基于构建虚拟多通道的欠定盲源分离方法研究

针对欠定盲源分离(underdetermined blind source separation，UBSS)的信源数估计和信号分离问题，探索基于小波分解的虚拟多通道构建及其在欠定盲源分离中的应用。通过小波分解构造虚拟观测信号，在欠定盲源分离模型的信源数估计和信号分离方面，结果较不理想，分析发现是由于采用小波变换构建虚拟的观测信号，只用到原观测信号的部分信息产生虚拟的观测信号，并没有增加接收信号中蕴含的信息，即并非像真实的天线阵列一样，针对信号的到达角，产生对应的阵列流型。结果表明：解决欠定盲源分离问题，必须依靠非负矩阵分解、张量分解或稀疏分量分析等思路。

Research on Underdetermined Blind Source Separation Based on Constructing Virtual Multi-channel

Aiming at the problems of source number estimation and signal separation in underdetermined blind source separation (UBSS), the construction of virtual multi-channel based on wavelet decomposition and its application in underdetermined blind source separation are explored. Constructing the virtual observation signal by wavelet decomposition is not ideal in the source number estimation and signal separation of the underdetermined blind source separation model, which is due to the fact that using wavelet transform to construct the virtual observation signal only uses part of the information of the original observation signal to generate a virtual observation signal, and does not increase the information contained in the received signal. That is to say, it is not like the real antenna array, which produces the corresponding array manifold according to the arrival angle of the signal. The results show that to solve the problem of underdetermined blind source separation, we must rely on non-negative matrix factorization, tensor decomposition or sparse component analysis.