Unitary Signal Constellations Based on Irreducible Finite Reflection Groups

Includes bibliographical references (pages 40-41).This thesis provides an introduction to the study of space-time constellations for wireless communications on a multiple-antenna environment. Full diversity unitary signal constellations for two transmitter antennas are constructed from 2 x 2 Hamiltonian matrices. These matrices are built using Slepian's group codes based on all irreducible finite reflection groups of rank 4. Diversity products of all such constellations are calculated, and an explicit example of one constellation is generated. An extension of the Hamiltonian design for the cases M = 3 and M = 4 transmitter antennas is proposed. While the 4 x 4 design offers the same performance of the 2 x 2 case, the diversity products of the 3 x 3 design are interesting. A design with matrices in SU(3) for three transmitter antennas is also investigated.