Constellation design and mapping for partially coherent correlated channel with coding

Space-time (ST) constellation design problem and bit mapping schemes for multiple-input multiple-output (MIMO) systems in correlated Rayleigh fading channels with imperfect channel estimation at the receiver are considered. The channel coefficients are assumed to be correlated in space and uncorrelated in time from one coherence interval to another after which they change to another independent realization according to the spatial correlation model. We further assume the channel error estimation variance, 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 on the average bit error probability (BEP) expression for spatially correlated channels and propose them as the constellation design criteria subject to average 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. Moreover, different mapping schemes may lead to different error rate performances. Thus, an efficient bit mapping scheme called binary switching algorithm (BSA) is proposed to use in order to find the optimal bit mappings. The Monte Carlo simulation results show that the designed constellation and its optimized bit mapping together with turbo codes outperform the earlier ones and the conventional constellations.