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

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.