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Study of the Algorithms of Blind Source Separation Based on the Models of the Systems

Author: YangLiu
Tutor: XieShengLi
School: South China University of Technology
Course: Signal and Information Processing
Keywords: Blind source separation Wigner-Ville distribution parallel factor analysis mutually correlated sources precoders
CLC: TN911.7
Type: PhD thesis
Year: 2013
Downloads: 65
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Abstract


Blind source separation (BSS) is a hot topic in signal processing domain in the last two decades. It attracts more and more attentions because of its wide applications in speech identification, neural networks, digital communication, biomedicine and so on. Although a lot of important research results and theories have been achieved, there still exist some problems, such as how to apply Time-Frequency (TF) representation to underdetermined BSS? How to use PARAllel FACtor Analysis (PARAFAC) to deal with BSS, even though the sources are not independent on each other? How to tackle the BSS of Single-Input-Multiple-Output (SIMO) Finite-Impulse-Response (FIR) system, which practically exists in digital communication field? How to separate mutually correlated sources? This thesis explores BSS problems with different models from the following four aspects:First, it presents a novel algorithm dealing with underdetermined BSS by using TF representation. A kind of quadratic TF distribution, Wigner-Ville Distribution (WVD). is used to convert the time-domain BSS model into TF domain model. Unlike traditional Sparse Component Analysis (SCA) methods, the proposed algorithm takes the negative value of the auto WVD of the sources into account while using Single Source Domain (SSD) assumption to estimate the mixing matrix. Then after extracting all the auto-term TF points, it utilizes Khatri_Rao product of two matrices to find out the auto WVD value of sources at every auto-term TF point. It does not impose any constraints on the number of active sources at any auto-term TF points as long as the number of sources is less than twice the number of observed mixtures. Moreover, further discussion about the extraction of auto-term TF points is made to verify the effectiveness of the proposed algorithm.Second, it introduces a new TF approach to the underdetermined BSS using the PARAFAC of third-order tensors. PARAFAC is usually applied to BSS under Independent Component Analysis (ICA) assumption which is not necessary in the presented algorithm. This algorithm exploits the diagonal structure of the Spatial TF Distribution (STFD) matrices of the sources at the auto-term TF points and constructs a third-order tensor using the STFD matrices of the observed mixtures. Then the channel and the sources can be estimated directly at the same time by parallel factor decomposition. Thus unlike traditional two-stage methods, there is no noise propagation from the estimation of mixing matrix to the estimation of sources.Third, it analyzes the blind equalization in SIMO FIR system in digital communication, and presents a novel algorithm by exploiting the Second-Order Statistics (SOS) of the channel outputs. Usually, SOS-based blind equalization is carried out via two stages. In the first stage, the SIMO FIR channel is estimated using a blind identification method, such as the recently developed Truncated Transfer Matrix (TTM) method. In the second stage, an equalizer is derived from the estimate of the channel to recover the source signal. However, this type of two-stage approach does not give satisfactory blind equalization result if the channel is ill-conditioned, which is often encountered in practical applications. On the contrary, the proposed algorithm can estimate the equalizer directly without knowing the channel impulse response, thus it can work well even in the case that the channel is ill-conditioned. Besides, it proves that the TTM method does not work under some situations.Finally, it considers the separation of mutually correlated sources in the over-determined/determined BSS, and presents an effective improvement of a recently developed algorithm. The improvement employs the novel precoders combining with the novel z transform to deal with blind equalization. Similar to the third algorithm proposed in this thesis, it needs not to estimate the channel at first. Besides, the improvement decreases the filter order of the precoders to only one, which simplifies the system greatly, reduces the computational complexity and improves the performance of the algorithm to a large extent.

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