The algebraic structure of frequency-selective MIMO channels

The theory of homogenous matrix polynomials provides a clear and powerful framework for the characterization of frequency selective multiple-input multiple-output (MIMO) channels. The concept proposed in this paper is a natural unification of methods, known from flat fading MIMO channels and frequency selective single-input single-output (SISO) channels. From the Kronecker canonical form of the channel equation, several subchannels can be identified. Each of them is related to an elementary divisor or minimal index of the channel. The elementary divisors are equivalent to the roots of the characteristic polynomial for SISO channels, whereas the minimal indices characterize the possible transmit or receive diversity in such channels. The knowledge of these values allows us to determine the necessary filter order, the minimal redundancy, and the conditions on the precoder such that a finite impulse response filter can suppress all intersymbol and interchannel interference completely.