基于线性阵列的欠定盲源分离几何分析

Geometrical Analysis of Underdetermined Blind Source Separation Based on Linear Array

采用线性阵列对欠定盲源分离问题进行建模,研究源信号的空间分布对欠定盲源分离的影响。利用二步法和稀疏分量分析解决欠定盲源分离问题,其中,混合矩阵的估计主要利用稀疏源信号的线性混合信号沿混合矩阵列向量方向线性聚类的特性。理论分析和仿真实验结果表明,当源信号在空间处于某些特定区域时,若采用线性聚类方法,混合矩阵是不可估计的,从而无法正确实现欠定盲源分离。

This paper models the problem of underdetermined blind source separation using linear array and discusses the effect of space distribution of sources on underdetermined blind source separation.At present,underdetermined blind source separation is mainly discussed in the context of sparse component analysis and is usually resolved by means of two-step strategy.The characteristic that linear mixture of sparse source signals clusters along vectors of mixing matrix is used to estimate the mixing matrix.It is theoretically analyzes that mixing matrix can not be correctly estimated when sources are located in some areas using linear clustering method.Hence,underdetermined blind source separation is intractable.Simulations confirm the correctness of theoretical analysis.