Statistical characterization of the output of nonlinear power-cubic detection unit for ultrashort light pulse communication in the presence of Gaussian noise

In this paper, an accurate model for the probability density function (pdf) of the random decision variable Y in an ultrafast digital lightwave communication system, utilizing power-cubic all-optical nonlinear preprocessor is presented. The proposed model can replace the prevalent Gaussian approximation, as the accuracy of the latter is discredited by Monte-Carlo simulation. The Log-Pearson type-3 probability density function (LP3 pdf) is shown to appropriately represents the random decision variable Y. Three characteristic parameters of the LP3 pdf are also obtained through the three moments of the decision variable Y. Finally, the system error probability is revisited using the obtained LP3 pdf of the decision variable, the result of which is in excellent consistency with rigorous Monte-Carlo simulation.