Journal of Jilin University(Engineering and Technology Edition) ›› 2025, Vol. 55 ›› Issue (3): 1093-1102.doi: 10.13229/j.cnki.jdxbgxb.20230578

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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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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

CLC Number: 

  • TN911

Fig.1

Smoothing function distribution chart"

Table 1

Comparison of algorithm calculation complexity"

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)

Table 2

Comparative analysis of principles and characteristics of different algorithms"

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

Fig.2

Effect of different smoothing functions on signal recovery"

Fig.3

Results of three-source DOA estimation"

Fig.4

Variation trend of root mean square error with SNR"

Fig.5

Variation trend of root-mean-square error with number of snapshots"

Fig.6

Variation trend of root mean square error with Alpha"

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