We study support patterns for covariance matrices that appear in the problem of stochastic time-varying channel identification.
The problem reduces to solving a linear system associated with measurement matrices having the form of Kronecker product of a Gabor system matrix by itself. The measurement matrix is controlled by a window which generates the Gabor system. In this paper, we investigate support patterns of the object vector which allow existence of a window that renders the linear system solvable. We present several classes of permissible patterns and also show how the corresponding window vector needs to be chosen.