High-rate space-time codes motivated by SU(3)

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 ideas, especially fixed-point-free (fpf) groups, have been used to design fully-diverse constellations of unitary matrices. Here we give systematic methods to design space-time codes which are appropriate for three-transmit- antenna differential modulation. The structures of the codes are motivated by the Lie group SU(3). One of the codes, called the AB code, has a fast decoding algorithm using the complex sphere decoder. The diversity products of the codes can be easily calculated and simulated performances show that the codes are better than the group-based codes [1] especially at high rates and as good as the elaborately-designed non-group codes[1].