Trellis-based feed-forward carrier recovery for coherent optical systems.

Nowadays, the coherent optical communication system plays an important role in communication field because of large capability and bandwidth. A coherent optical communication, based on high-order modulation and digital signal processing technologies, consists of optical transmitters, optical fiber lines, optical amplifiers and optical receivers. In the high-speed coherent optical communication system, the phase noise from the transmitter laser and the local oscillator laser can significantly degrade the performance of the signal transmission and detection, especially for the systems using high-order modulation format, such as m-ary phase shift keying (mPSK) and m-ary quadrature amplitude modulation (m-QAM). Therefore, investigations on laser phase noise compensation algorithm based on digital signal processing technologies has become more and more significant. In this work, a multi-ring carrier phase recovery algorithm is developed for compensating the laser phase noise in optical fiber communication systems using high-order modulation formats. Degradations on the performance of communication systems due to the laser phase noise have been investigated. The system performance using the proposed algorithm and the conventional Viterbi-Viterbi algorithm were also evaluated in 9-channel and 15- channel, 32-Gbaud, Nyquist-spaced QPSK, 16-QAM, 64-QAM and 256-QAM coherent transmission systems with considering the impact of the laser phase noise. It is found that the phase noise leads to stricter constraints on the linewidths of transmitter-side and receiver-side lasers, and it can greatly degrade the achievable information rates in communication systems. Besides, compared to the conventional Viterbi-Viterbi algorithm, which is usually applied in the QPSK system, our proposed algorithm can also well mitigate the laser phase noise in 16-QAM, 64-QAM and 256-QAM optical communication systems.
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In this paper, we compare the nonlinearity effects of single mode fiber (SMF) and non-zero dispersion shifted fiber (NZ-DSF) on the performance of optical coherent transmission systems. We estimate the nonlinearity effects of fiber, referred to as nonlinear interference noise (NLIN), by using the so-called enhanced Gaussian noise (EGN) model, and compute signal to noise ration (SNR) of optical coherent transmission system by considering NLIN and optical amplifier noise, referred to as amplified spontaneous emission (ASE) noise. By considering EGN model we optimize the lunch power of optical coherent systems considering SMF and NZ-DSF. Finally, a 100Gbps optical coherent transmission system is simulated and its results are compared with analytical results obtained based on the EGN model. The closeness between analytical and simulation results reveal the accuracy of the EGN model and the power optimization formulations.

A maximum likelihood sequence detection (MLSD) receiver is used to detect data sequences in single-carrier coherent optical systems in the presence of laser phase noise. It requires no explicit phase estimation and involves only linear operations. It consistently shows improvement in the OSNR penalty (e.g., 1.1 dB at BER = 10⁻⁴ with memory length L =3) and the laser linewidth tolerance (e.g., around 4 times that of DAML at 1dB OSNR penalty at BER = 10⁻⁴ with memory length L =3) over the well-known DAML and Mth power approaches in laser phase noise (LPN)-impaired coherent optical systems.

Several authors have recently investigated phase noise in semiconductor lasers and the related problems that arise when such lasers are employed in coherent optical communication systems. We report accurate measurements of high-frequency phase noise in single-mode injection lasers that show the presence of a peak in the phase-noise spectrum at the same frequency as that of the amplitude-noise peak. This peculiar phenomenon must be taken into account when one studies the characteristics of coherent optical communication systems.

This study evaluates the performance of binary- and M-ary-PSK coherent optical systems using cascaded optical amplifiers in the presence of noise originating from the detector, receiver, optical amplifiers, and the laser phase fluctuations. Our results on the analysis of these systems indicate that at an amplifier input power of −20 dBm and a system length of 10,000 km, the power penalties incurred due to the laser phase noise at a bit error rate of 10−9 correspond to 0.57, 0.99, and 3.38 dB at linewidths of 770.31, 101.86, and 6.37 kHz for binary-PSK, four-PSK, and eight-PSK systems, respectively. ©1996 John Wiley & Sons, Inc.

Theory of Optical Communications. Fiber Devices for Optical Communication Systems. Integrated Devices for Optical Communication Systems. Direct Detection Optical Communication Systems. Coherent Systems: Structure and Ideal Performance. Performance Degradation Sources in Coherent Optical Systems. Multilevel Coherent Optical Systems. Multichannel Optical Systems. Present--Day Systems Implementations. Appendices. Index.

The interplay between the stochastic intensity fluctuation of Raman pump laser and cross-phase modulation (XPM) effect in transmission optical fiber leads to additional phase noise, namely, relative phase noise (RPN) of signal in multi-level modulated coherent optical communication system. Both theoretical analysis and quantitative simulation have been performed to investigate the characteristics and impact of RPN. Being low-pass in nature, RPN is different from XPM induced phase noise in PSK/OOK hybrid system, and has not been considered yet. The noise power of RPN can accumulate incoherently along transmission links. With a proper signal model, we study the impact of RPN to the coherent optical communication system through Monte Carlo simulation. RPN will cause more cycle slips in Viterbi-and-Viterbi (V-V) phase estimation (PE), and the quantitative analysis of cycle slip probability is carried out. When using sliding window V-V without any optimization, the Q factor penalty of RPN on DQPSK signal can be as large as around 5 dB in strong RPN condition. However, it can be reduced by over 3 dB when using an optimal block size or optimal averaging weights.

The impact of phase to amplitude noise conversion for QPSK, 16-QAM, and 64-QAM coherent optical systems are investigated with electronically-compensated chromatic dispersion (CD). The electronic equalizer is shown to convert the phase noise from the local oscillator (LO) to amplitude noise, limiting the amount of CD that can ideally be compensated digitally. The simulation results demonstrate that the performance of coherent systems can significantly be degraded with digitally compensated CD and LO phase noise. The maximum tolerable LO linewidth is also investigated for the different modulation formats and found to become increasingly stringent for longer transmission distance and higher symbol rate.

This paper proposes a parametric network for the joint compensation of multiple linear impairments in coherent optical communication systems. The considered linear impairments include both static and time-variant effects such as in-phase/quadrature (IQ) imbalance, laser phase noise (PN), chromatic dispersion (CD), polarization mode dispersion (PMD), and carrier frequency offset (CFO). To jointly compensate for these considered impairments, the proposed network is composed of parametric layers that exploit the particular signal model of each impairment. The layers’ parameters are jointly learned during a training stage. This stage uses a supervised step that exploits the knowledge of some transmitted data (preamble and/or pilots) and a self-labeling step that uses the knowledge of the symbol constellation. In addition, a new validation technique that does not require a different dataset is developed to avoid overfitting. The parametric network performance is compared to classical digital signal processing (DSP), and Deep Learning (DL) approaches using simulated data. Simulation results show that the proposed network outperforms the competing approaches in terms of Bit Error Rate (BER) while maintaining a relatively reduced computational complexity. In the scenarios considered, compared to the parametric network, the DSP approach introduces an OSNR penalty between 0.2 dB and 1.7 dB at a BER of 4×10-3. Furthermore, simulation results demonstrate that the proposed network is way more flexible than other approaches since it can easily be adapted to a different scenario and coupled with other techniques.

There is a need to determine the suitability of laser sources for use in coherent transmission systems and to study the spectral characteristics and processes that determine phase and amplitude noise of these sources. A novel method for determining the laser lineshape, linewidth, and phase noise is presented. An optical-fibre, 4 x 4 multiport is used to derive amplitude and phase information of an optical signal by mixing it with a reference optical signal. Signal processing then yields the complex cross-correlation function of the two signals, (or for a single source, the complex auto-correlation function) in the frequency domain. It is intended that information, concerning the amplitude and phase noise of the source or sources, may then be derived or inferred by comparison. The initial system has been designed to operate at 1.55 μm wavelength with a distributed feedback laser.

Nonlinearity and Phase Noise Mitigation Using Feed-forward Carrier Phase Estimation and Digital Backward Propagation in Coherent QAM Transmission

For coherent and direct-detection Orthogonal Frequency Division Multiplexed (OFDM) systems employing radio frequency (RF) pilot tone phase noise cancellation the influence of laser phase noise is evaluated. Novel analytical results for the common phase error and for the (modulation dependent) inter carrier interference are evaluated based upon Gaussian statistics for the laser phase noise. In the evaluation it is accounted for that the laser phase noise is filtered in the correlation signal detection. Numerical results are presented for OFDM systems with 4 and 16 PSK modulation, 200 OFDM bins and baud rate of 1 GS/s. It is found that about 225 km transmission is feasible for the coherent 4PSK-OFDM system over normal (G.652) fiber.

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.

Application of multi-level coded modulation (MLCM) for 16-ary constellations in coherent systems is studied. An MLCM system with Reed-Solomon component codes and multi-stage decoder is considered. A systematic numerical method for finding set-partitioning and optimal code rates is presented. The method only requires the probability density function of received samples and can be applied to any constellation regardless of irregularity or lack of symmetry. Performance of the designed MLCM system is verified in presence of nonlinear phase noise and normal phase noise. For nonlinear phase noise limited system, it is shown that the block error rate (BLER) of the system can be improved using our approach for set-partitioning. For phase noise limited system, both BLER and bit error rate (BER) are studied for a phase noise optimized and square 16-quadrature amplitude modulation (16QAM). Post forward-error correction (FEC) BER performance of the optimized constellation over square 16QAM is studied for different levels of phase noise. It is shown that the optimized constellation along with MLCM system decreases the required signal-to-noise ratio by several dB at high phase noise regime and low post FEC BER.

Forward error correction (FEC) plays a vital role in coherent optical systems employing multi-level modulation. However, much of coding theory assumes that additive white Gaussian noise (AWGN) is dominant, whereas coherent optical systems have significant phase noise (PN) in addition to AWGN. This changes the error statistics and impacts FEC performance. In this paper, we propose a novel semianalytical method for dimensioning binary Bose-Chaudhuri-Hocquenghem (BCH) codes for systems with PN. Our method involves extracting statistics from pre-FEC bit error rate (BER) simulations. We use these statistics to parameterize a bivariate binomial model that describes the distribution of bit errors. In this way, we relate pre-FEC statistics to post-FEC BER and BCH codes. Our method is applicable to pre-FEC BER around 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> and any post-FEC BER. Using numerical simulations, we evaluate the accuracy of our approach for a target post-FEC BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> . Codes dimensioned with our bivariate binomial model meet the target within 0.2-dB signal-to-noise ratio.