Geometrically Shaped Constellations (2D) for a Low Complexity Partially-Coherent AWGN Demapper

2D geometrically shaped constellations that are simultaneously robust to both residual phase noise (RPN) and AWGN (named as LCM-RPN, where LC is the low-complexity receiver metric from [1]) for 8 to 64-ary PCAWGN reception using a mismatched PCAWGN model. We added AWGN-only shaped constellations (LCM-AWGN) to serve as a reference; the term M is the modulation cardinality.

Note: This is a supplementary dataset for journal submission. The uploaded constellations are optimised for a low-complexity PCAWGN demapper from [1], although they may also work well with the exact channel model and other PCAWGN approximations. Each of the constellations comes with linewidth symbol time product, SNR (i.e. signal to noise ratio) and RPN variance.  

[1] M. Sales-Llopis and S. J. Savory, "Approximating the Partially Coherent Additive White Gaussian Noise Channel in Polar Coordinates," in IEEE Photonics Technology Letters, vol. 31, no. 11, pp. 833-836, 1 June 1, 2019, DOI: 10.1109/LPT.2019.2909803.