A method for computing the probability of symbol error for space-time trellis codes is developed by means of results from large deviation theory for quadratic Gaussian forms. The issue is that in order to build a space-time trellis code with small probability of error it is sufficient to find a metric for the Viterbi decoding algorithm for which there exists a Cramer’s rate function who minimizes a criterion on the transfer function of the trellis system. In particular, this approach gives a theoretical explanation for a simulation result of [2].
The space-times coding is appropriate to multiple input multiple output antenna transmission. Assume a communication channel with n transmit and m receive antennas. Let A be the alphabet of information symbols and let