffer
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Direction-of-arrival (DOA) estimation refers to the process of retrieving the direction information of several electromagnetic waves/sources from the outputs of a number of receiving antennas that form a sensor array. DOA estimation is a major problem in array signal processing and has wide applications in radar, sonar, wireless communications, etc. With the development of sparse representation and compressed sensing, the last decade has witnessed a tremendous advance in this research topic. The purpose of this article is to provide an overview of these sparse methods for DOA estimation, with a particular highlight on the recently developed gridless sparse methods, e.g., those based on covariance fitting and the atomic norm. Several future research directions are also discussed.
Direction of arrival
Sparse array
Radar signal processing
Array Processing
Sensor array
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The problem of multiple incident signals' direction of arrival (DOA) estimation for spatially separated polarisation sensitive array (SS-PSA) is studied. The proposed SS-PSA is a sparse uniform array with orthogonally oriented and spatially separated dipole-triads. The proposed array can reduce the array mutual coupling by using the spatially separated polarised antenna instead of conventional spatially collocated polarised antenna. Moreover, the DOA estimation accuracy can be improved greatly due to the extended aperture offered by sparse array. Computer simulation results verify the effectiveness of the proposed algorithm.
Sparse array
Direction of arrival
Collinear antenna array
Sensor array
Angle of arrival
Aperture (computer memory)
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The problem of recovering low-rank matrix from only a subset of observed entries is known as the matrix completion problem. Many problems arising in compressive sensing, image processing, machine learning, can be usefully cast as this problem. In this paper, we propose an extended linearized augmented Lagrangian method of multipliers for the problem, and prove its global convergence. We show that all the resulting subproblems have closed-forms solutions. Finally, some numerical experiments are conducted to show its efficiency.
Augmented Lagrangian method
Matrix Completion
Matrix (chemical analysis)
Rank (graph theory)
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In two-dimensional direction of arrival (2D-DOA) estimation, planar arrays can estimate the elevation and azimuth angles simultaneously. However, many planar array topologies such as billboard, L-shaped, T-shaped, and 2D nested arrays suffer from mutual coupling that results from the small separation between the physical sensors (antennas), which limits the estimation capability of the sensor array. In an attempt to reduce mutual coupling between sensors, this article proposes sparse billboard and T-shaped arrays in which the number of closely separated sensors is significantly reduced. In addition to extending the CRB for fourth order coarray, this article also derives closed-form expressions for the sensor locations and the number of consecutive lags or the uniform degrees of freedom (uDOF), in the fourth-order difference coarray (FODC). Simulation results demonstrate the robustness of the proposed sparse arrays against mutual coupling.
Direction of arrival
Planar array
Robustness
Sparse array
Sensor array
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In this paper we consider the problem of direction of arrival (DOA) estimation with a sparse linear array, characterized by several separated subarrays. The proposed ambiguity resolution algorithm based on the MUSIC algorithm or conventional beamformer improves previous disambiguation scheme. A new ESPRIT-based DOA estimator is obtained for linear subarray-based sparse array. Simulation results are included to show the performance of proposed estimator.
Direction of arrival
Sparse array
Multiple signal classification
Angle of arrival
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Citations (26)
Sparse array design has been advantageous in re¬ducing receiver data, system's hardware and computational costs by the careful placement of available sensors such that the ob¬jective function is optimized. In this paper, we investigate sparse array design for maximizing the Signal-to-Interference plus noise ratio (SINR) which arises frequently in many applications. We propose a design approach which does not necessarily require any a priori knowledge of the interference environment and operates directly on the received data statistics. The data dependent design is achieved by adopting a low rank matrix completion, which ensures the availability of full data correlation matrix against all possible locations. The regularized successive convex approximation (SCA) is utilized to realize sparse beamformer design. We compare the performance of sparse array design with the commonly used arrays in terms of maximizing the SINR and show the effectiveness of the proposed algorithm under limited received data snapshots.
Sparse array
Matrix Completion
Matrix (chemical analysis)
Signal-to-interference-plus-noise ratio
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A method based on sparse array is applied to direction-of-arrival estimation of passive radar in this paper to increase the number of resolvable sources and improve the direction-of-arrival estimation performance for coprime array. The virtual symmetric non-uniform linear array of coprime array based on passive radar signal model is introduced. Considering the impact of direct wave, extensive cancellation algorithm is used to cancel the direct wave, with the conventional MUSIC with spatial smoothing algorithm and virtual aperture filling applied on the sparse array of passive radar; the resolution of target is low in the low signal-noise-ratio. To effectively improve the estimation of the target under the low signal-noise-ratio, a noise subspace reconstruction method is proposed. The proposed direction-of-arrival estimation method can improve the direction-of-arrival estimation performance of passive radar. The simulations are provided to demonstrate the effectiveness of the proposed method.
Direction of arrival
Sparse array
Smoothing
Coprime integers
Sensor array
Signal subspace
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Recently, extensive researches focus on the joint estimation of carrier frequency and direction-of-arrival, whereas the heavy computation burden and affordable hardware cost are always required therein. To alleviate the problem, we propose a relaxed coprime array based two-stage estimator, which can sequentially detect the frequencies and direction-of-arrival for multiple targets. Guided by the closed-form robust algorithm, this relaxation yields a higher array sparsity compared with existing sparse arrays. Specifically, the first stage aims to achieve the classification of the frequency and angle remainders arising from temporal-spatial undersampling, which is realized by combining spectrum correction with pattern clustering. By incorporating the closed-form robust Chinese Remainder Theorem into the remainder classification result, we obtain all the frequencies and direction-of-arrival in the second stage. Both performance analysis and numerical results were conducted to verify the effectiveness of the proposed estimator in the multi-target case.
Direction of arrival
Coprime integers
Sparse array
Chinese remainder theorem
Angle of arrival
Sensor array
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In this article, we mainly propose two improved coprime arrays (CAs) on array motion, ImCAAM1 and ImCAAM2, for direction of arrival (DOA) estimation, which can generate a longer consecutive difference co-array. Both the designs can solve the problem that part of lags, not surrounded by holes in difference co-array, have invalid use, when considering moving sparse array. The first scheme primarily implements two operations: compressing the interelement spacing of one subarray and staggering a certain distance between two subarrays. Two operations make contributions to increasing consecutive degrees of freedom (cDOF). Whereas the second one is able to further fill the remaining holes located at both the ends of virtual array. With the interelement spacing compress factor, equal to the number of elements of another subarray, and re-staggering the distance between subarrays, we can eventually obtain a longer full-populated virtual array. Finally, numerical simulations are presented to verify the efficacy of the proposed sparse array geometries using the subspace-based DOA estimation algorithm in terms of cDOF, spatial spectrum, and DOA estimation accuracy.
Coprime integers
Direction of arrival
Sparse array
Sensor array
Direction finding
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Citations (5)