Strict identifiability of multiple FIR channels driven by an unknown arbitrary sequence

The problem of blind identification of multiple finite impulse response (FIR) channels driven by a common input arises in a wide range of applications. It has received increasing attention in the signal processing community. A system of multiple FIR channels driven by an unknown input is said to be strictly identifiable if, in the absence of noise, the given channel outputs can only be realized by a unique (up to a constant) system impulse response and a unique input sequence. We show necessary and sufficient conditions for strict identifiability, and establish a connection among strict identifiability, a cross-relation-based (CR-based) identifiability and a Fisher information-based (FI-based) identifiability.