Modelagem Tensorial de Redes de Acopladores Ópticos e Estimativa de Parâmetros Baseada em uma Decomposição Generalizada de Tucker

Abstract

The study of signal transmission in optical fiber-based devices is usually done through computer simulations where the nonlinear Schroedinger equation (NLSE) must be solved, which requires the use of numerical methods such as Runge-Kutta fourth-order (RK4) or SSFM (Split-Step Fourier Method), as NLSE only has an analytical solution for very specific situations. In these methods, input signal parameters and information about the fiber or fiber-based device where the signal will propagate are provided, and from there, the signal parameters at the end of propagation are calculated. Mathematical models using tensors have been widely used in signal processing applications to design different types of communication systems, mainly in wireless networks. This work proposes the use of tensor models for the study of optical communication devices. In this thesis, the signals from a network of dual-core optical couplers are modeled as the matrix of multiway (tensor), which satisfy a NTD (nested Tucker decomposition). This tensor model is then used as a basis to develop an estimation algorithm, using the Monte Carlo method, which allows the network parameters to be estimated from the input and output signals. The performance of this algorithm was evaluated through computersimulations, in terms of NMSE (normalized mean squared error) for the estimated parameters and for the speed of convergence. Configurations with 2, 3, 4 and 5 layers of couplers in a noiseless network were tested, as well as systems subject to noise where scenarios with OSNR (optical signal-to-noise ratio) levels from 0 to 30dB were evaluated. For the tested configurations, good levels of NMSE with fast convergence were obtained, demonstrating the effectiveness of the proposed method as a promising tool for the study and design of optical devices, with a wide range of applications in the context of lightwave systems.