QAM to Circular Isomorphic Constellations

Employing high order constellations is inevitable in order to achieve higher spectral efficiency in satellite communication systems. In DVB-S2X standard, constellations with up to 256 points have been included. However, optimizing such high order constellations is a difficult task. In this paper we propose a very simple constellation design based on the radial map from QAM constellations to non-uniform APSK constellations. Our method provides a systematic way to generate a family of optimized high order constellations. We show that gains larger than 0.5 dB can be obtained with respect to the DVB-S2X constellations with 256 points. Even though the proposed constellations are essentially sub-optimal (in terms of maximizing the mutual information), they provide a very competitive test benchmark for the performance of high order constellations. Moreover, the proposed construction potentially allows for an efficient one-dimensional soft detection by an inverse mapping to the QAM. Finally, further optimization techniques are discussed.