Independent component analysis (ICA) is increasingly utilized to modern digital signal processing. Complex-valued FastICA, a fast fixed-point algorithm for ICA, is one of the most non-trivial algorithms for solving the ICA problems in the complex domain. Hitherto, there have been several attempts to give performance analysis for complex-valued FastICA. Rigorous theoretical analysis, however, still has room for improvement further. Consequently, the purposes of this paper are threefold: Firstly, the uniformity of the complex-valued FastICA estimator is constructed for the first time. Secondly, the stability of the complex-valued ICA algorithm is rigorously deduced based on the augmented generating matrix. Meanwhile, the local convergence of complex-valued FastICA algorithm is derived based on circular source signals. Finally, for improving the performance of separation, we select a novel alternative for nonlinearity based on the Tukey M-estimator in the complex-valued FastICA algorithm. Further, we prove the existence of local optimal solution and stability of the complex ICA problem based on the Tukey M-estimator. Simulations are presented to demonstrate the accuracy of our analysis. Additionally, the experimental results with synthetic data and complex-valued wind signal show the superiorities of the improved method.

独立分量分析（ICA）越来越多地用于现代数字信号处理。复值FastICA是ICA的一种快速定点算法，是解决复杂域中ICA问题的最简单算法之一。迄今为止，已经进行了多种尝试来对复值FastICA进行性能分析。但是，严格的理论分析仍有进一步改进的空间。因此，本文的目的有三点：首先，首次构造了复值FastICA估计量的均匀性。其次，基于增广生成矩阵，严格推导了复值ICA算法的稳定性。同时，基于循环源信号，推导了复值FastICA算法的局部收敛性。最后，为了提高分离性能，我们在复值FastICA算法中基于Tukey M估计器为非线性选择了一种新颖的替代方法。此外，我们基于Tukey M估计器证明了局部最优解的存在和复杂ICA问题的稳定性。仿真结果证明了我们分析的准确性。另外，利用合成数据和复数值风信号的实验结果表明了改进方法的优越性。