CIF: Small: Complex-Valued Statistical Signal Processing with Dependent Data

复值随机信号出现在许多科学和工程领域，如通信，雷达，声纳，海洋物理学，海洋学，光学，电磁学和声学。如果信号与其复共轭的互协方差函数为零，则该信号被称为正常信号，否则它是不正常信号。如果潜在的信号是不正确的，如果它们被视为不正确的，那么在性能上可以获得很大的好处。如果不能先验地知道感兴趣的信号是正确的还是不正确的，则必须从其噪声测量中获得该信息。现有的方法来确定的适当性是有限的情况下，测量组成的一系列独立的随机向量。实际的真实信号通常不包括独立的测量样本。这项研究的重点是设计来处理相关数据的方法。新的，有效的方法进行了研究，在这项研究中，重点是频域，不当的信号，和应用。信号被建模为平稳的，但不一定是高斯的。以下几点构成了本研究的核心。 (1)测试不适当的依赖多通道数据与任意分布不像过去的工作，这是有限的独立序列，通常假设为高斯。(2)随机复信号的比较，包括统计检验，以确定两个多通道随机信号是否具有相同的二阶统计量。这种测试在无线网络中的用户认证的应用进行了研究。(3)研究了在不需要结构化模型或高斯假设的情况下，利用广义似然比检验公式检测噪声中的多通道复信号。(4)本研究还涉及重新检查和修改所有上述方法，以使其对添加剂或创新离群值模型具有鲁棒性。

Complex-valued random signals arise in many areas of science and engineering such as communications, radar, sonar, geophysics, oceanography, optics, electromagnetics, and acoustics. If the cross-covariance function of the signal with its complex conjugate vanishes, the signal is called proper, otherwise it is improper. If the underlying signals are improper, much can be gained in performance if they are treated as improper. If it is not known apriori whether a signal of interest is proper or improper, this information must be obtained from its noisy measurements. Existing approaches to determination of propriety are limited to the case where the measurements consist of a sequence of independent random vectors. Practical real-life signals do not typically consist of independent measurement samples. This research focuses on approaches designed to handle dependent data. Novel, efficient approaches are investigated in this research with emphasis on frequency-domain, improper signals, and applications. The signals are modeled as stationary but are not necessarily Gaussian. The following thrusts form the core of this research. (1) Testing for impropriety of dependent multichannel data with arbitrary distribution unlike past work which is limited to independent sequences, typically assumed to be Gaussian. (2) Comparison of random complex signals involving statistical tests to ascertain if two multichannel random signals have the same second-order statistics. Application of such tests for user authentication in wireless networks is investigated. (3) Detection of multichannel complex signals in noise using a generalized likelihood ratio test formulation is studied, without requiring a structured model or Gaussian assumption. (4) This research also involves reexamination and modification of all aforementioned approaches to be robust with respect to additive or innovations outlier model.