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1. 长春理工大学 电子信息工程学院, 吉林 长春 130022
2. 吉林大学 通信工程学院, 吉林 长春 130022
3. 长春气象仪器研究所, 吉林 长春 130102
Received:08 January 2022,
Published Online:19 July 2023,
Published:31 May 2023
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Zebiao SHAN, Limin CHANG, Xiaosong LIU, et al. DOA Estimation Based on Approximate
Zebiao SHAN, Limin CHANG, Xiaosong LIU, et al. DOA Estimation Based on Approximate
针对现有基于压缩感知的DOA估计算法收敛速度慢、精度不高等问题
提出一种基于自然对数复合函数近似
l
0
范数的DOA估计算法。新算法采用一种自然对数复合函数来近似
l
0
范数
将求解
l
0
范数问题转化为近似
l
0
范数的最优化问题。采用牛顿迭代法获得自然对数复合函数(即近似
l
0
范数)的迭代表达式
通过内外双层循环的方法获得牛顿迭代的最优解
即通过外层循环控制函数逼近因子σ的大小
内层循环采用最陡梯度法对牛顿迭代表达式进行求解
经有限次迭代即可获得近似
l
0
范数的最优解
进而得到DOA的估计值。通过仿真实验验证新算法的有效性
结果表明新算法在单快拍条件下即可实现DOA有效估计
且与平滑
l
0
范数算法及其改进算法相比具有更快的计算速度和更高的估计精度。
A DOA estimation algorithm based on a natural logarithm compound function approximating
l
0
norm is proposed to address the issues of slow convergence and low accuracy of existing compressed-sensing-based DOA estimation algorithms. We transform the problem of solving the
l
0
norm into an optimization problem of approximating the
l
0
norm by using a natural logarithm compound function. The Newton iteration method is employed to obtain the iteration expression of the natural logarithm compound function (for approximating
l
0
norm).The optimal solution of Newton iteration is obtained through inside and outside double-loop iteration
where the outside loop controls the magnitude of function approximation f
actor σ
and the inside loop solves the Newton iteration expression using the steepest descent method. The optimal solution of the approximate
l
0
norm is obtained after finite iterations
and the estimated value of DOA can be obtained. Simulation results show that the proposed algorithm achieves effective DOA estimation under the condition of a single snapshot
and outperforms the existing smoothened
l
0
norm algorithm and its improved algorithms in terms of speed and accuracy.
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