Rate-adaptive space-time constellation design for partially coherent Rayleigh fading channels

We consider rate-adaptive space-time constellation design in Rayleigh fading channels with no channel state information (CSI) at the transmitter and partial CSI at the receiver. The receiver CSI estimate is assumed to be Gaussian and unbiased with known error variance. Bhattacharyya distance between the distributions of the received signals is derived. It is used to approximate the average pairwise error probability (APEP) of symbols from a space-time constellation. New spacetime constellations are designed to minimize the APEP approximation. The new constellations are considered with modulation adaptation. We solve numerically the maximum rate capable to support a target symbol error rate given the signal-to-noise ratio and estimation error variance. Computer simulations validate the accuracy of the bounds and demonstrate the performance improvements over the existing constellations.