Abstract: The MIMO channels were mostly used in the high data rate wireless communication. Trellis-coded modulation (TCM) was known to improve error performance in fading channels. An upper bound on the bit error probability was deduced by the formulation, which was in favour of the choice of actual design scheme. The bit error rate was estimated by the minimum average Euclidean distance. Through simulation, the estimation is very accurate at high signal-to-noise ratio.