An Application of the Bruhat Decomposition to the Design of Full Diversity Unitary Space–Time Codes

A full diversity constellation, that is, a set of unitary matrices whose differences have nonzero determinant, is a design criterion for codes with good performance using differential unitary space-time modulation. Fixed-point free groups and the infinite group SU(2) have been used to produce full diversity unitary group constellations. In this paper, we present a new Bruhat decomposition design for constructing full diversity unitary space-time constellations for any number of antennas. They are constructed from cosets of a unitary diagonal subgroup D, and our design has a particularly simple structure for the case where the number of transmitter antennas is prime. We also consider the extension of these constellation designs for an even number of transmitter antennas by replacing D with a Hamiltonian constellation. Some examples of proposed constellations for two to six transmitter antennas are given. Simulations show that our proposed constellations perform well in unknown Rayleigh fading channel.