On the design of quasi-orthogonal constellations: filling the empty threads

A systematic approach for constructing full diversity quasi-orthogonal constellation designs with rate 1 symbol per channel use is studied. The approach complements orthogonal constellation matrices to have rate one symbol per channel use while preserving the full diversity property of these matrices. A design example based on 4 transmit antennas, illustrates filling the empty thread in the orthogonal constellation matrix of rate 3/4 in order to obtain a rate one full diversity quasi-orthogonal constellation. The proposed approach is general for all orthogonal constellations having a threaded architecture, which includes most of the orthogonal constellations documented in the literature.