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、地球物理、海洋学、光学、电磁学和声学。如果信号及其复共轭的交叉协方差函数消失，则称该信号为固有信号，否则称其为反常信号。如果底层信号不正确，如果将其视为不正确，则可以在性能上获得很大的收益。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。现有的确定适当性的方法仅限于测量由一系列独立的随机向量组成的情况。实际生活中的信号通常不由独立的测量样本组成。本研究的重点是处理依赖数据的方法。本研究着重于频域、不当讯号及应用，探讨新颖、有效的方法。信号被建模为平稳的，但不一定是高斯的。以下几个要点构成了本研究的核心。(1)测试任意分布的依赖多通道数据的不适当性，不像过去的工作，仅限于独立序列，通常假设是高斯分布。(2)随机复信号的比较，涉及统计检验，以确定两个多通道随机信号是否具有相同的二阶统计量。研究了该测试在无线网络用户认证中的应用。(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杂信号。(4)本研究还涉及对上述所有方法的重新检查和修改，以使其在加性或创新离群值模型方面具有鲁棒性。

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.