Algebraic Design of Unitary Constellations for Uncoded and Trellis Coded Modulation of Non-Coherent Space-Time Systems

We design constellations for non-coherent space-time syst ems. Given in algebraic form, the constructed constellations are easy to design, enjoy full diversity, allow for a simplified maximum likelihood detector, and achieve performance comparable to existing designs that rely on com puter search. To exploit the structure of the proposed constellations and improve the performance, we further pur sue a trellis coded modulation (TCM) approach. Upper and lower bounds, and in some cases exact expressions, fo r the asymptotic symbol and bit error probability are derived, allowing us to quantify the performance, and co mpare among different TCM designs, or, uncoded alternatives.