摘要
盲信号分离是信号处理领域的一个重要研究课题,在语音识别、神经网络、数字通信、生物医学等领域都具有广泛的理论基础和应用前景,因而在短短二十多年内就已经取得了非常瞩目的研究成果。尽管该课题发展迅速,其依然存在如下问题：如何采用时频表示算法分离欠定混叠模型下的源信号?如何将平行因子分析工具应用到非独立元假设的盲分离领域?如何处理数字通信系统中真实存在的单输入-多输出有限脉冲响应信道的盲分离问题?如何分离相关源信号?本文依据所考虑的盲分离模型的不同,从如下几个方面继续探讨了盲分离问题：
第一,详细研究了应用时频表示处理欠定混叠盲分离问题的算法。选用二次时频变换魏格纳-威利分布(WVD:Wigner-Ville Distribution)变换作为稀疏表示,将欠定模型由时域变换到时频域。与传统的稀疏算法不同,该算法在采用单源区间估计混叠矩阵时充分考虑了源信号的WVD的负值。在将所有的自项时频点都提取出来后,该算法采用Khatri_Rao矩阵乘积估计源信号的WVD取值。该算法对在任意时频点取值非零的源信号的个数完全不作限制,只要求源信号的个数和观测信号的个数满足一定的不等式关系。此外,该算法对自项时频点的提取也做了详细的讨论。
第二,介绍了如何将平行因子分析工具应用到非独立信号的欠定混叠盲分离的一种算法。传统的平行因子分析与盲分离相结合的算法通常都是基于“源信号相互独立”的前提假设的,但该算法对源信号的相关性没有任何限制。该算法利用源信号在自项时频点的空间时频分布矩阵的对角线结构,结合平行因子分析,构造出一个三阶张量。通过平行因子分解算法,即可从该三阶张量中将信道和源信号的时频表示取值同时准确地估计出来。因此,与传统的二步法不同,该算法中不会产生噪声累积和传递,即：信道辨识不准确不会导致源信号恢复不准确。
第三,分析了在通信系统中实际存在的单输入-多输入有限脉冲响应系统的盲均衡问题,并提出了一种基于信号二阶统计量的算法。传统的算法通常分两步求解,即先将信道估计出来,再根据辨识信道求解均衡器,比如截断传输矩阵(TTM:Truncated Transfer Matrix)算法。本文提出的算法可以直接求解均衡器,因此即使在系统很不稳定的情况下,该算法依旧能取得很理想的效果,即鲁棒性很好。此外,本文还证明了TTM算法在某些参数设置下完全无效,而本文算法则不受这些参数限制。
最后,考虑了在超定/适定盲分离模型下如何分离相关源信号的问题,并提出了一种对已有算法改进效果显著的新算法。该算法引用概念新颖的预编码器,将信号从时域变换到z域后再对系统做盲均衡,并不需要将信道先估计出来。此外,该算法将预编码器的阶数降至最低,即一阶。这样做的好处有两点：简化了系统,需要处理的数据量明显减少；极大地提高了算法的性能和鲁棒性。
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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