Paolo Serena

Cross-Phase Modulation Induced by OOK Channels on Higher-Rate DQPSK and Coherent QPSK Channels

In this paper we show that, in hybrid wavelength division multiplexed systems, the performance of high datatrate QPSK channels impaired by cross-phase modulation (XPM) induced by the lower rate OOK channels can be simply estimated by an extension of a well-known linear model for XPM, and novel analytical expressions of the sensitivity penalty are provided. From such a model we prove that the reported QPSK penalty decrease with QPSK baud rate increase should be attributed to the action of the phase estimation process rather than to the walkoff effect. The model also simply shows how coherent QPSK is more affected by XPM than incoherent DQPSK, and allows to infer that even more impact is expected when the baudrate is further reduced through polarization multiplexing.

The RP method: a new tool for the iterative solution of the nonlinear Schrodinger equation

An original approach to the solution of the nonlinear Schrodinger equation (NLSE) is pursued in this paper, following the regular perturbation (RP) method. Such an iterative method provides a closed-form approximation of the received field and is thus appealing for devising nonlinear equalization/compensation techniques for optical transmission systems operating in the nonlinear regime. It is shown that, when the nonlinearity is due to the Kerr effect alone, the order n RP solution coincides with the order 2n + 1 Volterra series solution proposed by Brandt-Pearce and co-workers. The RP method thus provides a computationally efficient way of evaluating the Volterra kernels, with a complexity comparable to that of the split-step Fourier method (SSFM). Numerical results on 10 Gb/s single-channel terrestrial transmission systems employing common dispersion maps show that the simplest third-order Volterra series solution is applicable only in the weakly nonlinear propagation regime, for peak transmitted power well below 5 dBm. However, the insight in the nonlinear propagation phenomenon provided by the RP method suggests an enhanced regular perturbation (ERP) method, which allows the first order ERP solution to be fairly accurate for terrestrial dispersion mapped systems up to launched peak powers of 10 dBm.

Parametric-gain approach to the analysis of single-channel DPSK/DQPSK systems with nonlinear phase noise

This paper presents a novel method based on a parametric gain (PG) approach to study the impact of nonlinear phase noise in single-channel dispersion-managed differentially phase-modulated systems. This paper first shows through Monte Carlo simulations that the received amplified spontaneous emission (ASE) noise statistics, before photodetection, can be reasonably assumed to be Gaussian, provided a sufficiently large chromatic dispersion is present in the transmission fiber. This paper then evaluates in a closed form the ASE power spectral density by linearizing the interaction between a signal and a noise in the limit of a distributed system. Even if the received ASE is nonstationary in time due to pulse shape and modulation, this paper shows that it can be approximated by an equivalent stationary process, as if the signal were continuous wave (CW). This paper then applies the CW-equivalent ASE model to bit-error-rate evaluation by using an extension of a known Karhunen-Loe/spl acute/ve method for quadratic detectors in colored Gaussian noise. Such a method avoids calculation of the nonlinear phase statistics and accounts for intersymbol interference due to a nonlinear waveform distortion and optical and electrical postdetection filtering. This paper compares binary and quaternary schemes with both nonreturn- and return-to-zero (RZ) pulses for various values of nonlinear phases and bit rates. The results confirm that PG deeply affects the system performance, especially with RZ pulses and with quaternary schemes. This paper also compares ON-OFF keying (OOK) differential phase-shifted keying (DPSK) systems, showing that the initial 3-dB advantage of DPSK is lost for increasing nonlinear phases because DPSK is less robust to PG than OOK.

Modeling nonlinearity in coherent transmissions with dominant intrachannel-four-wave-mixing

By extending a well-established time-domain perturbation approach to dual-polarization propagation, we provide an analytical framework to predict the nonlinear interference (NLI) variance, i.e., the variance induced by nonlinearity on the sampled field, and the nonlinear threshold (NLT) in coherent transmissions with dominant intrachannel-four-wave-mixing (IFWM). Such a framework applies to non dispersion managed (NDM) very long-haul coherent optical systems at nowadays typical baudrates of tens of Gigabaud, as well as to dispersion-managed (DM) systems at even higher baudrates, whenever IFWM is not removed by nonlinear equalization and is thus the dominant nonlinearity. The NLI variance formula has two fitting parameters which can be calibrated from simulations. From the NLI variance formula, analytical expressions of the NLT for both DM and NDM systems are derived and checked against recent NLT Monte-Carlo simulations.

Which is the dominant nonlinearity in long-haul PDM-QPSK coherent transmissions?

The contribution of each nonlinear effect to system penalty is investigated in a 20×100km homogeneous WDM PDM-QPSK link over wide range of symbol rates and setups. XPolM is found to dominate 112Gb/s dispersion-managed links.

An Alternative Approach to the Gaussian Noise Model and its System Implications

This paper presents an alternative derivation of the Gaussian noise (GN) model of the nonlinear interference (NLI) in strongly dispersive optical systems. The basic idea is to exploit an enhanced regular perturbation expansion of the NLI, which highlights several interesting features of the GN model. Using the framework, we derive a fast algorithm to evaluate the received NLI power spectral density (PSD) for any input PSD. In the paper we also provide an asymptotic expression of the NLI PSD which further speeds up the computation without losing significant accuracy. Moreover, we show how the asymptotic expression can be used to optimize system performance. For instance, we are able to prove why a flat spectrum is best to minimize the NLI variance when the input is constrained to a fixed bandwidth and power. Finally, we also provide a generalization of the NLI GN model to arbitrarily correlated X and Y polarizations.

Transmission limitations due to fiber nonlinearity

We review recent advances in understanding Kerr nonlinear limitations in high-capacity long-haul coherent systems, with emphasis on PDM-QPSK transmissions. Both homogeneous and hybrid dispersion-managed WDM systems are addressed, as well as homogeneous non-dispersion-managed systems.

The performance of polarization switched-QPSK (PS-QPSK) in dispersion managed WDM transmissions

We investigate for the first time the performance of PS-QPSK in WDM nonlinear propagation. We show that the theoretical performance improvement of PS-QPSK compared to PDM-QPSK is even larger in nonlinear propagation.

A Time-Domain Extended Gaussian Noise Model

From first-order perturbation theory, we derive the autocorrelation function of the nonlinear interference in coherent optical links. We show that the fundamental assumptions of the Gaussian noise (GN) model regarding stationary Gaussian statistics of the transmitted signal can be removed for a more complete model accounting for the fine details of the cyclostationary modulation format. We first give an intuitive presentation of the theory, and then provide a formal mathematical treatment based on symbol cumulants and discuss its key assumptions and limitations. The proposed model includes dual polarization effects, wavelength-division multiplexing and the nonlinear signal to amplified spontaneous emission noise interaction along the line, thus neglecting only the impact of four-wave mixing.

On the nonlinear threshold versus distance in long-haul highly-dispersive coherent systems

We show that the accumulation rate of nonlinearity in highly-dispersive long-haul coherent links can also be measured from the nonlinear threshold decrease rate, and provide simulations of such rates for both single- and cross-channel effects. We then show how the estimated rate can be used for the overall system design.