使用二階統計量之盲蔽訊號分離應用於非穩態信號

Blind Source Separation For Non-stationary Siguals Using Second Order Statistics

林家齊(Chia-Chi Lin)

指導教授 ： 馬榮健 ； 祁忠勇

國立清華大學/電機資訊學院/通訊工程研究所/碩士(2007年)

https://doi.org/10.6843/NTHU.2007.00442

摘要

中文摘要

在訊號處理的領域中，盲蔽訊號源分離(blind source separation, BSS)是一種不需要任何預先得到的資訊，包括混合矩陣(mixing matrix)與信號源，就能從獨立信號源的線性混合訊號將信號源還原出來的一種方法。最近幾年，盲蔽訊號分離在各個領域已經逐漸被受到重視，例如無線通訊系統(wireless communication)、生醫訊號處理(biomedical imaging processing)、多路徑通道估測與等化(multi-path channel identification and equalization)、麥克風陣列信號處理(multi-microphone array processing)等。現存處理非穩態信號的演算法中，大多藉由同時對角化所有的共變異數矩陣(covariance matrix)來估測通道。例如，利用梯度下降法來對角化所有共變異數矩陣，或者利用假設信號源是高斯分布並且最小化其高斯相似度(Gaussian likelihood)。在本篇論文中，我們提出了新而且簡單的盲蔽訊號分離技術，這個技術應用於非穩態信號(non-stationary signals)並且利用其二階統計量(second order statistics)。我們的方法有效率地利用信號模型的代數結構和子空間結構(subspace structures)在有雜訊干擾之下還原信號源。首先我們利用一些假設推導出盲蔽辨識性(blind identifiability)，利用此性質，推演出交互投影法(alternating projection)來估測通道。接下來推導出子空間投影法的雜訊消除法。電腦模擬顯示在與其他現存演算法比較之下，我們的演算法在中、低訊噪比(SNR)下會有較好的效能表現，而在高訊噪比的時候，我們的演算法就沒有某些演算法好，例如ACDC演算法，但我們的演算法依然有可以接受且合理的效能。

關鍵字

盲蔽訊號分離 ； 非穩態信號 ； 二階統計量

並列摘要

Abstract

In the signal processing area, blind source separation(BSS) is a method aiming to recover independent sources from their linear instantaneous mixtures without resorting to any prior knowledge, such as mixing matrices and sources. Recent years have seen increased attention given to blind source separation in many areas, including wireless communication, biomedical imaging processing, multi-microphone array processing, and so on. In this thesis, we
propose a new simple BSS technique that exploits second order statistics for non-stationary sources. Our technique utilizes the algebraic structure of the signal model and the subspace structures so as to efficiently recover sources with interference of noise. Computer simulations have demonstrated that, in comparison with other existent methods, our method has better performance in the regimes of low and medium SNRs. At high SNRs, our method is not as
promising methods such as the method called AC("alternating
columns")-DC("diagonal centers") algorithm, but it gives reasonable performance.

參考文獻

L. Tong, V.C. Soon, Y.F. Huang, and R. Lin, AMUSE: "A new blind identification

source separation technique using second-order statistics,"

IEEE Trans. Signal Processing, vol. 45, no. 2, pp. 434-444,

Seungjin Choi and O Young Lee, "Nonstationary Source Separation," IEEE Tencon, 1999.

Ali Mansour, "The Blind Separation of Non Stationary Signals