Study On Several Problems In Blind Source Separation

Blind source separation (BSS) consists of recovering mutually independent(uncorrelated) but unavailable source signals only from their mixtures without a priorknowledge of the channels. On one hand, BSS methods restore the source signalswithout lots of prior knowledge of them, which makes it a promising technique in signalprocessing fields. On the other hand, due to the generality of BSS model, most of themeasurements fit this model quite well. Therefore, the BSS methods have a vastapplication perspective. This dissertation focuses on the blind separation ofNon-stationary source signals, and the separation of simultaneous mixtures of bothSuper and Sub-Gaussian source signals. In addition, we investigate the step size(learning rate) determination technique for BSS. The primary contributions in thisdissertation are summarized as follows.1. The mixing signals models of BSS are reviewed, three of them and their basicassumptions are discussed. The fundamental information theory materials related toBSS is given, which consists of the conceptions of entropy, mutual information andnegative entropy, and their basic properties. The criterion of independentcomponent analysis (ICA) is described. The cost function is discussed based onmutual information, then the commonly used natural gradient algorithm isdescribed, and the local stability of the algorithm is also discussed.2. For the blind separation of mixtures of non-stationary source signals, the orthogonalnatural gradient algorithm derived from non-holonomic constraints is proposed toovercome the non-stationary. On this basis, dependency measurements of the outputsignals are deliberated, as well as the relationship between dependencymeasurements and step size, therefore a variable step size orthogonal naturalgradient algorithm is presented, which exploits the dependency measurements ofthe output signals to select a proper step size. Finally the effectivenesses ofalgorithms are all proved by simulation results.3. To solve the problem of blind separation of simultaneous mixtures of super and sub-gaussian signals, we propose kurtosis sign based natural gradient algorithm andprobability density function based Equivariant Adaptive Separation viaIndependence (EASI) algorithm. The former utilizes a compound probabilitydensity function to uniformly illustrate two kinds of source signals, and then estimates the kurtosis sign of output signals online to determine parameters in thenonlinear function; the latter directly estimates the probability density function ofoutput signals using the output samples. Simulation results show that both methodsachieve separations for the mixtures of sub and super-gaussian sources.4. Step size plays an important role in the convergence speed and steady stateperformance in adaptive BSS algorithms. Therefore, the second order dependencymeasurement and higher order dependency measurement are defined. Therelationship between the dependency measurements of outputs and the step size isalso analyzed, and a fuzzy inference system (FIS) for the determination of step sizeis constructed. By combining fuzzy step size technique with the classical adaptivealgorithms or the proposed algorithms, the fuzzy step size based adaptive BSSalgorithms are presented. Simulation results show that compared with fixed stepsize algorithms, the convergence speeds of the fuzzy step size based algorithms arefaster, and their steady-state errors are smaller.