Full-diversity quasi-orthogonal space-time block codes for M-PSK modulations

It has been shown that the quasi-orthogonal spacetime block codes (QOSTBCs) can achieve full diversity by rotating the constellations of half the transmitted symbols. Although the rotation angle has been analytically derived for QAM constellations, for arbitrary M-PSK, the coding gain maximizing rotation angle can be found only by computer search. In this paper, a set of QOSTBCs for four transmit antennas that achieves full diversity for M-PSK modulations is presented. The orthogonal designs for real constellations and several QOSTBCs are also included in our formulation. With the same maximum-likelihood decoding complexity, the new codes have BER performance identical to the QOSTBC with constellation rotations. Without any constellation expansion, our scheme is superior to the QOSTBC with constellation rotations in implementations.