We present novel linearization methods for both of single pulse system and single-channel chirped return-to-zero (CRZ) system with the linearization assumption. Both of them show that the Gaussian fit is a good approximation over about two orders of magnitude, but deviate strongly at low probability densities. Linearization allows us to efficiently and accurately compute eye diagrams and bit error rates (BERs) without the use of Monte-Carlo simulations and allows us to greatly increase the accuracy at small BERs at a fraction of the computational cost. We compare these results to the standard Monte-Carlo simulation technique and find that they are agreed very well.
The conservative cascades process with multipliers generated by symmetric β distribution is introduced as an EPON upstream traffic model, which can catch the amplitude burst and temporal burst behaviors of real traffic simultaneously. The traffic matching and synthesizing methods are illustrated through an example.