Partially Coherent Constellation Design and Bit-Mapping with Coding for Correlated Fading Channels

The space-time (ST) constellation design problem and the related bit mapping schemes for multiple-input multipleoutput (MIMO) systems in spatially correlated Rayleigh fading channels with imperfect channel estimation at the receiver are considered. We assume that the channel estimation error covariance matrix, as well as transmit and receive correlation matrices are perfectly known both at the transmitter and at the receiver. We derive the cutoff rate (CR) and an upper bound (UB) on the average bit error probability (ABEP) expression for spatially correlated channels and propose them as the constellation design criteria subject to a given average transmit power constraint. Additionally, to use the resulting constellations together with forward error correction (FEC) codes requires efficient bit mapping schemes. Because these constellations lack geometrical symmetry in general, the Gray mapping is not always possible in the majority of the constellations obtained. Moreover, different mapping schemes may lead to highly different bit error rate (BER) performances. Thus, an efficient bit mapping scheme called the modified binary switching algorithm (MBSA) is proposed. It minimizes an upper bound on the ABEP (UB-ABEP) and is used to find the bit mapping schemes. Numerical examples show that the designed constellation and its optimized bit mapping together with turbo codes outperform the conventional constellations with respect to the frame error rate (FER).