  A Quasi-Orthogonal Space-Time Block Code (QO-STBC) is attractive because it
achieves higher code rate than Orthogonal STBC and lower decoding complexity
than nonorthogonal STBC. In this paper, we first derive the algebraic structure
of QO-STBC, then we apply it in a novel graph-based search algorithm to find
high-rate QO-STBCs with code rates greater than 1. From the four-antenna codes
found using this approach, it is found that the maximum code rate is limited to
5/4 with symbolwise diversity level of four, and 4 with symbolwise diversity
level of two. The maximum likelihood decoding of these high-rate QO-STBCs can
be performed on two separate sub-groups of symbols. The rate-5/4 codes are the
first known QO-STBCs with code rate greater 1 that has full symbolwise
diversity level.
