On the optimum design of unitary cyclic group space-time codes

In this letter, based on the exact pairwise-error probability, we derive the union bound on the symbol-error probability (SEP) of the differential unitary space-time (DUST) modulation employing group codes. Instead of using the rank-and-determinant or Euclidean distance criteria, we optimize the cyclic group codes such that the union bound on the SEP is minimized for a predetermined scenario, taking into account the number of transmit and receive antennas and the operating signal-to-noise ratio (SNR). Our simulation results show that for a wide range of SNRs, the codes with the minimum union bound for a particular SNR outperform the codes designed based on rank-and-determinant or Euclidean distance criteria.