在波达方向（Direction of Arrival，DoA）估计领域历经数十年研究后，最大似然（Maximum Likelihood，ML）算法如今在分辨能力方面仍具备最优性能。ML算法以多维搜索为代价，可显著降低阈值区域内的离群点产生机制，该区域的特征为每天线的快拍数和/或信噪比（signal to noise ratio，SNR）较低。本文旨在刻画ML算法在阈值区域的分辨能力。研究同时考察了条件版与无条件版ML算法，分析场景为天线数与快拍数均较大且量级相当的渐近情形。借助随机矩阵理论方法，本文证明两种代价函数的有限维分布在该渐近情形下服从高斯分布，并给出了对应渐近协方差矩阵的闭式表达式。这些结果可用于刻画分辨概率的渐近行为，分辨概率的定义为：在真实DoA处计算的代价函数值小于其在其他渐近局部极小值点处取值的概率。
英文摘要：
After decades of research in Direction of Arrival (DoA) estimation, today Maximum Likelihood (ML) algorithms still provide the best performance in terms of resolution capabilities. At the cost of a multidimensional search, ML algorithms achieve a significant reduction of the outlier production mechanism in the threshold region, where the number of snapshots per antenna and/or the signal to noise ratio (SNR) are low. The objective of this paper is to characterize the resolution capabilities of ML algorithms in the threshold region. Both conditional and unconditional versions of the ML algorithms are investigated in the asymptotic regime where both the number of antennas and the number of snapshots are large but comparable in magnitude. By using random matrix theory techniques, the finite dimensional distributions of both cost functions are shown to be Gaussian distributed in this asymptotic regime, and a closed form expression of the corresponding asymptotic covariance matrices is provided. These results allow to characterize the asymptotic behavior of the resolution probability, which is defined as the probability that the cost function evaluated at the true DoAs is smaller than the values that it takes at the positions of the other asymptotic local minima.
Reconfiguring Sparse Apertures: Partial-Mobility Planar FAS for 2-D DOA Estimation
South China University of Technology（华南理工大学）；Queen Mary University of London（伦敦大学玛丽女王学院）；University of Missouri（密苏里大学）；Hong Kong Metropolitan University（香港都会大学）
Super-resolution Multi-signal Direction-of-Arrival Estimation by Hankel-structured Sensing and Decomposition
Center for Connected Autonomy and AI（连接自主与人工智能中心）；Dept. of Electrical Engineering and Computer Science（电气工程与计算机科学系）；Florida Atlantic University（佛罗里达大学）；Air Force Research Laboratory（空军研究实验室）；AFRL/RI（空军研究实验室/RI）
