Equalization of a MIMO channel using FIR inverses

In the modern method of equalization, the problem of multiple-input multiple-output (MIMO) finite-impulse-response (FIR) channel equalization boils down to finding the MIMO FIR inverses. This correspondence proposes and proves a theorem that states the condition for the existence of these inverses, which are also FIR. A numerical example is provided to illustrate how the FIR inverses can be evaluated and used for equalization of a channel with known channel parameters.