On pairwise error probability of space-time codes

The authors consider a space-time coded system with Q transmit antennas and P receive antennas and assume under the quasi-static Rayleigh fading assumption that the channel is fixed for a duration of M symbol transmissions. Let S be a (Q×M) space-time code. Given S ∈ S is the transmitted codeword, the received signal is given by Y=√ρ_tHS + N, where ρ_t=ρ/Q, with ρ being the SNR. The components n_p,m, h_p,q of the noise matrix N and the (P×Q) channel fading-coefficient matrix H respectively, are independent, identically-distributed, zero-mean, complex Gaussian random variables.