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

We consider the blind deconvolution problem of FIR multiple-input multiple-output channel systems. The systems-theoretic foundation is established on the broadest class of equalizable channel systems. This class of equalizable channel systems is then characterized. Based on this characterization, a fundamental factorization property, called irreducible-allpass factorization, is shown. Based on this fact, it is shown that any equalizable FIR system can and only can be converted to a paraunitary system, through the whitening of the observations, using the second-order statistics. The current second order statistics techniques considered only those channel systems that are irreducible, only half of the irreducible-allpass factorization of equalizable channels.