Full-diversity high-rate non-coherent unitary STBCs: New designs and performance

In this paper, we propose new non-coherent spacetime block code (STBC) designs, which achieve full transmit diversity as well as high rates. We first present a search procedure to generate full-diversity non-coherent unitary space-time codebooks for any number of transmit antennas (n_t) and time slots (T ¿ 2n_t), using radial coordinates of points lying on the surface of a sphere in R^T-nt. The search method generates codebooks having a specified minimum chordal distance, which allows flexibility in achieving coding gain. Further, we propose another unitary design using circulant matrices for any n_t, by restricting the search only to suitable constellation sets in R² for the case of T = 2n_t. For the latter design, we present two different optimizations; i) to maximize the minimum chordal distance, and ii) to maximize the expected chordal distance. The proposed designs use an analytical design criterion which guarantees full diversity. The proposed designs are shown to outperform Jing and Hassibi codes reported previously in the literature.