【作者】 杨家轩；

【导师】 贾传荧；

【作者基本信息】 大连海事大学 ， 交通信息工程及控制， 2008， 博士

【摘要】 独立分量分析(ICA)作为统计信号处理和神经网络等领域的新方法,因具有优异的盲辨识、特征提取和表示能力,已经日益广泛地应用于通信、语音提取、图像增强和医学信号处理等领域。码分多址(CDMA)信号模型与ICA模型形式相似,将ICA适用于多用户检测问题,直接从期望用户的观测数据出发,利用ICA可以将用户信息序列从被多址干扰(MAI)污染的混合信号中分离出来。本文的主要工作如下:1.利用矩阵理论推导了独立分量分析的克拉美罗性能界。克拉美罗性能界是估计理论中无偏参数估计方差的下界,是评价参数估计性能最常用的度量。基于瞬时ICA模型推导了分离矩阵W的Fisher信息矩阵。为了准确衡量算法的分离精度,定义了增益矩阵G,并推导了关于G的克拉美罗性能界。克拉美罗性能界为独立分量分析算法性能评价提供了一种衡量准则。2.提出了广义高斯变量生成算法和自适应的FastICA算法。基于伽玛分布随机变量,综合运用随机变量变换法和舍选抽样法,提出了一种简便的广义高斯分布随机变量生成算法。该算法计算简单,通过调整分布参数的值,可产生具有任何形状参数和任何方差的广义高斯分布随机变量。为了克服传统FastICA算法中要依据先验信息选定合适的非线性激活函数的缺点,提出了一种自适应FastICA算法。该算法基于广义高斯模型,通过高斯模型的形状参数的优化和分离矩阵迭代结合,实现了激活函数向源信号评价函数的逼近,可以同步实现不同类型源信号的估计。并给出了算法的稳定性分析和仿真实验。3.提出了非参数广义高斯核ICA算法。当参数ICA算法不能分离信号时,基于广义高斯核函数,提出了非参数广义高斯核ICA算法。它在源信号密度函数全“盲”情况下,能实现正确分离,解决了如何选取估计信号评价函数的难题,可用于任意分布的源信号。广义高斯核函数可以根据源信号的高阶统计自适应地改变窗宽以适应不同源信号的要求。4.提出了基于负熵准则的FastICA盲多用户检测算法。该算法使用四次幂函数,把基于负熵的非高斯性测度转化为信号峰度的形式,降低了计算量。同时,算法充分考虑了各用户信号的统计独立性,在下行链路干扰用户的扩频码未知情况下,把目标用户的扩频码作为训练序列,并用于初始化FastICA算法的分离向量,使用随机梯度法进行优化计算,获得了优异的符号估计性能。对算法的计算复杂度的分析可以看出,计算量随着接收数据长度和用户数的增加而增加。在同步CDMA信道中与传统匹配滤波器、MMSE检测算法比较,MAI较低的时该算法检测性能与MMSE的性能接近;随着MAI增加,其性能明显优于MMSE算法。5.提出了基于非参数似然比准则的盲多用户算法。当建立的概率密度模型不准确时,参数ICA算法算法有时不能分离源信号,为此,提出了非参数ICA的检测算法。直接由观测信号样本出发,使用高斯核函数估计分离信号的概率密度函数,计算非参数似然函数比,结合梯度下降法和似然比准则进行目标用户的信号检测。通过试验仿真,与其它算法比较,结果表明该算法抑制多址干扰的能力介于FastICA检测和MMSE检测之间。更多还原

【Abstract】 Independent component analysis(ICA) is a new method in statistical signal processing and neural networks.As a result of its outstanding performance in blind identification and feature extraction or representation,ICA has been used wildly in various fields,for instance,communication systems,speech processing,image enhancement,and biomedical signal processing.Because the linear ICA model has the same form as the CDMA signal model,it can be used in multi-user detection.Utilizing ICA,the desired user information sequence can be separated from the mixture signals polluted by MAI.The main research works of this paper are presented as follows:1.The Cramer-Rao lower bound of ICA is established.Cramer-Rao lower bound is the variance lower bound of unbiased parameters estimation in estimation theory and the common measurement of evaluation performance of parameters estimation.A detail derivation of the Fisher information matrix for demixing matrix w is provided. Gain matrix G is defined,which can give the accuracy measurement of the estimation of the original signals.Cramer-Rao lower bound for gain matrix is deduced in the end and can give a general performance criterion for independent component analysis.2.Algorithm for generating generalized Gaussian distribution random variable and adaptive FastlCA algorithm are proposed.In order to simply create random variables of generalized Gaussian distribution with any shape parameter and any variance,an algorithm is proposed by combining transformations of random variable method and abandon-selection sampling method.The algorithm is derived by proper transformations based on gamma distribution random variables.The algorithm is computationally simple.Random variables of generalized Gaussian distribution with any shape parameter and any variance can be generated easily by adjusting the numerical values of these parameters.Different from traditional FastICA algorithms where the activation function is pre-designed by prior knowledge and fixed for all sources even in different types,an adaptive FastlCA algorithm is presented based on the generalized Gaussian model where the iterations for the paracmeters of the generalized Gaussian and the demixing vector are combined.The stability analysis is also given as well as computer simulation demonstrations.3.Nonparametric generalized Gaussian kernel ICA algorithm is designed.When parametric ICA algorithms can perform suboptimally or even fail to separate the source signals,nonparametric generalized gaussian kernel ICA algorithm can be used,which is based on generalized Gaussian kernel function,and is truly blind to the source signals.Nonparametric density estimation is directly evaluated from the observed signal samples.An important problem,of choose nonlinear functions as the probability density function estimation of the sources is solved in ICA.The algorithm changes window width adaptively in terms of higher statistics so that it is able to separate a wide range of source signals.4.A FastICA blind multi-user detection algorithm based on Neg-entropy is implemented.Function with power 4 is adopted as non-quadratic function,therefore, neg-entropy based non-Gaussianity measurement can be transformed into kurtosis form,which can decrease the computational complexity.Meanwhile,by exploiting the independence of the source signals of different users and utilizing spreading codes of target user as training sequence and initialization of unmixing matrix,excellent symbol estimation performances are obtained through stochastic gradient method while the codes of the interfering users in downlink are unknown.Analysis for computational complexity of our algorithm shows that computational complexity increases with length of receiving data and number of users.In this work,the ICA blind detection method is compared with traditional matched filter and well-known linear MMSE multi-user detector.Numerical simulations indicate that ICA based detection performance is comparable to MMSE detection when MAI is lower in synchronous CDMA channels.With the increase of MAI,the superior performance of ICA has significant improvement over exact-MMSE.5.A novel ICA blind detection algorithm based on nonparametric likelihood ratio criterionr is improved.Classical ICA algorithms rely on simple assumptions on the source statistics.Therefore,such algorithms can not perform optimally or even fail to produce the desired source separation when the assumed statistical model is inaccurate. This method is completely blind to the sources and has ability to separate the mixed sources simultaneously.The signal of desired user is detected by using kemel function to estimate probability density function and combining gradient descent method and likelihood ratio criterion.Finally,comparing this algorithm with others,namely FastlCA detection,MMSE,RAKE,the results show that this algorithm provides MAI interference suppression between FastICA detection and MMSE.更多还原