Representation theory for high-rate multiple-antenna code design

Multiple antennas can greatly increase the data rate and reliability of a w ireless communication link in a fading environment, but the practical succe ss of using multiple antennas depends crucially on our ability to design hi gh-rate space-time constellations with low encoding and decoding complexity . It has been shown that full transmitter diversity, where the constellatio n is a set of unitary matrices whose differences have nonzero determinant, is a desirable property for good performance. We use the powerful theory of fixed-point-free groups and their representat ions to design high-rate constellations with full diversity. Furthermore, w e thereby classify all full-diversity constellations that form a group, for all rates and numbers of transmitter antennas. The group structure makes t he constellations especially suitable for differential modulation and low-c omplexity decoding algorithms. The classification also reveals that the number of different group structur es with full diversity is very limited when the number of transmitter anten nas is large and odd. We, therefore, also consider extensions of the conste llation designs to nongroups. We conclude by showing that many of our desig ned constellations perform excellently on both simulated and real wireless channels.