Blind Source Signal Separation and Retrieval

近年来，随着高速数字计算机的飞速发展，一次处理大量数据已成为可能。在本研究中，我们考虑使用输出信号的二阶和/或四阶累积量对由多源信号驱动的离散时间线性信道系统进行盲反卷积（或盲均衡）。我们提出了几种设计均衡器的程序，并通过数字仿真研究了所提出程序的有效性。粗略地说，有两种设计均衡器的方法。(1)第一种方法是从通道输出盲目识别通道系统，然后设计相应的均衡器。(2)第二种方法是直接从均衡器输出设计均衡器。第二种方法被称为直接方法，这种方法更可取，因为它绕过了盲系统识别的过程，也绕过了信道系统的阶估计。在这项研究中，我们致力于采用直接的方法。我们提出了解决盲反卷积问题的新准则。基于这些准则，我们开发了实现盲反褶积的迭代算法，然后通过数字仿真研究了所提出算法的有效性。此外，我们还为FIR信道系统的盲反褶积建立了系统理论基础。在这种基本设置下，我们证明了每个可均衡信道系统都具有FIR不可还原-准酉分解。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称为白化器的滤波器简化为准准FIR系统。我们相信系统的理论基础为我们设计更先进的均衡器提供了一个原则。

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.