Optimized Nonuniform Constellation Rearrangement for Cooperative Relaying

The performance of cooperative relaying networks can be significantly enhanced by using constellation rearrangement (CoRe). In CoRe, the base-station and the relay-station use different constellations, each having the same number of signal points, to communicate with the user terminal. A number of CoRe schemes have been proposed in the literature based on uniform quadrature-amplitude modulation (QAM) constellations. However, it is still unclear whether nonuniform QAM constellations can further enhance the performance of CoRe. Toward this end, we investigate the problem of designing the optimum nonuniform QAM constellations for CoRe. Our motivation is that nonuniform constellations have the potential to outperform their uniform counterparts because the set of nonuniform constellations is a superset of uniform constellations. Nonuniform QAM constellations can be categorized as either decomposable or nondecomposable . Unlike nondecomposable QAM constellations, decomposable QAM constellations are generated from the Cartesian product of two pulse-amplitude modulation (PAM) constellations. We formulate an optimization problem to find the nonuniform constellations that have the minimum union bound on the uncoded symbol error rate (SER). Using convex analysis, we devise a search method to find globally optimum nonuniform decomposable constellations. We also devise a simple heuristic to find good locally optimum nonuniform nondecomposable constellations, which perform better than their decomposable counterparts.