Design of fully-diverse multi-antenna codes based on Sp(2)

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 construct four-transmit-antenna constellations appropriate for differential modulation based on the symplectic group Sp(2) These can be regarded as extensions of S.M. Alamouti's celebrated two-transmit-antenna orthogonal design which can be constructed from the group Sp(1) (see IEEE J. Sel. Area Commun., p.1451-8, 1998). We further show that the structure of the code lends itself to efficient maximum likelihood (ML) decoding via the sphere decoding algorithm. Finally, the performance of the code is compared with existing methods including Alamouti's scheme, Cayley differential unitary space-time codes and group based codes.