FIR inverses to MIMO rational transfer functions with application to blind equalization

Given a multi-input multi-output (MIMO) causal stable rational transfer function matrix H(z) = A(-1)(z)B(z) with N outputs and M inputs (N greater than or equal to M), it is shown that full column rank of B(z) for all z is a necessary and sufficient condition for the existence of a finite impulse response (FIR) left inverse g(z) such that B(z)H(z) = I. Upper bounds on the length of the FIR inverse are derived in terms of the lengths of the AR and the MA parts of H(z). The presented results are less stringent than the existing results. These results are then used to design FIR MIMO equalizers in a two-step procedure. In the first step, using only the correlation function of the MIMO system output (i.e. the data record), FIR filters are designed to equalise the received signals up to a full-rank mixing matrix. In the second step, higher-order statistics are used to design a separating matrix to unmix the signals.