On the degree of MIMO systems

MIMO channels and wireless communications systems have generated a great deal of renewed interest in linear system theory. This paper presents two results. The first is a simple proof based on first principles, of the known fact that the McMillan degree of a causal M times M MIMO system is at least as large as the degree of its determinant. The second is a new result which shows that the degree of the M x M system z^-1 G(z) is equal to the degree of G(z) plus M if and only if the causal system G(z) has an anticausal inverse.