According to the theory of single channel blind source separation (SCBSS), the algorithm based on virtual channel expansion must be established in a known source number, and most algorithms can only separate two source signals. When separating multiple source signals, the performance will deteriorate sharply. Since the existing methods of this kind use only a single algorithm for virtual channel expansion, they cannot retain all the source signals’ valuable information and effectively separate the multiple source signals. From the perspective of making the constructed virtual multi-channel signal contain enough information of the source signals as much as possible, this paper proposes a SCBSS algorithm based on improved wavelet packet and variational mode decomposition (IWP-VMD-SCBSS). Firstly, the source number is estimated according to the interval sampling method and the minimum description length (MDL) criterion. Secondly, the signal reconstruction method based on improved wavelet packet decomposition (IWPD) is used to reconstruct multiple purer virtual signals. Then the virtual signals are combined with the first intrinsic mode function (IMF) of two-level variational mode decomposition (VMD) and the original single-channel observed signal to constitute a virtual multi-channel signal. Finally, the joint approximate diagonalization of eigen-matrices (JADE) algorithm is used to process the virtual multi-channel observed signal to achieve BSS and obtain estimated source signals. The simulation results indicate that the IWP-VMD-SCBSS algorithm can achieve a lower symbol error rate (SER) than existing algorithms and lower computational complexity. It can solve the SCBSS problem of multiple communication signals effectively under an unknown source number.

根据单通道盲源分离（SCBSS）理论，基于虚拟通道扩展的算法必须建立在已知的信源数量上，并且大多数算法只能分离两个源信号。当分离多个源信号时，性能会急剧恶化。由于现有的此类方法仅使用单一算法进行虚拟通道扩展，因此无法保留所有源信号的有价值信息并有效分离多个源信号。从使构造的虚拟多通道信号尽可能包含源信号的足够信息的角度出发，提出一种基于改进小波包和变分模态分解的SCBSS算法（IWP-VMD-SCBSS）。首先，根据间隔采样方法和最小描述长度（MDL）准则估计源数。其次，采用基于改进小波包分解（IWPD）的信号重构方法来重构多个更纯净的虚拟信号。然后将虚拟信号与两级变分模态分解（VMD）的第一本征模态函数（IMF）和原始单通道观测信号相结合，构成虚拟多通道信号。最后，采用特征矩阵联合近似对角化（JADE）算法对虚拟多通道观测信号进行处理，实现BSS并获得估计的源信号。仿真结果表明，IWP-VMD-SCBSS算法能够实现比现有算法更低的符号错误率（SER）和更低的计算复杂度。能够有效解决未知源号下多个通信信号的SCBCS问题。