Optimizing quasi-orthogonal STBC through group-constrained linear transformation

We first derive the generic algebraic structure of a quasi-orthogonal STBC (QO-STBC). Next we propose group-constrained linear transformation (GCLT) as a means to optimize the diversity and coding gains of a QO-STBC. Compared with the constellation rotation (CR) technique reported in the literature, we show that QO-STBC with GCLT requires only half the number of symbols for joint detection in the maximum-likelihood (ML) decoder when square or rectangular QAM constellations are used, hence it has lower decoding complexity than QO-STBC with CR. We also derive analytically the optimum GCLT parameters for QO-STBC with a generic square or rectangular QAM constellation for four and eight transmit antennas. The resulting QO-STBCs with GCLT can achieve full transmit diversity, and they have negligible performance loss compared with QO-STBCs with CR at the same code rate.