复值数据中异常信号子空间维数的确定
Determining the Dimension of the Improper Signal Subspace in Complex-Valued Data
摘要：
如果复值信号与其复共轭相关，则复值信号是不适当的。不适当信号子空间的维数，即，复值测量中不适当分量的数量是一个重要参数，并且在大多数应用中是未知的。在这封信中，我们介绍了两种方法来估计这个维度，一个基于信息理论的标准和一个基于假设检验。我们还提出了这些方法的降秩版本，这些方法适用于观测数量与数据维度相当甚至更小的情况。与其他用于确定模型阶数的技术不同，我们的技术也适用于存在加性有色噪声的情况。
英文摘要：
A complex-valued signal is improper if it is correlated with its complex conjugate. The dimension of the improper signal subspace, i.e., the number of improper components in a complex-valued measurement, is an important parameter and is unknown in most applications. In this letter, we introduce two approaches to estimate this dimension, one based on an information- theoretic criterion and one based on hypothesis testing. We also present reduced-rank versions of these approaches that work for scenarios where the number of observations is comparable to or even smaller than the dimension of the data. Unlike other techniques for determining model orders, our techniques also work in the presence of additive colored noise.
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