适用于二维阵列的无格稀疏波达方向估计算法

针对现有的适用于2维阵列的无格稀疏波达方向(DOA)估计方法性能不足的问题，该文提出一种新的方法。对2维阵列，从原子L0范数出发，证明其值等于一个以矩阵秩为目标函数的半定规划(SDP)问题的最优解。对该矩阵使用第1类有限阶贝塞尔函数近似表达，构造新的秩优化SDP问题。根据低秩矩阵恢复理论，对该SDP问题的目标函数使用log-det函数方法平滑替代，然后使用优化最小(MM)算法求解，最后通过(半)正定Toeplitz矩阵的范德蒙分解方法实现无格DOA估计。在MM算法求解模型时，使用样本协方差矩阵构造初始优化问题，减少算法迭代。仿真实验结果表明，相较于基于网格的MUSIC和其他无格DOA估计方法，该文方法具有更好的均方根误差(RMSE)性能与对相邻源的分辨能力；在快拍数充足且信噪比(SNR)较高时，适当的第1类贝塞尔函数阶数选择可以实现与较大阶数接近的RMSE性能，同时能减少运行时间。

Gridless Sparse Method for Direction of Arrival Estimation for Two-dimensional Array

For the fact that current gridless Direction Of Arrival (DOA) estimation methods with two-dimensional array suffer from unsatisfactory performance, a novel girdless DOA estimation method is proposed in this paper. For two-dimensional array, the atomic L0-norm is proved to be the solution of a Semi-Definite Programming (SDP) problem, whose cost function is the rank of a Hermitian matrix, which is constructed by finite order of Bessel functions of the first kind. According to low rank matrix recovery theorems, the cost function of the SDP problem is replaced by the log-det function, and the SDP problem is solved by Majorization-Minimization (MM) method. At last, the gridless DOA estimation is achieved by Vandermonde decomposition method of semidefinite Toeplitz matrix built by the solutions of above SDP problem. Sample covariance matrix is used to form the initial optimization problem in MM method, which can reduce the iterations. Simulation results show that, compared with on-grid MUSIC and other gridless methods, the proposed method has better Root-Mean-Square Error (RMSE) performance and identifiability to adjacent sources; When snapshots are enough and Signal-Noise-Ratio (SNR) is high, proper choice of the order of Bessel functions of the first kind can achieve approximate RMSE performance as that of higher order ones, and can reduce the running time.