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

Abstract

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

CLC Number:

TN911.7

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.

Figures/Tables 11

Fig.1

Table 1

Algorithm flow"

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 $η ?$

Table 1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Table 2

Algorithm complexity"

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		$O (16 M 3 L 3 l o g ? μ)$

Table 2

Fig.9

References 17

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Two-dimensional DOA estimation algorithm for polarization-sensitive arrays based on atomic norm minimization

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