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首页> 外文期刊>Mathematical Problems in Engineering >Superresolution 2D DOA Estimation for a Rectangular Array via Reweighted Decoupled Atomic Norm Minimization
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Superresolution 2D DOA Estimation for a Rectangular Array via Reweighted Decoupled Atomic Norm Minimization

机译：通过重新重复解耦原子符号最小化的矩形阵列的超级级别2D DOA估计

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摘要

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 l(0) norm and a series of relaxation formulations. The atomic l(0) 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 l0 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.
机译：本文提出了一种基于原子L（0）规范的优化和一系列弛豫制剂的矩形阵列的超级化二维（2D）到达（DOA）估计算法。阵列响应的原子L（0）规范描述了源的最小数量，其源自原子标准最小化（ANM）问题。然而，通过使用ANM对于2D角度估计来产生高计算复杂性。虽然名为Demoupleed原子规范最小化（DAM）的改进算法具有降低的计算负担，但是在角度估计方面仍然相对较低。为了克服这些限制，我们提出了原子L0规范的直接最小化，这被证明是相当于正半纤维（PSD）形式的解耦等级优化问题。我们的目标是解决这个等级最小化问题，并恢复两个分离的脚趾矩阵，其中编码了方位的感兴趣的角度。由于等级最小化是NP难题，进一步提出了一种新颖的稀疏替代功能，以有效地近似于两个分离的等级函数。然后，通过上述松弛获得的新优化问题可以通过多种化最小化（MM）方法来实现。该算法的分辨率大大提高了，同时保持与大坝算法相同的计算复杂性。此外，在没有关于源的数量的情况下，可以使用单个快照进行角度估计，并且由于其迭代性质，算法对噪声稳健。此外，所提出的代理功能可以比现有功能更快地实现局部会聚。

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  • 来源
    《Mathematical Problems in Engineering》 |2019年第15期|16.1-16.13|共13页
  • 作者

    Liu Ming-Ming; Dong Chun-Xi; Dong Yang-Yang; Zhao Guo-Qing;

  • 作者单位

    Xidian Univ Sch Elect Engn Xian 710071 Shaanxi Peoples R China;

    Xidian Univ Sch Elect Engn Xian 710071 Shaanxi Peoples R China;

    Xidian Univ Sch Elect Engn Xian 710071 Shaanxi Peoples R China;

    Xidian Univ Sch Elect Engn Xian 710071 Shaanxi Peoples R China;

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