On design criteria and construction of noncoherent space-time constellations

We consider the problem of digital communication in a Rayleigh flat fading environment using a multiple-antenna system, when the channel state information is available neither at the transmitter nor at the receiver. It is known that at high SNR, or when the coherence interval is much larger than the number of transmit antennas, a constellation of unitary matrices can achieve the capacity of the non-coherent system. However, at low SNR, high spectral efficiencies, or for small values of coherence interval, the unitary constellations lose their optimality and fail to provide an acceptable performance. In this work, inspired by the Stein’s lemma, we propose to use the Kullback-Leibler distance between conditional distributions to design space-time constellations for non-coherent communication. In fast fading, i.e., when the coherence interval is equal to one symbol period and the unitary construction provides only one signal point, the new design criterion results in PAM-type constellations with unequal spacing between constellation points. We also show that in this case, the new design criterion is equivalent to design criteria based on the exact pairwise error probability or the Chernoff information. When the coherence interval is larger than the number of transmit antennas, the resulting constellations overlap with the unitary constellations at high SNR, but at low SNR they have a multilevel structure and show significant performance improvement over unitary constellations of the same size. The performance improvement becomes especially more significant when a large number of receive antennas are used. This property, together with the facts that the proposed constellations eliminate the need for training sequences and are most suitable for low SNR, makes them a good candidate for uplink communication in wireless systems. Index Terms Non-coherent constellations, space-time codes, multiple antenna systems, fading channels, channel coding, wireless communications.