Nonlinear Noise Statistics in a High-Speed Optical Communication Line Without Dispersion Compensation

The communication line without compensation of dispersion is considered. It is shown analytically and numerically that the field power in the fiber on almost the entire length of the communication line is given by the $$\chi _{2}^{2}$$ distribution. Using the 8-PSK format as an example, we have obtained the dependences of the phase noise dispersion in the chirp parameter of initial pulses. It is found that the accumulated phase shift has the normal distribution with a dispersion decreasing upon an increase in the chirp of the initial Gaussian pulses. We propose an adequate linear estimate of the accumulated nonlinearity.