Constellations for Imperfect Channel State Information at the Receiver

We consider the problem of digital communication in a Rayleigh flat fading environment using a multiple antenna system. We assume that the transmitter doesn’t know the channel coefficients, and that the receiver has only an estimate of them with some known estimation error. Inspired by the Stein’s lemma, we propose to use the Kullback-Leibler distance between distributions assigned to the transmitted symbols as a performance criterion. Using this performance criterion, we derive a design criterion based on maximizing the minimum KL distance between constellation points. As an example, we design constellations for a single transmit antenna system using the above criterion, and through simulation, show that the new constellations can provide a substantial improvement in the performance over existing and widely-used constellations.