With their ability to handle an increased amount of information, multivariate and multichannel signals can be used to solve problems normally not solvable with signals obtained from a single source. One such problem is the decomposition signals with several components whose domains of support significantly overlap in both the time and the frequency domain, including the joint time-frequency domain. Initially, we proposed a solution to this problem based on the Wigner distribution of multivariate signals, which requires the attenuation of the cross-terms. In this paper, an advanced solution based on an eigenvalue analysis of the multivariate signal autocorrelation matrix, followed by their time-frequency concentration measure minimization, is presented. This analysis provides less restrictive conditions for the signal decomposition than in the case of Wigner distribution. The algorithm for the components separation is based on the concentration measures of the eigenvector time-frequency representation, that are linear combinations of the overlapping signal components. With an increased number of sensors/channels, the robustness of the decomposition process to additive noise is also achieved. The theory is supported by numerical examples. The required channel dissimilarity is statistically investigated as well.