Partially Coherent Multiple Antenna Systems: Design Criterion and Construction Methods for Constellations and Coded Modulation
Borran, Mohammad Jaber
Partially coherent constellations; imperfect channel state information; space-time codes; multiple-antenna systems; fading channels; channel coding; wireless communications
We consider multiple-antenna communication systems in Rayleigh fading channel, where the transmitter does not know the channel coefficients and the receiver has only an estimate of them. We further assume that the transmitter and receiver know the statistics of the estimation error. We refer to this system as partially coherent system, for which we derive the expressions for the optimal detector and study the code and constellation design problems. Finding the Chernoff bound intractable, and inspired by Steinâ s Lemma, we propose to use the Kullback-Leibler (KL) distance between conditional distributions to design space-time codes and constellations for partially coherent systems. We show that the KL distance is relatively easy to derive and work with, and furthermore, provides an efficient design criterion. Using the KL-based design criterion, we construct constellations for multiple-antenna systems which can be decoded in the presence of channel estimation errors, and thus are suitable for fading scenarios with short coherence intervals. 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. The new partially coherent constellations provide significant performance improvement over the conventional single-antenna PSK and QAM constellations and multiple-antenna techniques such as Bell Labâ s Space-Time (BLAST) architecture and Orthogonal Transmit Diversity (OTD) schemes, when the estimation variance is comparable to the reciprocal of the signal-to-noise ratio. More specifically, we show that by using the proposed constellations, the error floors due to the estimation errors can be reduced by as much as one order of magnitude. Next, we bring coding into the picture and derive a KL-based design criterion for partially coherent coded modulation. We also propose a construction method for partially coherent coded modulation using the idea of mapping by set partitioning. We show that, in the presence of channel estimation errors, the proposed codes provide substantial performance improvement over the conventional coded modulation techniques, and the gains in this case are even larger than the gains obtained in the case of uncoded systems.