With the rapid growth of wireless networks and multimedia applications, next generation cellular systems are expected to support data rates that are orders of magnitude higher than those currently available. Due to the limited amount of battery power in the mobile handsets, more power efficient signaling techniques need to be developed. Outdoor cellular systems are also required to be able to operate in rapidly fading environments. Exploiting multiple transmit and receive antennas to meet some or all of the above requirements have been recently proposed and extensively investigated. Nevertheless, designing signal constellations and codes that meet all of the above requirements and have practical design and decoding complexities still remains a challenge.
In this work, we consider the code and constellation design problem for digital communication in a Rayleigh fading environment using a multiple-antenna system. We assume that the channel coefficients are not known at the transmitter, and are only partially known at the receiver. Inspired by the Stein's lemma, we propose to use the Kullback-Leibler distance between conditional distributions to design space-time constellations. We show that this distance, while being relatively easy to derive and work with, provides an efficient performance and design criterion.
Using the KL-based design criterion, we construct codes and constellations for multiple-antenna systems which can be decoded non-coherently or in the presence of channel estimation errors, and thus are suitable for fast block fading scenarios. We also show that the new constellations are more efficient than the existing designs for non-coherent systems at low signal-to-noise ratios or high spectral efficiencies. The new partially coherent constellations, on the other hand, provide significant performance improvements when the estimation variance is comparable to the reciprocal of the signal-to-noise ratio.
We also propose a recursive construction for real unitary constellations with low decoding complexity, derive a KL-based design criterion and construction method for partially coherent coded modulation, and design partially coherent constellations for a multi-carrier system in a multipath environment. We show that, in the presense of channel estimation errors, the proposed codes and constellations achieve significant performance improvement over the conventional coding and modulation techniques.