On the optimum design of differential unitary space-time modulation

For asymptotically high SNR, the design criteria of the differential unitary space time (DUST) coding advocated in [12][13] are based on the rank-and-determinant criterion. For large number of receive antennas or low SNR scenarios, the Euclidean distance criterion is appropriate for differential unitary space-time codes [21]. In practical systems with a reasonable number of transmit and receive antennas, the SNR is neither asymptotically high nor asymptotically low. So the interesting question would be: What is a good code design criterion at medium range SNR? In this work, based on the exact pairwise error probability, we derive the union bound on the symbol error probability (SEP) of the DUST modulation. Instead of using the rank-and-determinant or Euclidean distance criteria, we optimize the 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 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.