Evaluation of average bit error probability for space-time coding based on a simpler exact evaluation of pairwise error probability

The moment generating function method previously proposed by the author for the analysis of uncoded and coded digital communication over fading channels using only a single transmitter is applied to provide a simple exact evaluation of the pairwise error probability (PEP) for space-time coded systems with multiple transmitters. In certain scenarios, the PEP (and therefore the approximation to the average bit error probability (BEP)) can be evaluated in closed form. An example of such a closed-form evaluation is presented for the 4-state space-time code described in the literature with both slow (constant over the length of a codeword) and fast (constant over the duration of a symbol) Rayleigh fading. The method also has the additional advantage of allowing for direct evaluation of the transfer function upper bound on average BEP for the latter case.