Near-optimal non-uniform constellation rearrangement for cooperative relaying

In constellation rearrangement (CoRe), the basestation and the relay use different constellations, with the same modulation level, to communicate with the user terminal. Unlike the existing CoRe techniques, which are restricted to uniform constellations, we propose to use non-uniform quadrature amplitude modulation (QAM) constellations for CoRe. We devise an optimization to find the optimal QAM constellation, which minimizes an upper bound on the symbol error rate (SER). We show how to decompose the optimization problem, which is not convex, into a set of convex optimization problems to solve it. Since the set of non-uniform constellations is a superset of uniform constellations (used in literature), the proposed non-uniform CoRe outperforms all the existing uniform CoRe schemes, with respect to the SER bound. Simulation results show that the proposed non-uniform CoRe scheme yields large gains, with no additional complexity penalty.