IDENTIFICATION OF MULTIPLE-INPUT MULTIPLE-OUTPUT CHANNELS UNDER LINEAR SIDE CONSTRAINTS

We investigate the impact of having additional information in a form of linear constraints in the channel identification problem. With those constraints taken into account, the problem turns into solving a linear system that is associated with a block matrix where each submatrix is either a Gabor system matrix or a matrix prescribed by the linear constraints. So, the identifiability hinges on whether one can find some generating windows of the Gabor systems for which the full linear system is solvable. We show that in single-input single-output (SISO) settings as well as in multiple-input multiple-output (MIMO) settings, linear constraints consisting of a single equation are beneficial for channel identification, as there always exist windows for which the corresponding full linear system is solvable. Concerning multiple linear constraints, however, there exists a set of linear constraints with two equations for which the full linear system is singular for all choices of windows. In the SISO case, we also provide some sufficient conditions on the linear side constraints under which the full linear system is solvable.