On optimal linear space-time constellations

Space-time constellations that are linear over the field of complex numbers are considered. Relevant design criteria for these constellations are summarized and some fundamental limits to their achievable performances are established. A new family of constellations that achieve optimal or near optimal performance with respect to the different criteria is presented. The proposed constellations belong to the threaded algebraic space-time signaling framework and achieve the optimal minimum squared Euclidean distance and the optimal delay in addition to the full rate, full diversity properties. For systems with one receive antenna, these constellations also achieve the optimal peak-to-average power ratio for QAM and PSK input constellations, as well as optimal coding gains in certain scenarios. The framework is general for any number of transmits and receives antennas and allow for realizing the optimal tradeoff between multiplexing rate and diversity.