Utilização de códigos esféricos ótimos, álgebra dos quatérnios e fibração de Hopf discreta na construção de modulações em quatro dimensões aplicadas a sistemas de comunicações ópticas coerentes - Doval, Danyel Morais [UNESP] (2021)
This work presents a construction of four-dimensional modulations applied in coherent optical communications systems, using concepts and results of optimal spherical codes, Quaternions Algebra and discrete Hopf fibration.The modulations built in this work are a combination of the Polarization-Shift Keying (PolSK) with Phase-Shift Keying (PSK), thus generating a mPolSK-nPSK modulation, where m is the amount of points taken in a Poincaré sphere and n is the amount of angles psi considered in the PSK modulation. In this work, we consider the m points from optimal spherical codes in order to obtain signal constellations with the greatest possible distance between the symbols and, we applied discrete Hopf fibration to transform three-dimensional points into four-dimensional points and vice versa. From the obtained signal constellations, we also performed the labeling of their symbols in four-dimensional coordinates and through the association of these symbols with Hamilton's quaternions, we mapped the signal constellations in QAM partitions. Finally, from the results presented, an algorithm was applied in MatLab that simulates the constructed 4D modulations, in a noisy coherent optical communication system. To minimize the effects of noise, an artificial intelligence algorithm that classifies the decision thresholds of QAM partitions was applied.