Design rules for extended super-orthogonal space-time trellis codes

Super-orthogonal space-time trellis codes (SOSTTCs) can be systematically designed by computer by using the generator matrix representation. However, an exhaustive search becomes prohibitively complex as the number of states or the constellation size increases. Even for 8PSK, the complexity would be prohibitive. In this paper, it is shown that the number of matrices that generate unique codes and satisfy the set-partitioning rules is significantly smaller than the total number of possible matrices. Rules for the design of the generator matrices so that set-partitioning rules are satisfied are proposed. These rules lead to significant complexity reductions and are required for MPSK or MQAM SOSTTCs and codes with more than two transmit antennas. New QPSK and 8PSK SOSTTCs with spectral efficiencies of 2 and 3 b/s/Hz, respectively, which outperform previously known codes are presented.