宽带模态不变性：宽带DOA估计的一种新方法
Wideband Modal Orthogonality: A New Approach for Broadband DOA Estimation
摘要：
传感器阵列的宽带波达方向（DOA）估计技术已被广泛研究。然而，需要事先信息的数量和方向的源或要求沉重的计算负荷，使大多数这些技术在实践中不太有用。本文提出了一种低复杂度的基于子空间的宽带信号DOA估计框架--宽带模态正交（WIMO），并据此设计了两种DOA估计器。首先，在均匀谱情况下，给出了空时协方差矩阵（STCM）的一个封闭近似。与非零特征值相关联的STCM的特征向量是宽带源在给定带宽和方向上的模态分量。WIMO的思想是从近似的STCM中提取期望DOA处的这些特征向量，并测试它们与估计的噪声子空间的正交性。在非均匀谱的情况下，WIMO思想可以通过数值积分来近似STCM。幸运的是，STCM近似和模态提取可以离线执行。WIMO算法无需谱分解、聚焦等常规处理步骤，无需先验信息，即可实现DOA估计。几个数值例子进行比较的WIMO性能与国家的最先进的方法。仿真结果表明，提出的两种DOA估计器在分辨率和估计误差的概率以及几个数量级的运行时间加速方面取得了优异的性能。
英文摘要：
Wideband direction of arrival (DOA) estimation techniques for sensors array have been studied extensively in the literature. Nevertheless, needing prior information on the number and directions of sources or demanding heavy computational load makes most of these techniques less useful in practice. In this paper, a low complexity subspace-based framework for DOA estimation of broadband signals, named as wideband modal orthogonality (WIMO), is proposed and accordingly two DOA estimators are developed. First, a closed-form approximation of spatial-temporal covariance matrix (STCM) in the uniform spectrum case is presented. The eigenvectors of STCM associated with non-zero eigenvalues are modal components of the wideband source in a given bandwidth and direction. WIMO idea is to extract these eigenvectors at desired DOAs from the approximated STCM and test their orthogonality to estimated noise subspace. In the non-uniform spectrum case, WIMO idea can be applied by approximating STCM through numerical integration. Fortunately, STCM approximation and modal extraction can be performed offline. WIMO provides DOA estimation without the conventional prerequisites, such as spectral decomposition, focusing procedure and, a priori information on the number of sources and their DOAs. Several numerical examples are conducted to compare the WIMO performance with the state-of-the-art methods. Simulations demonstrate that the two proposed DOA estimators achieve superior performance in terms of probability of resolution and estimation error along with orders of magnitude runtime speedup.
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