Low Complexity Method for Blind Source Extraction for Stationary Mixed Kurtosis Sign Signals

Blind source separation (BSS) or Independent component analysis (ICA) is a statistical analysis technique for expressing hidden components of random variables or signals. ICA is a generative model for the observed multivariate data. In this model the source signals are assumed to be nongaussian and mutually independent, and they are called the independent components of the observed data. The mixing environment is assumed to be linear and nonlinear, and also unknown. ICA can be seen as an extension to principal component analysis and factor analysis. ICA is a much more powerful technique, however, capable of finding the underlying factors or sources when these classic methods fail completely. The results of using the ICA technique are not only mutually independent but are also mutually decorrelated. The application of the ICA technique covers several essential areas such as speech separation, steganography or cryptography, data communication, double-talk detection or echo cancellation, sensor signal processing, microarray array processing, biomedical source processing, fault diagnosis, feature extraction, financial time series analysis, and data mining [2, 9, 12, 13, 20, 25]. The measurements of the ICA technique are given as a set of sequential or parallel signal separation, time dependency, stationary and non-stationary sources and linear and nonlinear mixtures. Many articles on ICA were published during the past two decades in a large number of journals and conference proceedings in the fields of signal processing [1, 2, 4, 6, 7, 12, 22, 25, 26, 27], artificial neural networks [3, 8, 11, 9, 10, 15, 17, 18, 23, 29], statistics [7, 13, 20], information theory [2, 17, 28, 30], and various application fields [12, 20]. In the literature, they proposed two significant points of research for ICA problems which are source density estimation—the probability density function of the sources— and the cost function or contrast function. The source density estimations are, for example, Edgeworth expansion [13] and Gram-Charlier expansion [2]. Approximation functions with low complexity computation were presented in consequence [12, 10, 27]. Contrast functions for ICA are based on information theories and high order statistics (HOS). Information theory concerns the signal information evaluations which are maximum likelihood estimation (ML) [6, 19], information maximization (Infomax) [5, 25], and mutual information (MI) [2, 12]. HOS are second order statistics 2 [1, 7] and 4 order cumulant [13, 21], and kurtosis [7, 12, 20, 25]. The significant issues of the ICA problem discussed in this dissertation are an approximation of a probability density function for demixing of super-gaussian and sub-gaussian channels, the practical objective or a contrast function, and an optimal unsupervised learning equation.