基于自然对数复合函数近似l_(0)范数的DOA估计  

DOA Estimation Based on Approximate l_(0)Norm of Natural Logarithm Composite Function

作　　者：单泽彪[1,2,3] 常立民 刘小松 王宇祥[1] SHAN Zebiao;CHANG Limin;LIU Xiaosong;WANG Yuxiang(School of Electronic and Information Engineering,Changchun University of Science and Technology,Changchun 130022,Jilin,China;College of Communication Engineering,Jilin University,Changchun 130022,Jilin,China;Changchun Meteorological Instrument Research Institute,Changchun 130102,Jilin,China)

机构地区：[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

出　　处：《兵工学报》2023年第5期1521-1528,共8页Acta Armamentarii

基　　金：国家自然科学基金项目(61571462);吉林省自然科学基金项目(YDZJ202301ZYTS412)。

摘　　要：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 factorσ,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.

关 键 词：波达方向估计 压缩感知 近似l_(0)范数 自然对数复合函数 

分 类 号：TN911[电子电信—通信与信息系统]