Esquemas de Modulação Não-Linear Associadas a Superfícies Mínimas

— In this paper we use a geometrical interpretation that associates twisted modulation schemes to surfaces in Eucli-dian space to design and analyze new non-linear modulations. Thus, an approximate expression for the mean-square error was derived and applied to spaces of constant sectional curvature, indicating the use of hyperbolic space for the project of modulations. Moreover, non-linear modulations associated with minimal surfaces were related the minimization of the mean-square error and a modulation associated with the helicoide minimal surface was proposed. Finally, we determine a condition involving the noise average energy and the mean and Gaussian curvatures with the objective of to minimize the threshold error.