Asymptotic Approximation of the Probability Density Function of the Nonlinear Phase Noise Using the Method of Steepest Descent

Fiber-optic communication systems using phase shift keying (PSK) modulation may suffer from nonlinear phase noise. In this paper, an asymptotic approximation of the probability density function (p.d.f.) of the normalized nonlinear phase noise is derived by taking the inverse Laplace transform of its moment generating function and using the method of steepest descent. For comparison, the inverse Laplace transform of the moment generating function is also numerically evaluated using numerical quadrature. Comparison of the analytical and numerical results, for specific examples, indicates that the method of steepest descent is more accurate and, therefore, is preferable for semi-analytical calculations of the error probability.