ANALYSIS OF PERTURBATION COEFFICIENTS IN THE PROBLEM OF FILTERING NONLINEAR DISTORTIONS IN FIBER OPTICS

The article is devoted to the analysis of the perturbation coefficients of the nonlinear distortion compensation model in fiber-optic communication lines. The case of long-range signal transmission is considered, for which the effect of signal dispersion is in some sense more significant than nonlinear distortion. This makes it possible to use an approximation of the nonlinear Schrodinger equation based on perturbation theory with respect to a small parameter of nonlinearity 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 have been carried out to study the structure of the coefficient matrix. It has been found that this matrix is well approximated by a small rank in the absence of attenuation and amplification. In addition, it was found that when taking into account the effects of signal attenuation and amplification, the rank of the matrix approaching the original matrix with a fixed error is higher than in experiments without attenuation. Research confirms that taking into account the symmetry of the matrix and its approximation with a small rank can reduce the computational complexity of the nonlinear distortion filtering algorithm for a single symbol from O(N²) to O(RN ln N), where N is the size of the matrix and R is its rank.

nonlinear optics, nonlinear Schrodinger equation, perturbation theory, mathematical modeling, low-rank approximation