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

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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.