Partially coherent constellations for multiple-antenna systems

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. We further assume that the transmitter and receiver know the statistics of the estimation error. We will refer to this system as a partially coherent system. In an earlier work, we had derived a design criterion for the partially coherent constellations based on maximizing the minimum KL distance between conditional distributions. We had also designed single transmit antenna constellations using this criterion, which showed substantial improvement in the performance over existing and widely-used constellations. In this work, using the KL-based design criterion, we design partially coherent constellations for multiple antenna systems, and evaluate their performance through simulation. We show that, even with only a few percent channel estimation error, the new constellations achieve significant performance gains over the conventional constellations and existing multiple antenna techniques. The proposed constellations are multi-level, with multi-dimensional spherical constellations at each level. We also propose a recursive construction for the constituent spherical subsets of the multiple-antenna partially coherent constellations.