基于信号峭度的复值盲分离算法研究

发布时间：2018-07-09 16:18

本文选题：独立分量分析 + 复值　；参考：《东北大学》2014年硕士论文

【摘要】：盲源信号分离(Blind Source Separation, BSS)是当前信号处理研究的热点之一,应用十分广泛。独立分量分析方法(ICA)是近年来发展起来的一种有效的盲信号分离技术,在许多领域扮演着重要角色。随着它不断的发展,许多独立分量分析算法(ICA)应用领域要求直接或间接地分离复值信号,进一步讲,实数ICA算法是复数ICA算法的一个特例,复数ICA具有重要的理论和应用价值,在语音信号、图像处理、天线阵列等许多领域都有广泛的应用。在近几年时间里,有关的理论和算法研究都得到了较快的发展,并且提出了许多的有效的算法。目前,复数ICA理论逐渐成熟,新算法不断涌现,已经成为国际上信号处理领域的一个研究热点。首先,介绍了复值ICA算法的基本理论、典型的ICA算法及其分离性能指标。其基本理论主要有信息论、复值ICA的数学模型、可解性分析及不确定性等。典型的ICA算法主要包括最大熵算法、JADE算法、随机梯度算法和自然梯度算法等。其次,重点研究了基于峭度的代价函数。在复值信号的盲分离算法中,经常采用信号的峭度最大化作为代价函数。针对这一问题,以复数标准峭度代替复数峭度,将复数信号的标准峭度最大化作为新的代价函数,并采用修正的复值拟牛顿迭代算法对代价函数进行优化。用该算法对混合QAM信号进行分离,仿真实验结果表明,改进后的算法具有很好的分离效果,相比于峭度最大化为代价函数的分离算法,收敛性能也有明显提高。最后,为了降低算法复杂度并提高算法鲁棒性,在算法中采用了“自下而上”的方法引入非线性函数。在第三章的基础上,通过引用非线性函数改进代价函数,进而推导出新的分离向量迭代公式。仿真实验证明了改进后的算法具有很好的分离效果；通过比较还可看出,改进后的算法具有更快的收敛速度,更高的收敛效率。
[Abstract]:Blind Source Separation (BSS) is one of the hotspots in signal processing and is widely used. Independent component analysis (ICA) is an effective blind signal separation technique developed in recent years and plays an important role in many fields. With its continuous development, many independent component analysis (ICA) applications require the separation of complex signals directly or indirectly. Furthermore, real ICA algorithm is a special case of complex ICA algorithm, and complex ICA has important theoretical and practical value. It has been widely used in many fields, such as speech signal, image processing, antenna array and so on. In recent years, the related theories and algorithms have been developed rapidly, and many effective algorithms have been proposed. At present, the complex ICA theory has matured and new algorithms have been emerging, which has become a research hotspot in the field of signal processing. Firstly, the basic theory of complex ICA algorithm, typical ICA algorithm and its separation performance index are introduced. The basic theories include information theory, mathematical model of complex ICA, solvability analysis and uncertainty. Typical ICA algorithms include maximum entropy algorithm, random gradient algorithm and natural gradient algorithm. Secondly, the cost function based on kurtosis is studied. The maximization of kurtosis is often used as a cost function in blind separation of complex signals. In order to solve this problem, the canonical kurtosis of complex signals is maximized as a new cost function instead of complex kurtosis, and the modified quasi Newton iterative algorithm is used to optimize the cost function. The proposed algorithm is used to separate mixed QAM signals. The simulation results show that the improved algorithm has a good separation effect, and the convergence performance of the improved algorithm is significantly improved compared with the separation algorithm with the cost function of maximization of kurtosis. Finally, in order to reduce the complexity of the algorithm and improve the robustness of the algorithm, the "bottom-up" method is used to introduce nonlinear functions. On the basis of chapter 3, a new iterative formula of separation vector is derived by using nonlinear function to improve the cost function. The simulation results show that the improved algorithm has a good separation effect, and the improved algorithm has faster convergence speed and higher convergence efficiency.
【学位授予单位】：东北大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.7

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