Blind Source Signal Separation and Retrieval

近年来，随着高速数字计算机的迅速发展，一次处理大量数据已成为可能。在这项研究中，我们考虑了盲反卷积（或盲均衡）的离散时间的线性信道系统的多个源信号驱动使用的输出信号的二阶和/或四阶累积量。本文提出了几种设计均衡器的方法，并通过数字仿真研究了这些方法的有效性。(1)第一种方法是从信道输出中盲识别信道系统，然后相应地设计均衡器。(2)第二种方法是直接从均衡器的输出设计均衡器，第二种方法被称为直接方法，这是优选的，因为它绕过了盲系统辨识过程，也绕过了信道系统的阶估计。我们致力于采用直接的方法进行研究，提出了解决盲解卷积问题的新准则。在此基础上，提出了实现盲解卷积的迭代算法，并通过数字仿真验证了算法的有效性，为FIR信道系统的盲解卷积奠定了系统理论基础。在这个基本的设置，我们表明，每一个均衡的信道系统有一个FIR不可还原paraunitary分解。基于这一事实，我们证明了任何可均衡的信道系统都可以通过一个称为白化器的滤波器化为一个仿酉FIR系统。我们认为，系统理论基础为设计进一步的均衡器提供了原则。

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 deconvolution ( or blind equalization) of a discrete-time linear channel system driven by multiple source signals using the second-order and/or the fourth-order cumulants of the output signals. We proposed several procedures for designing equalizers and investigated the effectiveness of the proposed procedures through digital simulations.Roughly speaking, there are two approaches to design equalizers.(1) The first approach is to blindly identify the channel system from the channel outputs and then to design an equalizer accordingly.(2) The second approach is directly to design an equalizer from the equalizer outputs.The second approach is called the direct approach, which is preferable, because it bypasses the process of blind system identification, and also bypasses the order estimation of the channel system. We devoted ourselves to take the direct approach in this research.We proposed new criteria for solving the blind deconvolution problem. Base on these criteria, we developed iterative algorithms for attaining blind deconvolution, and then we investigated the effectiveness of the proposed algorithms through digital simulations.Moreover, we established a system-theoretical foundation for the blind deconvolution of an FIR channel system. In this fundamental setting, we showed that every equalizable channel system has an FIR irredusible-paraunitary factorization. Based on this fact, we showed that any equalizable channel system can be reduced to a paraunitary FIR systemby a filter called a whitener. We believe that the system-theoretical foundation gives us a principle for designing futther advanced equalizers.