基于含噪复值ICA信号模型的快速不动点算法

摘要

The complex fast fixed-point algorithm, also called complex FastICA, is one of the most important algorithms for Blind Signal Separation (BSS). However, the performance of this algorithm deteriorates when it is used to separate the noisy mixed sources, especially in the low SNR case, since the covariance matrix of whitened observations is not an identity matrix but a diagonal matrix. This paper bases on the present complex FastICA. First, the mixed sources defined with complex Independent Component Analysis (ICA) signal model are projected onto the signal subspace. Thus, the denoising and decorrelating from mixed signal samples can be handily achieved. Then, the learning rule of the algorithm is modified, where the effect of white Gaussian noise is taken into account. Therefore,the BSS performance of complex FastICA is improved markedly. In this paper, the learning rule of denoised noncircular FastICA (nc-FastICA) is derivated and the detailed procedure is given. Simulation results demonstrate the effectiveness of the proposed algorithm.%复数快速不动点算法亦称为复数 FastICA 算法，是盲信号分离的一类重要算法。然而，该算法对被噪声污染的混合源的分离效果较差，尤其是在低信噪比的情况下。这主要是由于在噪声环境下，被白化过后的信号样本的相关矩阵不再是单位阵而是一个对角矩阵。该文基于复信号快速不动点算法，首先将基于含噪复值ICA信号模型的混合源投影到信号子空间，以便进行去噪和去相关处理，然后对现有的复数 FastICA 算法的学习规则做了修正，从而在迭代更新过程中考虑了噪声的影响，因此将显著提高复数 FastICA 算法的盲信号分离性能。文中给出了去噪非圆信号nc-FastICA算法的推导和步骤，仿真结果说明了该算法的有效性。