Abstract
Blind source separation (BSS) is a popular topic in many practical applications such as beamforming (array processing), image/speech processing and biomedical signal analysis with multiple sensors at receivers. The multidimensional observation vector is assumed to be given by x[n]=As[n]+w[n](1.1)where A is a PxK mixing matrix,s[n] is a Kx1 source signal vector and w[n] is a Px1 additive noise vector. The key objective of BSS is to separate and estimate the source signals s[n] from the received measurement vector x[n] without any knowledge of the mixing matrix.Some existing second-order statistics (SOS) methods, such as Tong et al.’s algo-rithm for multiple unknown signals extraction (AMUSE) method [1] and Belouchrani et al.’s second-order blind identification (SOBI) [2], are two-step approaches includ-ing a whitening procedure followed by the determination of an unknown unitary ma-trix. In the whitening procedure, the noise variance has to be accurately estimated to structure the whitening matrix. However, when the noise variance is either unknown or cannot be estimated, these methods may no longer be effective. After the whiten-ing procedure, an unknown unitary matrix needs to be identified in order to estimate the mixing matrix A. The AMUSE algorithm performs diagonalization of the whit-ened covariance matrix at only one time lag not equal to zero to estimate the unitary matrix. However, it is not possible to determine a time lag such that the eigenvalues of the whitened covariance matrix, i.e., the autocorrelation functions of source signals, are distinct. When the spectra of the source signals are very similar, joint diagonali-zation of more than one whitened covariance matrices with different time lags will improve robustness. Based on this concept, the SOBI algorithm simultaneously di-agonalizes [3] a set of the whitened covariance matrices. Thus it can be seen that these SOS methods require more strict condition on the spectra of the source signals which corresponds to the second-order identifiability condition found in [4].A Higher-order statistics (HOS) method such as Ding et al.’s kurtosis maximization algorithm (KMA) [5], designs a weight vector through the gradient type optimization algorithm with slow convergence rate and high computational load to extract a tem-porally independent or colored source signal. In view of these shortcomings, Chi and Chen proposed a fast KMA (FKMA) [6] with a fast convergence rate and low com-putational load. Unlike SOS methods, these HOS methods only permit the source signals to be non-Gaussian but do not have any condition on the spectra of the source signals. Although the FKMA (including the KMA) is theoretically applicable to both the cases of temporally independent and colored source signals, we empirically found that the performance of the FKMA significantly degrades as the source signals are temporally colored especially when the signal-to-noise ratio (SNR) is low. An insight of this observation is that the FKMA may converge to an undesired solution under low SNR due to the relatively small absolute kurtosis of the temporally colored source signal. In this thesis, a novel space-time BSS algorithm, the blind source ex-traction-inverse (BSE-INV) algorithm, is proposed, which involves a blind beam-forming processing using the FKMA followed by a blind deconvolution processing using the SISO-IFC [14], to improve the convergence property and also the perform-ance of the FKMA for the case of temporally colored source signals.This thesis is organized as follows. In Chapter 2, FKMA is reviewed and the ef-fects of the temporally colored source signals on FKMA are described. In chapter 3, the proposed blind source extraction-inverse (BSE-INV) algorithm is presented for BSS. In Chapter 4, some simulation results are provided to justify the efficacy and feasibility of the proposed BSE-INV algorithm. Finally, some conclusions and future researches regarding this thesis are given in Chapter 5.