On the error probability performance of transmit diversity under correlated Rayleigh fading

Third-generation cellular systems are expected to provide high data rate wireless multimedia services. In this paper, we investigate the effects of spatial fading correlation on the bit error probability performance of MIMO systems employing orthogonal space-time block coding (STBC), in the presence of Rayleigh fading. To this end, we derive the characteristic function of the signal-to-noise ratio (SNR) at the output of the STBC decoder, when spatial fading correlation is assumed. The characteristic function turns out to be a linear combination of Laplace transforms weighted by the eigenvalues of the channel correlation matrix, where each element corresponds to an elementary gamma probability density function. Based on this observation, and exploiting the linearity of the Laplace transform, we derive closed-form expressions for the bit error rate (BER) of one and two-dimensional M-ary modulation schemes such as PAM and QAM, when STBC is employed over correlated Rayleigh fading channels.