Structured covariance matrix estimation in the presence of missing-(complex) data is addressed in this paper with emphasis on radar signal processing applications. After a motivation of the study, the array model is specified and the problem of computing the maximum likelihood estimate of a structured covariance matrix is formulated. A general procedure to optimize the observed-data likelihood function is developed resorting to the expectation-maximization algorithm. The corresponding convergence properties are thoroughly established and the rate of convergence is analyzed. The estimation technique is contextualized for two practically relevant radar problems: beamforming and detection of the number of sources. In the former case an adaptive beamformer leveraging the EM-based estimator is presented; in the latter, detection techniques generalizing the classic Akaike information criterion, minimum description length, and Hannan–Quinn information criterion, are introduced. Numerical results are finally presented to corroborate the theoretical study.

中文翻译：

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通过期望最大化对雷达应用的缺失（复杂）数据进行结构化协方差矩阵估计

本文讨论了存在缺失（复杂）数据时的结构化协方差矩阵估计，重点是雷达信号处理应用。在研究动机之后，指定阵列模型并制定计算结构化协方差矩阵的最大似然估计的问题。优化观测数据似然函数的一般程序是借助期望最大化算法开发的。彻底建立了相应的收敛性质并分析了收敛速度。估计技术适用于两个实际相关的雷达问题：波束成形和源数量检测。在前一种情况下，提出了一种利用基于 EM 的估计器的自适应波束成形器；在后者中，介绍了概括经典 Akaike 信息标准、最小描述长度和 Hannan-Quinn 信息标准的检测技术。最后给出数值结果以证实理论研究。