Optimization of high-order non-uniform QAM constellations

Spectrally efficient transmission on the physical layer is a crucial attribute of state-of-the-art transmission systems. The latest broadcast and terrestrial point-to-point systems such as DVB-T2, DVB-C2 or LTE use LDPC- or Turbo-codes jointly with QAM constellations to achieve capacity approaching the Shannon limit. However, since the gap between the BICM capacity of conventional uniform QAM constellations and the Shannon limit increases for larger SNR, constellation shaping is required to closely approach the Shannon limit when leaving the low SNR region. We propose non-uniform QAM constellations with modulation orders until 1024k-QAM approaching the Shannon limit up to 0.036 b/s/Hz at 29 dB SNR, corresponding to a short-coming of 0.108 dB. To maintain low-complexity 1-dimensional demapping of each component, the symmetry of the constellations is kept. In addition, we propose quadrant symmetric non-uniform QAM constellations optimized in both dimensions, to improve the performance of the constellations at low SNR.