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

Abstract—Fully diverse constellations, i.e., sets of unitary ma-trices whose pairwise differences are nonsingular, are useful in multiple-antenna communications, especially in multiple-antenna differential modulation, since they have good pairwise error prop-erties. 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 (2). They can be regarded as extensions of Alamouti’s celebrated two-transmit-antenna orthogonal design which can be constructed from the group (1). We further show that the structure of (2) codes lends itself to efficient maximum-likelihood (ML) decoding via the sphere decoding algorithm. Finally, the performance of (2) codes is compared with that of other existing codes including Alamouti’s orthogonal design, a 4 4 complex orthogonal design, Cayley differential unitary space–time codes and group-based codes. Index Terms—Differential unitary space–time modulation, fully diverse, Lie algebra, Lie group, sphere decoding, wireless commu-nication systems. I