Statistics of nonlinear noise in a high-speed optical communication line without dispersion compensation

A communication line without dispersion compensation is considered. It is shown analytically and numerically that almost over the entire length of the communication line, the field power in the fibre is given by the distribution χ²₂. Using the 8-PSK format as an example, the dependences of the phase noise dispersion on the chirp parameter of the initial pulses are obtained. It is found that the accumulated phase shift has a normal distribution, whose dispersion decreases with increasing chirp of the initial Gaussian pulses. An adequate linear estimate of the accumulated nonlinearity is proposed.