Generalized Constellation Rearrangement in Cooperative Relaying

In constellation rearrangement (CoRe), the base-station and the relay use different constellations, with the same number of signal points, to communicate with the user terminal. In contrast to the existing CoRe techniques, which restrict the possible constellations, we propose generalized quadrature amplitude modulation (QAM) constellations. Since generalized CoRe schemes do not restrict constellations, they have the potential of outperforming all other CoRe schemes, with a complexity penalty in decoding. We pose an optimization to find the generalized QAM constellations, which minimize an upper bound on the uncoded symbol error rate (SER). However, since the optimization is not convex, it is not possible to find constellations with globally minimum SER in a reasonable time. Nevertheless, we use a convex solver to find constellations, which are local minima to the optimization. We input the best known restricted CoRe constellations as starting points to the solver to find constellations, which are guaranteed to improve SER. We demonstrate the significant gains achieved by the proposed CoRe scheme with simulations.