Superresolution 2D DOA Estimation for a Rectangular Array via Reweighted Decoupled Atomic Norm Minimization
TL;DR: This paper proposes a superresolution two-dimensional direction of arrival (DOA) estimation algorithm for a rectangular array based on the optimization of the atomic norm and a series of relaxation formulations that offers greatly improved resolution while maintaining the same computational complexity as the DAM algorithm.
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Abstract: This paper proposes a superresolution two-dimensional (2D) direction of arrival (DOA) estimation algorithm for a rectangular array based on the optimization of the atomic norm and a series of relaxation formulations. The atomic norm of the array response describes the minimum number of sources, which is derived from the atomic norm minimization (ANM) problem. However, the resolution is restricted and high computational complexity is incurred by using ANM for 2D angle estimation. Although an improved algorithm named decoupled atomic norm minimization (DAM) has a reduced computational burden, the resolution is still relatively low in terms of angle estimation. To overcome these limitations, we propose the direct minimization of the atomic norm, which is demonstrated to be equivalent to a decoupled rank optimization problem in the positive semidefinite (PSD) form. Our goal is to solve this rank minimization problem and recover two decoupled Toeplitz matrices in which the azimuth-elevation angles of interest are encoded. Since rank minimization is an NP-hard problem, a novel sparse surrogate function is further proposed to effectively approximate the two decoupled rank functions. Then, the new optimization problem obtained through the above relaxation can be implemented via the majorization-minimization (MM) method. The proposed algorithm offers greatly improved resolution while maintaining the same computational complexity as the DAM algorithm. Moreover, it is possible to use a single snapshot for angle estimation without prior information on the number of sources, and the algorithm is robust to noise due to its iterative nature. In addition, the proposed surrogate function can achieve local convergence faster than existing functions.
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Citations
Efficient Super-Resolution Two-Dimensional Harmonic Retrieval With Multiple Measurement Vectors
TL;DR: An efficient solution for super-resolution two-dimensional (2D) harmonic retrieval from multiple measurement vectors (MMV) based on the atomic norm minimization (ANM), which allows an efficient relaxation under certain conditions, which leads to low computational complexity of the same order as the 1D case.
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Crosscorrelation and DOA Estimation for L-Shaped Array via Decoupled Atomic Norm Minimization
TL;DR: In this paper, a two-phase method for 2D direction-of-arrival (DOA) estimation with L-shaped array based on decoupled atomic norm minimization (DANM) is proposed.
A 2D-DOA Sparse Estimation Method with Total Variation Regularization for Spatially Extended Sources
Zhihong Liu,Qingyu Liu,Zunmin Liu,Chao Li,Qixin Xu +4 more
TL;DR: A novel 2D-DOA sparse estimation method with total variation regularization is proposed for spatially extended sources. The method utilizes total variation regularization to group non-zero coefficients together and achieve sparsity. It has better robustness to noise, sparsity, and estimation speed with higher resolution than traditional methods.
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Two-dimensional grid-free compressive beamforming with spherical microphone arrays
TL;DR: In this article, a two-dimensional grid-free compressive beamforming method with spherical microphone arrays is proposed for 360° panoramic identification of acoustic sources, and the DOAs of sources are estimated through polynomial rooting and utilizing the dual optimal variables.
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