Research On Blind Signal Processing And Separation

As a new signal processing technology, blind signal processing(BSP) is developed in the last century. After years of expansion on theory and practice, it has become an important technology of signal processing. Independent component analysis(ICA) is a tool for blind signal processing, which has no prior knowledge of the transmission channel state, but only use the statistical method to separate the mixed-signals. With development of blind signal processing, some new problems appear gradually at present. The main motivation of this research is to foucus these problems, which including: robustness of fixed point algorithm; outliers processing in ICA data; ICA for multiple noises; the entending of complex valued ICA algorithm and the application of ICA in other area. The main results of this thesis can be summarized as:1. For the algorithm of fast fixed-point for real signals in independent component analysis that using the non-polynomial functions in iteration, a robust contrast function based on maximum negentropy approximation is proposed. In the conventional study of ICA, especially in interation of fast fixed-point algorithm, there are three non-polynomial functions proposed by Hyv?rinen for negentropy approximation. However, if outliers mixed in source signals or in the observed data, their performance will become poor or even valid. Based on the polynomial expansion, we give a more robust non-polynomial function. It can matain the effectiveness of separation performance for ICA whether the signals mixed with outliers or not.2. The outliers mixed in observed signals are the second studied topic. Because outliers can damage the statistical properties of the data, if these signals processed directly after whiten that will lead to a poor separation result. Combining with the robust estimation theory, we put forward to process the data by nonlinear projection analysis before the whitening, and construct observation signals about the outliers threshold decision method, then giving a method of removing outliers and signal reconstruction, therefore, the algorithm can avoid the influence of outliers.3. We study the problem of noisy ICA in real signal. Using the characteristic of higher order statistics that out influence of Gaussian noise, the joint approximate diagonalization eigen-matrices(JADE) method based on four order accumulations is proposed to use in two dimensional mixed situation. With Givens rotation method, it can fast to realize the two order matrix diagonalization, which reduces the influence of Gauss on the separation performance. However, with the increasing of signal’s dimension, JADE leads to a slow convergence and amount of computation. Although the real noise ICA algorithm has a fast convergence speed, however, it only discuss the Gauss white noise but without considering the case of impulse noise. In this work, we extend the noisy ICA problem to a more complex situation that the signals are mixed with both impulsive noise and Gaussian noise. Based on analysis of whiting projection observed data, we give the threshold of impulse. Combining with the way of outliers analysis and statistics, a dynamic pass filter is also given for processing impulsive components and the way of reconstructing signals. Because using the principle of average computing, the proposed method will not damage the statistical properties of the data. So it can keep the conventional noisy ICA algorithm work effectively when the observed signal do not contain impulse noise.4. Extending the complex valued ICA algorithm to the general noisy situation. With analysis of the covariance of observed data and noise, we give the complex valued component of the deviation with respect to remove noisy components. Using the Newton iterative method, we derive complex valued signal separation algorithm to the noisy situation. If it occurs in noise free condition, the proposed algorithm will become to the noise free complex valued ICA fixed-point algorithm format that proposed by Hyv?rinen. The simulation results show that the proposed method has its effective separation.5. Based on the ICA method, the JADE algorithm is proposed to used for the optical polarization division multiplexed optical orthogonal frequency division multiplexing(PDM-OOFDM) systems for blind polarization demultiplex. In conventional polarization multiplexing system, constant modulus algorithm(CMA) is used for blind demixing polarization multiplexing. However, this method requires multiple filter coefficients update, the convergence time is longer, and CMA algorithm for polarization multiplexing can lead to the singularity probelm. Combining with the classical ICA method, JADE algorithm is proposed used to PMD-OOFDM system of blind de-polarization multiplexed signals. Using this method, one can separate the receiving terminals that mixed with Gaussian white noise signal components, and it also improves the system performance of the polarization signals. Further, it avoids the problem of singularity for CMA. The simulation results show that this method can work effectively.