Unitary matrices for the noncoherent differential MIMO channel
It is well known that unitary matrices are required for transmission
over noncoherent MIMO channels. Furthermore, these matrices have to
achieve full diversity, that is, the determinant of the
difference of any two matrices has to be nonzero. Among the algebraic
approaches to that problem, the representation of fixed point free
groups has been studied (Shokrollahi et al.), and the use of Lie groups
representation has been considered (Hassibi et al.).
We present a new approach using cyclic algebras,
which yields infinite families of fully diverse unitary matrices.
F. Oggier, E. Lequeu.
"Families of unitary matrices with full diversity ",
ISIT 2005, Adelaide.
A first application of the technique studied above yields a generalization
of families of matrices obtained by Shokrollahi et al. using fixed point
free groups. This is presented in
F. Oggier.
"First applications of cyclic algebras to noncoherent MIMO channels ",
Allerton 2005.
The general machinery as well as new code constructions for 3 and 4
antennas are presented in:
F. Oggier.
"Cyclic Algebras for Noncoherent Differential Space-Time Coding"
[.ps],submitted, June 2006.