Construction of Circular Quadrature Amplitude Modulations (CQAM)

Circular quadrature amplitude modulations (CQAM) are introduced as an alternative to mono-dimensional ASK constellations (and their QAM Cartesian product) for probabilistic shaping with non-binary error-correcting codes. We propose an exact construction method via recursive equations for bi-dimensional CQAM constellations. We show that CQAMs are subsets of the hexagonal lattice A2 for a particular alphabet size. Then we describe CQAM constructions in three dimensions from the D3 (fcc) lattice and from Fibonacci spirals.