Unitary Space-Time Group Codes: Diversity Sums From Character Tables

Diversity sum, which is calculated from the Frobenius norm of the difference of two distinct elements in a signal constellation, is the significant parameter to predict a unitary group constellation having a good performance in low SNR. In this paper, we propose a method to compute the diversity sum of a unitary group constellation using a character table. Some examples of using our method to different unitary groups: cyclic groups, dicyclic groups and the special linear groups are given. We also define the term faithful group constellation, that is, its diversity sum is greater than 0. One example, in this paper, is the projective special linear group PSL2.