Optimum Design of Differential Unitary Space-Time Modulation

In this paper, we propose an extended class of unitary signal constellations for differential unitary space-time modulation (DUSTM). We also derive an approximation of the upper bound on the symbol error probability (SEP) as a general criterion to find the optimum codes. This criterion is valid for both group or non-group constellations. For asymptotically high or low signal-to-noise ratio (SNR), signal-constellation parameters are usually determined based on the rank-and-determinant (diversity product) or the Euclidean distance (diversity sum) criterion. Since both these criterion are SNR-independent, the search results are not necessarily optimum parameters in medium to low SNRs. Thus instead of using diversity sum or product, we search for the constellation parameters to minimize the union-bound based criterion, taking into account the number of receive antenna and the operation SNR. Simulation results show that the constellations optimized for the union-bound based criterion outperform the previous codes resulting from rank-and- determinant (diversity product) or Euclidean distance (diversity sum).