A single-channel blind source separation algorithm based on improved wavelet packet and variational mode decomposition

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.