Bandwidth-efficient linear Modulations for multiple-antenna transmission

Some M × T modulation matrices for M transmit antennae and T symbol periods, with M = 2, 3, 4 and T = 2, and M = T = 4 are studied. A transmission rate of M symbols per channel use and a transmit diversity order of min(M,T ) are achieved over a quasi-static fading channel when using rotated versions of a multi-dimensional quadratic amplitude modulation with spectral efficiency 2 bits per symbol. Extension to input constellations with higher spectral efficiencies is then considered. The modulations are then generalized to any number of transmit antennae M and any number of symbol periods T , such that a transmission rate of M symbols per channel use, and a transmit diversity of T are achieved under fast fading (ergodic scenario). By means of signal space diversity, the proposed modulations exploit the degrees of freedom of multi-antenna channels and have moderate detection complexity at moderate and large SNRs.