Analysis of Perturbation Coefficients in the Problem of Filtering Nonlinear Distortions in Fiber Optics
摘要
Perturbation coefficients of the model for compensating nonlinear distortions in fiber-optic communication lines are analyzed. The case of signal transmission over long distances is considered, for which the effect of signal dispersion is in some sense much more significant than nonlinear distortions. This allows using an approximation of the nonlinear Schrödinger equation based on the perturbation theory for a small nonlinearity parameter to describe the signal propagation process. Using this approximation, analytical expressions are obtained for the coefficients of the first-order model in the case of a Gaussian pulse shape. A number of numerical experiments are carried out to study the structure of the coefficient matrix. It is found that this matrix is well approximated by a low-rank matrix under the condition of the absence of attenuation and amplification. In addition, it is found that when taking into account the effects of signal attenuation and amplification, the rank of the matrix approximating the original matrix with a fixed error is greater than in experiments without attenuation. Research confirms that taking into account the symmetry of the matrix and its approximation by a low-rank matrix makes it possible to reduce the computational complexity of the nonlinear distortion filtering algorithm for one symbol from