On the construction of space-time Hamiltonian constellations from group codes

Full diversity signal constellations for any numbers of transmitter antennas and for any orders which are constructed from 2×2 Hamiltonian matrices are investigated in this paper. The diversity product of a 2×2 Hamiltonian constellation equals one half of the Euclidean distance between two points in C². By considering the transformation from R⁴ to C², the idea of group codes is used to construct a high diversity product constellation for any order L. The (L,4) cyclic group codes are considered to obtain L 4-dimensional codewords for group codes. We show that our 2×2 Hamiltonian constellations have higher diversity product than orthogonal and diagonal constellation designs. We extend our construction to the general case for any numbers of transmitter antennas M>2 by using a direct sum of 2×2 Hamiltonian matrices for M even, and a direct sum of 2×2 Hamiltonian matrices with the L^th roots of unity for M odd. It is shown that these constellations outperform cyclic groups and some of those obtained using fixed-point free groups.