Combined Variational Mode Decomposition and Singular Spectral Analysis for Blind Source Separation in Low Signal-to-Noise Ratio Environments

摘要

Singular Spectral Analysis (SSA) is a powerful technique for separating arbitrary co-channel signals in a single channel receiver. The technique is based on a subspace projection using eigenvector decomposition (EVD). While choosing the number of eigenvectors in the EVD may be straightforward, selecting the window length, $L$, for the projections is important, and an inaccurate estimation can lead to poor performance. Estimating the window length is easy, but only if the signal-to-noise ratio (SNR) is high. In this paper, we apply a variational mode decomposition (VMD) algorithm to denoise the signal prior to the SSA, and show that the estimation of $L$ is far more accurate. The VMD, which requires the number of modes $K$ in the signal decomposition as an input, is not sensitive to accurately estimating $K$. In addition, we observe that denoising with the VMD prior to using the SSA makes performance of the combined VMD/SSA algorithm not as sensitive with respect to $L$, with negligible variation in MSE between the signals and their estimates to the choice of $L$. We demonstrate this by simulation, using chirp and speech signals.