| Research Abstract |
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.
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