Fundamental Researches on Blind Source Signal Retrieval

近年来，随着高速数字计算机的快速发展，一次处理海量数据已成为可能。在本研究中，我们考虑利用被加性白噪声或有色高斯噪声污染的输出信号的二阶和/或四阶累积量，对离散时间线性系统进行盲辨识和盲解卷(或盲均衡)。我们首先讨论了不可观测有色信号驱动的多通道线性系统的辨识问题。结果表明，未知系统的传递函数矩阵可辨识到广义置换矩阵的乘法后。然后，我们考虑了多通道线性系统的盲解卷积(或盲均衡)问题，并提出了求解该问题的多级最大化准则和单级最大化准则。给出了多信道盲均衡的一个充要条件。我们提出了一种新的无约束多阶段准则来解决盲反卷积问题。基于这些多阶段准则，我们发展了多通道盲解卷积的迭代算法。为了与本项目中的理论结果进行比较，我们通过数字仿真研究了所提算法的有效性。

Recently, with the rapid development of high-speed digital computers, it is practically possible to processing a huge size of data all at once. In this research, we considered blind identification and blind deconvolution (or blind equalization) of a discrete-time linear system using the second-order and/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 deconvolution problem. Based on these multistage criteria, we developed iterative algorithms for multichannel blind deconvolution. In irde to corrobolate the theiretical results developed in this project, we investigated the effectiveness of the proposed algorithms through digital simulations.