Contributions to independent component analysis, sensor array and complex valued signal processing
Array and multichannel signal processing techniques are key technologies in wireless communications, radar, sonar and biomedical systems. In array signal processing, signals from multiple sources arrive simultaneously at a sensor array, so that each sensor array output contains a mixture of source signals. The multichannel output is then processed to provide information about the parameters of interest, e.g. the Direction-of-Arrival (DOA) of the source signals or the mixing system in the case of independent component analysis (ICA). Application areas include communications, radar, sonar and biomedicine. An important aspect is that the multichannel output is commonly complex-valued. In this thesis, new statistical procedures and several analytical results for array and multichannel signal processing are developed and derived. Also theoretical performance bounds of estimators are established. Experimental results showing reliable performance are given on all of the presented methods. In the area of array signal processing, the work concentrates on beamforming, high-resolution DOA estimation and estimation of the number of sources. The methods developed are robust in the sense that they are insensitive to largely deviating observations called outliers and to non-Gaussian noise environments. In the area of complex-valued ICA, we propose two new classes of demixing matrix estimators that add a new dimension of flexibility and versatility to complex-valued ICA since distinct estimators within the same class can have largely different statistical (robustness, accuracy) properties. Hence one can choose an estimator from the class that yields the best results to the specific application at hand. A simple closed form expression for the Cramér-Rao bound (CRB) is derived for demixing matrix estimation problem as well. Its usefulness is illustrated with a simulation study. In this thesis, the mathematical and statistical aspects of complex-valued signal processing are also addressed. Probability models, estimation bounds and novel statistics characterizing complex-valued signals are proposed. Specifically, complex elliptically symmetric (CES) distributions are proposed and studied, CRB for constrained and unconstrained complex-valued parameter estimation are derived, detectors of circularity are proposed and statistics such as circularity quotient and complex cumulants are derived.