Statistical Modeling and Performance Characterization of an Ultrafast   Digital Lightwave Communication System Using a Power-Cubic Optical Nonlinear   Preprocessor (Extended Version)
  In this paper, we present an analytical approach in obtaining the probability density function (pdf) of the random decision variable Y, formed at the output of power-cubic all-optical nonlinear preprocessor followed by the photodetector. Our approach can be used to accurately evaluate the performance of ultrafast pulse detection in the presence of Gaussian noise. Through rigorous Monte-Carlo simulation, the accuracy of widely used Gaussian approximation of decision variable Y is refuted. However, in this paper we show that the so called Log-Pearson type-3 probability density function (LP3 pdf) is an excellent representation for the decision variable Y . Three distinguishable parameters of the LP3 pdf are obtained through analytical derivation of three moments of the decision variable Y . Furthermore, toward a more realistic model, in addition to ASE Gaussian noise, the effects of shot and thermal noises are also included. Finally, using the presented analytical approach, it is shown that power-cubic preprocessor outperforms its quadratic counterparts, i.e., Second Harmonic Generation (SHG) and Two Photon Absorption (TPA) devices, in high power regime where shot and thermal noises can be neglected. 
Mahdi Ranjbar Zefreh and Jawad A. Salehi
cs.IT math.IT