基于原子范数最小化的极化敏感阵列二维波达方向估计算法

doi:10.13229/j.cnki.jdxbgxb.20230791

摘要/Abstract

摘要：

为解决极化敏感阵列中压缩感知类波达方向（DOA）估计算法产生的网格失配带来估计精度下降的问题，本文针对单偶极子阵列在原子范数最小化（ANM）理论的基础上提出一种二维DOA和极化参数的联合估计算法。首先，利用正交极化敏感阵列的特性，分别构造不同极化方向的接收模型，并证明该模型可以消除极化参数的影响，符合ANM模型。其次，通过求解半正定规划问题得到一个半正定的Toeplitz矩阵，随后基于矩阵束算法恢复DOA信息；最后，利用DOA信息和广义特征值理论恢复出极化参数。通过仿真实验验证了本文算法的有效性和优越性。

关键词: 无网格波达方向估计, 正交极化敏感阵列, 原子范数最小化, 网格失配

Abstract:

To address the challenge of estimation accuracy degradation resulting from off-grid caused by compressive sensing-like direction of arrival （DOA） estimation algorithm in polarization-sensitive arrays， this paper presents a joint estimation algorithm for two-dimensional DOA and polarization parameters utilizing the theory of atomic norm minimization （ANM） applied to a single dipole array. Firstly， the proposed algorithm constructs receiving models for different polarization directions using the orthogonal polarization sensitive array's characteristics， which can accommodate the influence of polarization parameters and adhere to the ANM model. Secondly， the algorithm solves a positive semi-definite programming problem to obtain a positive semi-definite Toeplitz matrix， from which DOA information is recovered using the matrix-pencil algorithm. Lastly， the polarization parameters are retrieved using the DOA information and the generalized eigenvalue theory. The effectiveness and superiority of the proposed algorithm are demonstrated through simulation experiments.

Key words: gridless direction of arrival estimation, orthogonal polarization sensitive arrays, atomic norm minimization, off-grid

中图分类号:

TN911.7

陈涛,李敏行,赵立鹏. 基于原子范数最小化的极化敏感阵列二维波达方向估计算法[J]. 吉林大学学报(工学版), 2025, 55(5): 1772-1779.

Tao CHEN,Min-xing LI,Li-peng ZHAO. Two-dimensional DOA estimation algorithm for polarization-sensitive arrays based on atomic norm minimization[J]. Journal of Jilin University(Engineering and Technology Edition), 2025, 55(5): 1772-1779.

图/表 11

图1

表 1

算法流程"

基于ANM的极化敏感阵列二维DOA估计算法
输入	阵列接收到的多快拍信号
输出	入射信源的DOA估计结果 $? ?$ 和 $θ ?$ 及极化参数估计结果 $γ ?$ 和 $η ?$
步骤1	将极化阵列接收信号分为 $x 1$ 和 $x 2$
步骤2	构建如式（7）所示的DOA估计模型
步骤3	构建式（13）中的半正定规划问题
步骤4	通过解该半正定规划问题得到最优解Toeplitz矩阵 $T o e p (u)$
步骤5	对Toeplitz矩阵进行Vandermonde分解，根据式（14）和式（15）恢复入射信号的DOA估计信息 $? ?$ 和 $θ ?$
步骤6	构建如式（17）所示的优化问题
步骤7	根据式（19）计算广义特征向量 $e$
步骤8	根据式（20）计算极化域估计结果 $γ ?$ 和 $η ?$

表 1

图2

图3

图4

图5

图6

图7

图8

表 2

算法复杂度"

算法		复杂度
$l 1$ -SVD		$O (16 M 3 P 3)$
秩亏MUSIC		$O [8 M 2 L + 16 M 3 + 240 (4 M 2 - 2 M K)]$
ANM		$O (16 M 3 L 3 l o g ? μ)$

表 2

图9

参考文献 17

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