Optimal transport theory for processing and classifying OAM superpositions distorted by turbulence

We propose the use of orbital angular momentum (OAM) states to form modulation symbols in a free-space laser communication link affected by atmospheric turbulence. A collection of superpositions of 2 and 4 active OAM modes are used for transmitting digital information. To sense and decode the data we compare three candidate architectures, based on a Mode Sorter, a Shack-Hartmann and phase flattening holograms. In this work we use concepts of Optimal Transport, particularly the Wasserstein distance and barycenter, for an optimal selection of OAM superpositions and a more appropriate processing of OAM spectra, leading to more accurate detection, achieving a classification error smaller than 1/1000 in intermediate to strong turbulence conditions.