Optimal Decomposable QAM Constellations for Minimizing Symbol-error Probability

This paper presents signal space constellations that minimize symbol-error probability in an uncoded communications system. We develop a modified projected gradient optimization method to solve for these constellations that scales efficiently, enabling the optimization of very large constellations. The optimized constellation shapes show significant improvements in symbol-error probability over a wide range of channel conditions compared with uniformly-spaced constellations. At high SNR, small deviations from uniform spacing can make substantial improvements in system performance. These results have promising applications to low-complexity systems with real-time data transmission requirements.