Study On ICA And Its Application To Array Signal Processing

Independent component analysis(ICA) is a method for finding underlying components from multivariate (multidimensional) statistical data. What distinguishes ICA from other methods is that it looks for components that are both statistically independent and non-Gaussian. The aim of ICA is to extract independent components given only observed data that are mixtures of the unknown sources without any knowledge of the mixed channel. This dissertation aims at the study of the theories and applications ICA. The main work can be summarized as follows:1. This dissertation reviews briefly the principles and the methods in the ICA. The prewhitening and the classify of signals is presented. The conditions of nonlinear function in ICA are discussed, and the ICA is compared with PCA.2. Based on the optimal estimation function, a method for estimation of the score function is developed. By using the Gaussian mixture model, an EM algorithm for approximating the probability density of the data is presented, and a stochastic gradient method is given to separate the independent components. To improved the accuracy and stability of the algorithm, an iterative method for estimating the pdf of data is presented, which can perform the separation of mixed sub-Gaussian and super-Gaussian sources. The optimal learning rate problem is studied, and the performance of the method is shown by computer simulations.3. For separation of complex valued signals, frequency domain implementations is better than time domain implementations. By studying the Hebbian learning and the fast fixed-point algorithm, a improved EHA is obtained. The simulations show the effectiveness of this method.4. The application of the independent bases in array signal processing is studied. The independent bases are denned for ICA. Using the independentbases in ICA, the DOA of signals can be estimated. Then the property of the prewhitening as a self-organizing beamformer is discussed.