5.3 Error Probability Motivated Design Methodology

Maximum-likelihood (ML) decoding is generally assumed when deriving space-time code designs. With instantaneous channel realizations perfectly known at the receive side, the ML decoder computes an estimate of the transmitted codeword according to

(5.2)

where the minimization is performed over all possible codeword vectors C. When a codeword C is transmitted through n _t antennas, we are interested in the probability that the ML decoder decodes the codeword E = [ e ₀ e _{T -1}] instead of codeword C. This probability is known as the pairwise error probability (PEP) and is classically studied as a measure of error performance. When the PEP is conditioned on the channel realizations , it is defined as the conditional PEP [Pro01],

(5.3)

where is the Gaussian -function (see Appendix A). The average PEP, denoted as P( C ? E), is finally obtained by averaging the conditional PEP of (5.3) over the probability distribution of the channel gains. Quite naturally, the system performance is in general, especially at high SNR, dominated by the couples of codewords that lead to the worst PEP. This worst PEP is referred to as the worst-case PEP or the maximum PEP, and is a fundamental concept in code design.

However, we stress that it is always better to account for the whole PEP spectrum, since the total error performance may also be highly affected by the occurrence of some codeword pairs not responsible...