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. They each are related to an elementary divisor or minimal indice of the channel. The elementary divisors are equivalent to the roots of the characteristic polynomial for SISO channels whereas the minimal indices characterise the possible transmit or receive diversity in such channels. The knowledge of these values allows us to determine the necessary filter length and redundancy such that a finite impulse response filter can cancel all intersymbol and interchannel interference completely.