一种基于加权改进平滑l_(0)范数的DOA估计方法

A DOA estimation method based on weighted improved smoothing l_(0) norm

为了解决基于平滑l_(0)范数最小化方法在低信噪比、少快拍下求解波达方向(DOA)估计精度不高的问题,提出一种加权改进平滑l_(0)范数方法。首先将空间进行等角度均匀划分,构造稀疏表示的DOA估计模型,并利用奇异值分解获取接收信号子空间;由于直接求取压缩感知l_(0)范数是非确定性多项式难(NP-hard)问题,提出一种逼近程度更高的复合优化平滑函数去拟合l_(0)范数,并采用加权机制,加速稀疏解的获取;选择一个恰当的递减序列(ρ_(1),ρ_(2)…ρ_(k)),针对每个ρ,通过不断迭代采用最速下降法求解所提复合优化函数的最小解,最终将重构信号映射到空间划分网格,从而得到DOA估计值。仿真结果表明,该方法相比原始的平滑l_(0)范数最小化方法、L1-SVD和正交匹配追踪(OMP)算法在低信噪比、少快拍下具有更优的DOA估计性能。

In order to solve the problem of low accuracy of direction of arrival(DOA)estimation based on smooth l_(0)norm minimization method under low signal-to-noise ratio and few snapshots,a weighted improved smooth l_(0)norm method is proposed.Firstly,the space is evenly divided at equal angle to construct a sparse DOA estimation model,and the received signal subspace is obtained by singular value decomposition.Since it is non-deterministic polynomial hard(NP-hard)to obtain the compressed sensing norm directly,a composite optimization smoothing function with higher approximation is proposed to fit the norm,and a weighting mechanism is used to accelerate the acquisition of sparse solution;An appropriate sequence (ρ1,ρ2…ρk) is determined.For each ρ,the steepest descent method is used to solve the minimum value of the proposed composite optimization function through continuous iteration.Finally,the reconstructed signal is mapped to the spatial grid,so as to obtain the DOA estimation value.Simulation results show that compared with the original smoothing norm minimization method,L1-SVD and orthogonal matching pursuit(OMP)algorithm,the algorithm has better DOA estimation performance under low signal-to-noise ratio and less snapshots.