Euclidean Distance Maximizing Rotations for Quasi-Orthogonal Space-Time Codes with MPSK Symbols

Most classes of quasi-orthogonal space-time codes proposed in the literature require the use of rotated constellations for the interfering symbols to ensure full diversity. Since there is no analytical result available to get the exact probability of error in terms of the rotation angle, the optimization of the rotation angle has been done with respect to the Euclidean distance or the diversity product criteria. This paper provides analytical expressions for the optimal rotation angles for the Euclidean distance criteria for any M-PSK (phase shift keying) constellation.