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

/pdf/a-time-domain-extended-gaussian-noise-model-17lrkxb674.pdf

A Time-Domain Extended Gaussian Noise Model

Previous investigations have revealed that the impairments of the cross-phase modulation (XPM) in dense wavelength-division multiplexing (DWDM) systems include two aspects: the XPM-induced phase noise and the XPM-induced polarization scattering. Such XPM phenomena are strongly dependent on the transmission system configurations and are nonintuitive. In this paper, a simple fiber model is proposed to facilitate the determination of XPM effects. By employing this model, the phase noise and polarization scattering are calculated based on the system configurations and the time-consuming computation by the split step Fourier method is avoided. The proposed model is verified by the dual polarization quadrature phase-shift keying coherent DWDM experiments and simulations in terms of the variance and autocorrelations of phase noise and polarization crosstalk as well as their dependence on relative polarization states and the overall Q-impairment. The proposed model helps deeper analysis of XPM phenomena, and eventually, leads to development of various XPM mitigation methods through transmission system design and coherent receiver DSP.

Simple Fiber Model for Determination of XPM Effects

We describe in detail the recently proposed four-dimensional modulation format family based on 2-ary amplitude 8-ary phase-shift keying (2A8PSK), supporting spectral efficiencies of 5, 6, and 7 bits/symbol. These formats nicely fill the spectral efficiency gap between the dual-polarization (DP) quadrature PSK (QPSK) and DP 16-ary quadrature-amplitude modulation (16QAM), with excellent linear and nonlinear performance. Since these modulation formats just use different parity bit expressions in the same constellation, similar digital signal processing can be seamlessly used for different spectral efficiency. A series of nonlinear transmission simulation results shows that this modulation format family outperforms the conventional modulation formats at the corresponding spectral efficiency. We also investigate the adaptive equalizer for these modulation formats.

Nonlinearity-Tolerant Four-Dimensional 2A8PSK Family for 5–7 Bits/Symbol Spectral Efficiency

We present a detailed statistical model of nonlinear interference noise (NLIN) in optical communication systems. We demonstrate an efficient method of calculating second-order statistics of the NLIN coefficients, particularly their temporal autocorrelation and cross correlation. The model is highly accurate in predicting system performance metrics such as bit-error-rate and signal-to-noise ratio, and is shown to provide better accuracy with respect to models that use the NLIN variance alone, particularly when accounting for the adaptive filtering of realistic receivers.

Modeling the Bit-Error-Rate Performance of Nonlinear Fiber-Optic Systems

http://www.tlc.unipr.it/bononi/ricerca/BSR_oft_10.pdf

Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats

Starting from a model of random nonlinear polarization rotations for the effect of cross-polarization modulation in DWDM systems, we derive the mean distribution of the time-dependent polarization states at an arbitrary location within an optical link. We show that this distribution is fully parameterized by the degree of polarization of the particular wavelength channel, and we derive expressions to approximate this parameter for general optical links consisting of multiple optically amplified and dispersion-compensated spans, as well as related power thresholds. From the analytical expressions we derive a method to significantly reduce the detrimental effects.

/pdf/a-statistical-treatment-of-cross-polarization-modulation-in-28kockofg9.pdf

A Statistical Treatment of Cross-Polarization Modulation in DWDM Systems

We show theoretically and with the aid of computer simulations that the nonlinear depolarization induced by cross-polarization modulation leads to crosstalk between the polarization-division multiplex (PolDM) subchannels during their demultiplexing. This additive crosstalk can be approximated as additive Gaussian noise, and we derive expressions to estimate its variance. It can lead to significant penalties of up to several decibels for PolDM transmission and must be properly accounted for. We also show why time-interleaving both subchannels can significantly reduce these penalties.

Cross-Polarization Modulation in Polarization-Division Multiplex Transmission

A method for removing signal interference in a passive optical network, the passive optical network including an optical line terminal, a splitting unit coupled with the optical line terminal, an optical network unit coupled with the splitting unit, and an identification signal uniquely associated with the optical network unit; the method comprising the steps of sending a first signal, detecting the first signal, comparing the detected first signal with the identification signal and decoupling the optical network unit from the splitting unit if the comparing step results in a mismatch.

Method and apparatus for preventing signal interference in a passive optical network

The invention refers to a method for operating an amplifier with a first amplifier stage (A1) and a second amplifier stage (A2), pumped by a single pump light source (11) generating a primary pump signal (SPUMP), which is split into first pump signal (S1) and a second pump signal (S2) according to a variable splitting factor (α) for pumping the first amplifier stage (A1) and the second amplifier stage (A2) respectively. The splitting factor (α) is varied to achieve an optimized noise figure.

Method for controlling an erbium doped fiber amplifier (EDFA) and amplifier arrangement

An optical amplifier configuration for WDM (wavelength division multiplex) systems uses a common pump source connected to an input of an optical splitter deploying pump light via variable optical attenuators to a plurality of optical amplifiers. Control circuits determine individually the output powers of the amplifiers by varying the attenuations of the variable optical attenuators. Amplifier units based on PLC technology are implemented to reduce the size.

Dario Setti

Papers

A Statistical Treatment of Cross-Polarization Modulation in DWDM Systems

Cross-Polarization Modulation in Polarization-Division Multiplex Transmission

Method and apparatus for preventing signal interference in a passive optical network

Method for controlling an erbium doped fiber amplifier (EDFA) and amplifier arrangement

Optical Amplifier Configuration