吉林大学学报(工学版) ›› 2025, Vol. 55 ›› Issue (3): 1093-1102.doi: 10.13229/j.cnki.jdxbgxb.20230578

• 通信与控制工程 • 上一篇    

Alpha稳定分布噪声下基于近似l0范数稀疏重构的波达方向估计

单泽彪1,2,3(),薛泓垚1,刘小松1(),姚瑞广1,陈广秋1   

  1. 1.长春理工大学 电子信息工程学院，长春 130022
    2.吉林大学 通信工程学院，长春 130022
    3.长春气象仪器研究所，长春 130012
  • 收稿日期:2023-06-08 出版日期:2025-03-01 发布日期:2025-05-20
  • 通讯作者: 刘小松 E-mail:zbshan@126.com;liuxs@cust.edu.cn
  • 作者简介:单泽彪（1986-），男，副教授，博士.研究方向：阵列信号处理，压缩感知技术.E-mail：zbshan@126.com
  • 基金资助:
    吉林省自然科学基金项目(20250102050JC)

Direction of arrival estimation based on approximate l0 norm sparse reconstruction under Alpha stable distribution noise

Ze-biao SHAN1,2,3(),Hong-yao XUE1,Xiao-song LIU1(),Rui-guang YAO1,Guang-qiu CHEN1   

  1. 1.School of Electronic and Information Engineering，Changchun University of Science and Technology，Changchun 130022，China
    2.College of Communication Engineering，Jilin University，Changchun 130022，China
    3.Changchun Meteorological Instrument Research Institute，Changchun 130012，China
  • Received:2023-06-08 Online:2025-03-01 Published:2025-05-20
  • Contact: Xiao-song LIU E-mail:zbshan@126.com;liuxs@cust.edu.cn

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摘要：

针对Alpha稳定分布噪声背景下基于压缩感知的波达方向（DOA）估计方法在低信噪比、小快拍数条件下估计性能较差的问题，提出了一种基于近似l0范数稀疏重构的DOA估计算法。首先利用分数低阶统计量结合KR子空间法，重塑分数低阶矩矩阵抑制Alpha稳定分布噪声，构造稀疏测向模型。然后通过指数族分布函数分析其平滑性和陡峭性，构造最优的平滑函数近似l0范数求解稀疏测向模型。同时针对离格效应造成的算法误差，将偏移量引入在格稀疏测向模型，对导向矢量矩阵进行一阶泰勒级数展开，建立离格稀疏测向模型，并利用交替迭代法计算信号分量和偏移量，进而得到离格DOA估计值。最后，通过仿真实验验证了本文算法在Alpha稳定分布噪声背景下DOA估计的有效性和优越性。

关键词: 信息处理技术, 波达方向估计, 稀疏重构, Alpha稳定分布, 近似l0范数

Abstract:

Aiming at the problem of poor estimation performance of the compression-aware DOA estimation method based on compression in the context of Alpha stable distribution noise under the conditions of low signal-to-noise ratio and small number of fast beats， a DOA estimation algorithm based on approximate l0 norm sparse reconstruction is proposed. The fractional low-order statistic combined with KR subspace method is used to reshape the fractional low-order moment matrix to suppress the Alpha stable distribution noises and construct the sparse measurement direction model. The smoothness and steepness of the function are analyzed by the exponential family distribution function， and a optimal smoothing function approximating the l0 norm is constructed to solve the sparse measured direction model. For the algorithm error caused by the off-grid effect， the offset is introduced into the in-grid sparse vectorization model， and the first-order Taylor series expansion is performed on the guide vector matrix to establish the off-grid sparse vectorization model. The algorithm uses the alternating iteration method to calculate the signal components and offsets to obtain the off-grid target DOA estimates. The effectiveness and superiority of the proposed algorithm for direction angle estimation in the background of Alpha stable distribution noise is verified by simulation experiments.

Key words: information processing techniques, direction of arrival estimation, sparse reconstruction, Alpha stable distribution, approximate l0 norm

中图分类号: 

  • TN911

图1

平滑函数分布图"

表1

算法计算复杂度对比"

算法复杂度
ESL0O(min(M2,Q))+O(5K)
EOGSL0O(min(M2,Q))+O(7K)
R-OMPO(Q(2M)2)+O(Q)
R-OGOMPO(Q(2M)2)+O(Q)+O(4K)

表2

不同算法原理及特性对比分析"

不同算法算法原理特性适用场景
ESLO近似l0范数计算复杂度低，估计精度高在格
EOGSL0近似l0范数+最小二乘交替迭代计算复杂度低，估计精度高离格
R-OMP正交匹配追踪计算复杂度高，估计精度低在格
R-OGOMP正交匹配追踪+最小二乘交替迭代计算复杂度高，估计精度低离格

图2

不同平滑函数对信号恢复效果图"

图 3

三信源DOA估计结果"

图4

均方根误差随信噪比变化趋势图"

图5

均方根误差随快拍数变化趋势图"

图6

均方根误差随特征指数变化趋势图"

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