Upper bound on the error probability for space-time codes in fast fading channels

We present exact union bounds on the error probability of space-time codes in fast Rayleigh and Rician fading channels. Using Craig´s formula for the Gaussian Q-function, an exact pairwise error probability (PEP) of space-time codes is expressed in the form of a single finite-range integral whose integrand involves in the moment generating function (MGF) of a nonnegative random variable. Based on this expression, the exact union bounds for a geometrically uniform space-time trellis code (STTC) over fast fading channels can be obtained by using the transfer function bounding technique.