Pep-bound rotation angle optimization of 8-transmit-antenna quasi-orthogonal space-time block codes

We derive a new expression for the rotation angles that maximize the diversity (eigenvalue) product of the 8 x 8 two-symbol decodable quasi-orthogonal space-time block code (QO-STBC). We show that the previously proposed sum-eigenvalue maximization criterion for the design of rotation angles is not relevant/applicable to the 8-transmit-antenna QO-STBCs and we suggest, instead, minimum eigenvalue maximization. Finally, working directly with the pairwise-error-probability (PEP) upper bound expression, we obtain new true PEP-upper-bound optimal rotation angles. Simulation studies demonstrate and compare the error rate of the three design criteria (diversity product, minimum eigenvalue, PEP upper bound).