Fundamental Researches on Statistical Systems Modeling

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Recently, with the rapid development of high-speed digital computers, there has been increasing interests in applying higher-order statistics called cumulants to several modeling problems of dynamic or static systems. In this research, we consedered blind idntification and blind deconvolution (or blind equalization) of a discrete-time linear system using the third-order or the fourth-order cumulants of the output signals contaminated by additive white or colored Gaussian noise. We first dealt with the problem of identification of multichannel linear systems driven by unobservable colored signals. It was shown that the transfer function matrix of an unknown system is identified up to post-multiplication of a generalized permutation matrix. Then we considered the blind deconvolution (or blind equalization) problem of multichannel linear systems, and propose a multistage maximization criterion and a single-stage maximization criterion for solving this problem. We derived a necessary and sufficient condition for multichannel blind equalization. We proposed a new unconstrained multistage criterion for solving the blind deconbolution problem. Based on these multistage criteria, we developed iterative algorithms for multichannel blind deconvolution.