Effect of transmit antenna configuration on rank-determinant criteria of space-time trellis codes

We derive a new upper bound for the pairwise error probability of space-time codes in a quasi-static Rayleigh fading channel, considering antenna configuration at the transmitter side. The design criterion for existing space-time trellis codes is based on the rank and the determinant of the distance matrix between two code words. In particular, the diversity advantage of the space-time code is associated to the rank of the distance matrix. We show that when the transmit antenna region is small, the diversity advantage given by the space-time code is reduced by the transmit antenna configuration and the diversity advantage of the code depends on the rank of the antenna configuration matrix. We also show that the uniform linear array antenna configuration diminishes the diversity advantage provided by the space-time code while the uniform circular array antenna configuration does not affect the diversity advantage of the space-time code.