Blind identifiability of a linear dynamic communication channel model

The article describes the problem of developing a mathematical model of data transmission channel in communication systems in the case when signals at the channel input channel are unknown at the channel output. Development of mathematical models directly from observed data constitutes an identification problem, and the case under consideration belongs to the blind identification problem. The work consistently examines the concept of linear dynamic system identifiability in state space and shows the connection of this concept with the observability and controllability concepts. A number of statements about identifiability of a linear dynamic system describing communication channel are proved. In particular, it is shown that if the system is identifiable, it is sufficient to use the input-output model for its description, while the input-state-output model is redundant. Further, based on the proven statements, blind identifiability conditions are formulated for the case of a discrete system with one input and multiple outputs, which are imposed on the components of the system’s transfer matrix.