论文标题
关于有条件和无条件最大似然估计的分辨率概率
On the Resolution Probability of Conditional and Unconditional Maximum Likelihood DoA Estimation
论文作者
论文摘要
经过数十年的到达方向研究（DOA）估计，如今的最大似然（ML）算法在分辨率能力方面仍然提供了最佳性能。以多维搜索为代价，ML算法在阈值区域中的异常生产机制显着降低，在该区域，每个天线的快照数量和/或信号与噪声比（SNR）的数量较低。本文的目的是表征阈值区域中ML算法的分辨率能力。 ML算法的条件和无条件版本均在渐近状态下研究，在渐近方案中，天线的数量和快照的数量均大，但幅度较大。通过使用随机矩阵理论技术，两种成本函数的有限维分布均显示为在该渐近状态下的高斯分布，并提供了相应的渐近协方差矩阵的封闭形式表达。这些结果允许表征分辨率概率的渐近行为，该行为的定义为在真doas上评估的成本函数的概率小于其在其他渐近局部最小值位置上所采用的值。
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.
