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.

[1]  P. P. Vaidyanathan,et al.  Role of Anticausal Inverses in Multirate Filter-Banks-Part 1: System Theoretic Fundamentals , 1993 .

[2]  Matsue Shimane,et al.  A System-Theoretic Foundation for Blind Equalization of an FIR MIMO Channel System , 2000 .

[3]  Ruey-Wen Liu,et al.  A system-theoretic foundation for blind equalization of an FIR MIMO channel system , 2000, 2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353).

[4]  See-May Phoong,et al.  Minimum redundancy for ISI free FIR filterbank transceivers , 2002, IEEE Trans. Signal Process..

[5]  K. V. S. Hari,et al.  Filter Bank precoding for FIR equalization in high-rate MIMO communications , 2006, IEEE Transactions on Signal Processing.

[6]  Thomas Kailath,et al.  Linear Systems , 1980 .

[7]  P. Vaidyanathan.  Multirate Systems And Filter Banks , 1992 .