A system-theoretic foundation for blind equalization of an FIR MIMO channel system

The system-theoretic foundation for blind equalization of a finite-impulse response (FIR) MIMO channel system in the channel-filter setting is investigated. In this setting, a general definition of equalizable channel system is presented, and its characterization is given: Every equalizable channel system has an FIR irreducible-paraunitary factorization. Based on this fact, we show that any equalizable channel system can be reduced to a paraunitary FIR system by a filter, called a whitener. It is shown that one such whitener can be designed by a linear prediction-based approach. It is also shown that if the original FIR channel system has no transmission zero at the origin, then the above paraunitary FIR channel system is a static system.