Space-time code design for three-transmit-antenna systems

Fully diverse constellations, i.e., a set of unitary matrices whose pairwise differences are nonsingular, are useful in multi-antenna communications especially in multi-antenna differential modulation, since they have good pairwise error properties. Recently, group theoretic ideals, especially fixed-point-free (fpf) groups, have been used to design fully diverse constellations of unitary matrices. Here we give a systematic method to design space-time codes which are appropriate for three-transmit-antenna differential modulation. The structure of the code is motivated by the Lie group SU(3). The code has a fast decoding algorithm using sphere decode. The diversity product of the code can be easily calculated and simulated performance shows that the code is better than the group-based codes especially at high rates and is as good as the elaborately-designed nongroup code.