Code design for the low SNR noncoherent MIMO block Rayleigh fading channel

Code design for the low SNR MIMO non-coherent correlated Rayleigh fading channel is considered. Design rules which exploit the correlations in the transmit antennas in the MIMO case, to provide gains over the corresponding SIMO case are presented. The Chernoff bound on the average pairwise error probability (APEP) is used to study the effect of the receive correlation matrix on system performance at different SNR regimes. Based on a lower bound on the APEP, which is related to the Bhattacharya coefficient, a technique is proposed to design codes for use with transmit beamforming, with codewords having unequal prior probabilities. The motivation for such codes with unequal priors arises from recent information theoretic results on the low SNR channel. Such constellations are shown to perform substantially better than constellations designed assuming equal priors, at low SNRs.