Improved 16-QAM constellation labeling for BI-STCM-ID with the Alamouti scheme

We design constellation labeling maps for bit-interleaved space-time coded modulation with iterative decoding (BI-STCM-ID) over Rayleigh block-fading channels using the Alamouti scheme and N_r receive antennas. To achieve the largest asymptotic coding gain from the constellation labeling, we propose a new design criterion that maximizes the (-2N_r)-th power mean of the squared Euclidean distances associated with all "error-free feedback" events in the constellation. Based on this power mean criterion, we show that the labeling optimization problem falls into the category of quadratic assignment problems. We propose two novel 16-QAM labeling maps that are particularly designed for N_r=1 and N_r=2, respectively. Numerical results show that both labeling maps achieve about 1 dB coding gain over the conventional 16-QAM modified set partitioning labeling.