一种用于矩形阵列的二维波达方向估计方法

Method for estimation of the two-dimensional direction of wave arrival using the rectangular array

针对现有使用均匀矩形阵列或稀疏矩形阵列的二维无格波达方向估计方法的性能欠佳的问题,提出一种基于二阶特普利茨矩阵重构和二维旋转不变参数估计技术的无格波达方向估计方法。使用均匀矩形阵列或稀疏矩形阵列,对其接收信号的协方差矩阵进行二阶特普利茨结构表达,通过log-det稀疏测度与正定约束构造约束优化问题,并使用优化最小算法求解,最后通过二维旋转不变参数估计技术估计源的二维波达方向,即方位角与俯仰角。这种方法需要多次求解半定规划问题,计算复杂度相对较高,但能获得更好的波达方向估计性能。在仿真实验中,这种方法在均匀矩形阵列或稀疏矩形阵列条件下均有非常低的均方根误差,接近克拉美罗界,证明了其良好的波达方向估计性能。

To improve the performance of existing two-dimensional (2-D) grid-less irection of arrival(DOA) estimation methods using the uniform rectangular array(URA) or sparse rectangular array(SRA),a novel 2-D grid-less DOA estimation method based on doubly Toeplitz matrix reconstruction and 2-D ESPRIT is proposed.First,using URA or SRA,the doubly Toeplitz structure of the associated covariance matrix is established.Second,by applying the log-det sparse metric and semi-definite positive constraints,the constrained optimization problem is presented and solved by the majorization-minimization (MM) algorithm.Finally,the azimuth angles and elevation angles are estimated by the 2-D ESPRIT method.The proposed method needs to solve semi-definite programming (SDP) problems repeatedly,which results in a high complexity,while it always provides a superior performance of DOA estimation.In simulations,the proposed method has a very small root-mean-square error (RMSE) in the case of URA and SRA,which can approach the Crammer-Rao bound.Simulation results prove the good performance of the proposed method.