Compensation Of Nonlinear Phase Noise Research Articles

Inter-channel nonlinear phase noise compensation using optical injection locking.

We propose optical injection locking (OIL) to enable compensation of the inter-channel nonlinear phase noise, which is dominated by cross-phase modulation (XPM). In this paper, injection locking is used to create a local oscillator for a homodyne receiver from a residual carrier. The locking is fast enough to follow XPM-phase distortion, but slow enough to reject the signal bands, which are spaced slightly away from the pilot. The homodyne receiver thus partially cancels XPM, as it is common to the signals and the pilot. An experimental 7-channel WDM system gives 1-dB (0.7-dB) improvement in the peak Q of the center channel, for QPSK (16-QAM) modulated OFDM subcarriers, and increased the transmission reach by 320 km. The optimum performance was achieved at an injection ratio of -45 dB, with the injected power as low as -24.5 dBm.

Low-Complexity One-Step Digital Back-Propagation for Single Span High-Capacity Coherent Transmissions

A low-complexity one-step digital back-propagation (DBP) scheme is proposed to mitigate intrachannel and interchannel fiber nonlinearities in high-capacity single span transmissions. Compared with conventional coherent receivers, the only additional calculation is a low-complexity nonlinear phase noise compensation stage operated between bulk chromatic dispersion (CD) compensation and adaptive equalizer. The required number of real additions and multiplications per sample are only (6N + 2) and (2N + 6), respectively, where N is the number of compensated wavelength-division-multiplexing (WDM) channels. With the proposed one-step DBP, we demonstrate that the nonlinear noise can be suppressed by >60% in single channel experiments and >40% in seven-channel WDM simulations.

Machine Learning Techniques in Optical Communication

Machine learning techniques relevant for nonlinearity mitigation, carrier recovery, and nanoscale device characterization are reviewed and employed. Markov Chain Monte Carlo in combination with Bayesian filtering is employed within the nonlinear state-space framework and demonstrated for parameter estimation. It is shown that the time-varying effects of cross-phase modulation (XPM) induced polarization scattering and phase noise can be formulated within the nonlinear state-space model (SSM). This allows for tracking and compensation of the XPM induced impairments by employing approximate stochastic filtering methods such as extended Kalman or particle filtering. The achievable gains are dependent on the autocorrelation (AC) function properties of the impairments under consideration which is strongly dependent on the transmissions scenario. The gain of the compensation method are therefore investigated by varying the parameters of the AC function describing XPM-induced polarization scattering and phase noise. It is shown that an increase in the nonlinear tolerance of more than 2 dB is achievable for 32 Gbaud QPSK and 16-quadratic-amplitude modulation (QAM). It is also reviewed how laser rate equations can be formulated within the nonlinear state-space framework which allows for tracking of nonLorentzian laser phase noise lineshapes. It is experimentally demonstrated for 28 Gbaud 16-QAM signals that if the laser phase noise shape strongly deviates from the Lorentzian, phase noise tracking algorithms employing rate equation-based SSM result in a significant performance improvement ( $>$ 8 dB) compared to traditional approaches using digital phase-locked loop. Finally, Gaussian mixture model is reviewed and employed for nonlinear phase noise compensation and characterization of nanoscale devices structure variations.

Chromatic dispersion and nonlinear phase noise compensation based on KLMS method

In this study, kernel least mean square (KLMS) algorithm with fractionally spaced equalizing structure is proposed for electrical compensation of chromatic dispersion (CD) and nonlinear phase noise (NLPN) in a dual polarization optical communications system with coherent detection. We consider single mode fiber channel. At the receiver, the additive optical noise is represented as additive white Gaussian noise. Phase modification is utilized at high signal powers to maintain the validity of Gaussian model of noise. We consider QAM and PSK modulations and evaluate the performance of the proposed method in terms of error rate, phase error, and error vector magnitude (EVM). The results are obtained in both linear and nonlinear regimes. In the linear region, the KLMS algorithm can compensate CD and NLPN effectively and outperforms the existing compensation methods such as LMS, minimum mean square error (MMSE), and time domain FIR filter. In nonlinear regime, where the input power is higher, NLPN is stronger which results in compensation performance degradation. However, KLMS still achieves better results than the above algorithms.

Compensation of Nonlinear Phase Noise Using the Effective Negative Nonlinearity of a Nonlinear Amplifying Loop Mirror

The nonlinear amplifying loop mirror (NALM) has been explored for use as a nonlinear phase-shift compensator (NPSC). Operation conditions for a tunable effective negative nonlinearity are considered and the NALM parameter optimization is discussed for direct bit-error-ratio (BER) improvement by postcompensation after a nonlinear transmission line. In this configuration, the fundamental limits for NPSC are estimated for differential quadrature phase-shift keying (DQPSK) using a simplified model. Numerical simulations of a 20 Gb/s RZ-DQPSK transmission system confirmed the applicability of this model and showed a significant BER improvement in a realistic transmission line. Alternatively, the fiber launch power per span could be increased by 2 dB for the same BER.

Self-Coherent Decision-Feedback-Directed 40-Gb/s DQPSK Receiver

A novel 40-Gb/s differential quadrature phase-shift keying receiver is theoretically proposed, improving direct detection by 4.2 dB for self-phase-modulation-limited single-channel transmission, approaching ideal coherent homodyne performance using a recirculating delay line interferometric integrated-optical circuit front-end combining decision feedback and nonlinear phase-noise compensation

Optical phase conjugation for ultra long-haul phase-shift-keyed transmission

Nonlinear phase noise (Gordon-Mollenauer phase noise) can limit the transmission distance for phase-shift-keyed modulation formats. In this paper, the compensation of nonlinear phase noise by a midlink optical phase conjugation (OPC) is studied. A proof-of-principle experiment is presented showing an over 4-dB improvement in Q factor when OPC is employed in a differential phase-shift-keying (DPSK) system. Also, an ultra long-haul OPC-based differential quadrature phase-shift-keying (DQPSK) transmission experiment is studied to show the impact of self-phase modulation (SPM)-induced impairments, including nonlinear phase noise, in a transmission line. OPC results in a 44% increase in transmission distance when compared to a conventional transmission system using dispersion compensating fiber (DCF) for chromatic dispersion compensation.

Mid-span compensation of nonlinear phase noise

The nonlinear phase noise, often called the Gordon–Mollenauer effect, is correlated with the intensity of the optical signal. With a single linear compensator, the optimal location is not preceding the receiver but located at about 2/3 of the fiber link. When N compensators are approximately optimally placed, the standard deviation of nonlinear phase noise is reduced by a factor of 2N+1. The optimal compensation factors are all approximately equal to each other.