协方差矩阵稀疏表示在网格失配波达方向估计中的应用

Application of Array Covariance Matrix Sparse Representation in Grid Mismatching DOA Estimation

该文利用了入射信号在空域的稀疏性,将波达方向(DOA)估计问题描述为在网格划分的空间协方差矩阵稀疏表示模型,并将其松弛为一个凸问题,从而提出了一种网格匹配下的交替迭代方法(AIEGM)。传统的基于稀疏重构的波达方向估计算法由于其模型的局限性,一旦入射角不在预先设定的离散化网格上,就会造成估计性能的急剧恶化。针对这个问题,该算法可以在离散化网格比较粗糙的前提下,通过交替迭代的方法求解一系列基追踪去噪(BPDN)问题,对于不在网格上的真实角度估计值进行修正,从而达到更精确的波达方向估计。仿真结果证明了AIEGM算法的有效性。

To estimate the true （unknown） directions which may not exactly fall on the preselected grid, a novel direction- of-arrival （DOA） estimation method based on the sparse spatial covarianee model and the off-grid representation of the steering vector with Taylor expansion is presented. Utilizing the spatial sparse property of incident signals, this paper for- mulates the DOA estimation problem as an array covariance matrix sparse representation model in a discretized grid, and re- laxes the model as a convex problem. Thus, an alternating iterative estimator with grid matching （AIEGM） is proposed. Because of the limitations of grid-based model, the estimation performance of conventional methods based on sparse signal reconstruction can be highly deteriorated if the true directions of arrival are not on the preseleeted discretized grid. The pro- posed algorithm solves a series of basis pursuit denoising （BPDN） problems on a coarse grid for that problem, and revises the DOA estimation results to achieve higher estimation accuracy and has lower computational complexity than the existing off-grid DOA estimation methods. Simulation results confirm the efficacy of AIEGM.