We propose a new method for effective numerical simulation of transmission system performance and study of correlated noise evolution along an optical fiber with nonlinear parametric interaction between the amplified spontaneous emission (ASE) and the modulated optical signal. The method is based on an evaluation of the noise covariance matrix by using full nonlinear Schrödinger equation (NLSE) and an analytical model for the optical receiver. Using extensive brute-force Monte Carlo simulation as a verification tool, we test the accuracy of the method and illustrate the analytical receiver model limitations in the case of moderate as well as substantial growth of non-Gaussian optical noise along the optical fiber transmission link.