Importance sampling for polarization-mode dispersion

Abstract

Abstract-The basic theory of importance sampling (IS) as relevant to polarization-mode dispersion (PMD) in optical fibers is discussed, and its application to Monte Carlo (MC) simulations of PMD-induced transmission impairments is demonstrated. The use of IS allows rare PMD events to be simulated much more efficiently than with standard MC methods. As a consequence, methods employing IS provide natural and effective tools to assess PMD-induced impairments and outages in optical transmission systems at realistic probability levels.Index Terms-Importance sampling (IS), Monte Carlo (MC) simulations, optical fiber communications, polarization-mode dispersion (PMD).

Accurate Receiver Model for Optical Fiber Systems with Polarization Induced Performance Degradation

“…8, we use importance sampling in the Monte Carlo simulations of PMD [Biondini et al, 2002], ] combined with the semi-analytical model in Eq. (13) to calculate the power penalty with respect to the optimized receiver at 10 -5 outage probability level for the NRZ and raised-cosine RZ systems operating in a transmission fiber system with 10 ps of mean DGD (10% of the bit period).…”

Statistical Errors in Biasing Monte Carlo Simulations With Applications to Polarization-Mode Dispersion Compensators

“…Prior to the advent of importance sampling methods to calculate the outage due to PMD, it was not possible to directly compute outage probabilities of 10 −5 or lower in systems with PMD compensators, and it was common to assume when modeling compensators with a fixed differential group delay (DGD) element that the element should be chosen to minimize the mean DGD after compensation. When importance sampling became available, it was no longer necessary to make this assumption, which proved to be incorrect [9], [10], [22]. The reason is that outages are caused by rare events with large DGDs.…”

“…Despite these difficulties, biasing MC methods have been increasingly used to study optical fiber communications systems and components since their introduction to study PMD compensators [9], [10]. Other applications have included determining the performance of soliton [11] and quasilinear [12], [13] amplitude-shift-keyed systems that are dominated by noise impairments or that are dominated by impairments due to crossphase modulation [14], [15], determining the performance of soliton [16] or quasilinear [17] differential-phase-shift-keyed systems that are impaired by noise, studying induced crosstalk [18], [19], and calculating the noise in semiconductor amplifiers [20], [21].…”

Efficient computation of outage probabilities due to polarization effects in a WDM system using a reduced Stokes model and importance sampling

“…We extend the analysis in [5] by taking into account the effect of PDG, discussing how the effectiveness of the importance-sampling method depends on the number of WDM channels and on the PDG, and by explaining the method in more detail. Importance sampling was first applied to optical fiber communications by Biondini et al [6], where it was used to study the PMD-induced differential group delay in a fiber or an emulator with a limited number of sections. The method has also been applied to study the effectiveness of both electronic [7] and optical [8] PMD compensators.…”