On design criteria and construction of non-coherent space-time constellations

We consider a non-coherent communication system with M transmit and N receive antennas in a block Rayleigh flat fading channel with coherence interval of T symbol periods. Inspired by Stein's lemma, we propose the use of Kullback-Leibler distance between distributions to approximate the exponential decay rate of pairwise error probabilities. The design problem is then to seek constellations that have the largest minimum Kullback-Leibler distance between the received distributions assigned to their elements (maximin code design). The resulting constellations coincide with the unitary designs at very high SNR or very low rates. But for high rate codes or at low SNR, different signal sets are obtained which show better probability of error performance.