Space-time constellation design for partial CSI at the receiver

We consider the design of space-time constellations when the channel state information that is available at the receiver is an estimate of the channel coefficients with known error covariance. This setup encompasses the well-studied scenarios of perfect and no channel knowledge and allows a smooth transition between these two cases. We perform an asymptotic pairwise error probability analysis and derive a criterion to design constellations matched to the level of channel knowledge available at the receiver. Moreover, we use the criterion to assess the power tradeoff between data transmission and channel coefficient acquisition for any given specific set of constellations. Simulation results illustrate the benefit of the proposed criterion.